~WONG-Radiologic Image Compr a Review

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Radiologic Image Compression-A ReviewSTEPHEN WONG, LOREN ZAREMBA, DAVID GOODEN, AND H. K. HUANG

The objective of radiologic image compression is to reducethe data volume of and to achieve a low bit rate in the digitalrepresentation of radiologic images without perceived loss ofimage quality. How ever, the dem and fo r transmission bandwidthand storage space in the digital radiology environment, especiallypicture archiving and communication systems (PACS) and telera-diolog y, and the proliferating use of various ima gin g modalities,such as magnetic resonance imaging, computed tomography, ultra-sonography, nuclear medicine, computed radiography, and digitalsubtraction angiography, continue to outstrip the capabilities ofexisting technologies. The availability of lossy coding techniquesfor clinical diagnoses further implicates many complex legal andregulatory issues.This pape r reviews the recent progress of lossless and lossyradiologic image compression and presents the legal challengesof using lossy compression of medical records. To do so, wefirst desc ribe the fundamental conce pts of radio logic imaging anddigitization. Then, we examine current compression technologyin the field of medical imaging and discuss important regulatorypolicie s and legal questions facing the use of compression inthis field. We conclude with a summ ary of future challenges andresearch directions.

I. INTRODUCTIONRadiology is a major application domain of medical

imaging technology. About 30% of radiology examinationsin the United States are taken directly in digital media. Themajor imaging modalities include: computed tomography(CT), magnetic resonance imaging (MRI), ultrasonography(US), positron emission tomography (PET), single pho-ton emission computerized tomography (SPECT), nuclearmedicine (NM), digital subtraction angiography .(DSA),and digitalflurography (DF) [l o], [MI. These modalitieshave revolutionized the means to acquire patient images,provide flexible means to view anatomical cross sectionsand physiological states, and reduce patient radiation doseand examination trauma. The other 70% examinationson skull, chest, breast, abdomen, and bone are done inconventional X-rays. Different kinds of film digitizers, such

Manuscript rceived February 27, 1994; revised October 3, 1994.S. Wong and H. K . Huang are with is with the Laboratory forRadiological Informatics, Department of Radiology, School of Medicine,The University of Califomia at S an Francisco (UCSF), San Francisco, CA94143 USA.L. Zaremba is with the O fficeof Device Evaluation, Center for Devicesand Radiological Health, Rockville, MD 20850 USA.D. Gooden is with the Departmen t of Biom edical Physics, Saint FrancisHospital, Tulsa, OK 74136 USA.IEEE Log Number 9407056.

as laser scanner, solid-state camera, drum scanner, andvideo camera, can be used to convert X-ray films into digitalformat for processing [69].The trend in medical imaging is increasingly digital. The

basic motivation is to represent medical images in digitalform supporting image transfer and archiving and to ma-nipulate visual diagnostic information in useful and novelways, such as image enhancement and volume rendering.Another push is from the picture archiving and commu-nication systems (PACS) community who envisions an alldigital radiology environment in hospitals for acquisition,storage, communication, and display of large volumes ofimages in various modalities [71], [91], [97]. The amountof digital radiologic images captured per year in the UnitedStates alone is at the order of petabytes, i.e., 1015, andis increasing rapidly every year. Individual investigatorsof medical imaging in the past have been working ontheir own modalities in isolation. The picture archivingand communication systems technology provides a systemintegration solution for these islands of automation andfacilitates the mining or extraction of the rich informationcontained in medical images in a way that more than theindividual sum of each of the imaging technologies. Severallarge-scale PACS have been successfully put into clinicaloperation [82], [97], [117], [50] , 74].Image compression facilitates PACS as an economicallyviable alternative to analog film-based systems by reducingthe bit size required to store and represent images, whilemaintaining relevant diagnostic information. It also enablesfast transmission of large medical images over a PACSnetwork to display workstations for diagnostic, review,and teaching purposes. Even over a fiber distributed datainterchange (FDDI) network of 100 megabits per sec (Mb/s)and at an optimistic 20% actual transfer rate (i.e., 20Mb/s), it would take 13 s to transmit a digitized chestimage of 4 K x 4 K x 12-b resolution; whereas manymedical applications demand the display of image in lessthan 2 s [148], [73]. This transmission problem is fur-ther aggravated in wide area network (WAN) applicationswhich often include low-bandwidth channels, such as long-distance telephone lines or an Integrated Services DigitalNetwork (ISDN) of data rate 144 kilobits per second (Kb/s).Teleradiology is an exciting WAN application that aims tobring expert radiological service available in major urban

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medical centers into rural areas and small towns [14],[142], [91], [13], [50], [109]. This new technology dealswith the acquisition of images and patient records and thetransmission of them over a wide area network to oneor more remote sites where they can be displayed forconsultation or diagnosis.Technically, all image data compression schemes canbe broadly categorized into two types. One is reversiblecompression, also referred to as lossless. A reversiblescheme achieves modest compression ratios of the order oftwo, but will allow exact recovery of the original imagefrom the compressed version. An irrreversible scheme,or a lossy scheme, will not allow exact recovery aftercompression, but can achieve much higher compressionratios, e.g., ranging from ten to fifty or more. Generallyspeaking, more compression is obtained at the expense ofmore image degradation, i.e., the image quality declinesas the compression ratio increases. Another type of com-pression which is used in medical imaging is clinical imagecompression, which stores a few medically relevant images,as determined by the physicians, out of a series of real-time images and thus reduces the total image size. Thestored images may or may not be further compressed bythe reversible scheme. In an ultrasound examination, forexample, the radiologist may do two records at 30 imagesper second of data collection, but keep only 4-8 framesand discard the rest.Image degradation may or may not be visually apparent.The term visually lossless has been used to characterizelossy schemes that result in no visible loss under nor-mal radiologic viewing conditions [1241. A compressionalgorithm that is visually lossless under certain viewingconditions, e.g., a 19-in video monitor at a viewing distanceof 4 ft, could result in visible degradations under morestringent conditions, e.g., a 14 x 17-in image printedon film. A related term used by the American Collegeof Radiology and National Electrical Manufacturing As-sociation (ACFUNEMA) is information preserving. TheACFUNEMA standard report defines a compression schemeto be information preserving if the resulting image retainsall of the significant information of the original image [2].Both visually lossless and information preserving aresubjective definitions and extreme caution must be taken intheir interpretations.Currently, lossy algorithms are not being used by theradiologists in clinical practice. The reason is that lossycompression has raised new legal questions and regulatorypolicies for the manufacturers, the users, and the UnitedStates Food and Drug Administration (FDA) [168], [53].The physicians and radiologists are concerned with the legalconsequences of an incorrect diagnosis based on a lossycompressed image. There is, however, insufficient clini-cal testing to develop reasonable policies and acceptablestandards for the use of lossy processing on medical images.In this paper, we review the recent progress of radio-logic image compression, discuss technical and the relatedlegal challenges, and present the research directions. Theorganization of this paper is as follows. Section I1 describesWONG et al.: RADIOLOGIC IMAGE COMPRESSION-A REVIEW

the fundamentals of radiologic images. Section I11 dis-cusses the framework of compression involved in medicalimaging, including the notions of progressive transmissionand difference pyramid. Section IV presents several ad-vanced techniques of lossless radiologic image coding whileSection V reviews the popular, as well as experimental,methods for lossy image compression. Section VI examinesthe important legal and regulatory issues of radiologicimage compression. Our summary and suggestions forfuture research are found in Section VII.11. CHARACTERISTICSOF DIGITAL ADIOLOGICMAGES

This section briefly describes the fundamental concepts ofradiologic imaging as related to digitization and compres-sion. Many of these concepts are derived from conventionalradiographic imaging and digital image processing. For anextensive treatment of these subjects, see [1241, E691, 1841,~ 1 .A . Digital Radiologic Images

A digital radiologic image is a digital image acquiredby a certain radiologic procedure. It is a two-dimensionalM x N array of non-negative integers f (x ly ) , where1 5 x 5 M and 1 5 y 5 N are the coordinates ofanatomical structures in the image. The image segmentrepresented by the coordinates (x,y) is called a pictureelement, or a pixel, and f ( x l y ) s its functional valueor gray level. The radiologic procedure can be X-rays,ultrasound, computerized tomography, nuclear magneticresonance, or another digital modality. Depending on thedigitization procedure or the radiologic procedure, the graylevel can range from 0 to 255 (8-b), 0 to 511 (9-b), 0 to1023 (10-b), 0 to 2047 (1 1-b), and 0 to 4095 (12-b). Thesegray levels represent some physical or chemical propertiesof the object structure. As an example, in an image obtainedby digitizing an X-ray film, the gray level value of a pixeldenotes the optical density of the square area of that film.For X-ray computerized tomography (XCT), the gray levelvalue represents the relative linear attenuation coefficientof the tissue. For magnetic resonance imaging (MRI), itcorresponds to the magnetic resonance signal response ofthe tissue.A two-dimensional (2-D) radiologic image has a size ofA4 x N x lc b, where 2k equals the gray level range. The sizeof an image and the number of images taken in one patientexamination vary with modalities. Table 1 lists the averagenumber of megabytes per patient examination generated byradiologic imaging technologies [451, [37], where any 12-b image is represented by 2 bytes in memory. The plainX-ray films of images of higher resolution requirement canbe digitized by 4 K x 4 K x 12-b digitizers [69], [90].In contrast with most other types of biomedical images, aradiologic image is monochrome, i.e., there is no need todo color compression.There are two common means to convert analog imagesfrom an X-ray film into digital formats. This can bedone either using a film digitizer or through computed

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Table 1 Radiologic Image Sizes

153650

Modality

159.50.8 or 1.6

CTMRIDSADigital FluorographyUltrasoundSPECTPETCRDigitized Film

Image Dimension512 x 512256 x 2561024 x 10241024 x 1024512 x 512128 x 128128 x 1282048 x 20482048 x 2048

Gray Level (hits)12128868 or 16161212

radiography (CR) [69]. A film digitizer converts an X-ray film to digital numbers, and among various types ofdigitizers, the laser scanning digitizer is considered as thegold standard because it can best preserve the resolutionof the original film images. Computed radiography usesa photostimulable phosphor imaging plate as an X-raydetector. The latent X-ray image formed in an imagingplate is scanned and excited by a laser beam to emit lightphotons which are detected and converted into electronicsignals. These signals are translated into digital signals toform a digital X-ray image.Currently, magnetic tapes are the widely used storagemedia in hospitals, but a typical magnetic tape can onlyarchive about less than a hundred CT image examinationson average. As a result, some hospitals have switchedto optical disks as their primary storage media. A top-of-the-line optical jukebox containing 1-2 terabits (Tb)of data can support a reasonable access time, but at aprohibitive cost. Even that, the growing rate of radiologicimages of various modalities captured would soon taxeven such optical technology to its limit. For example,the digital radiology department of a 1500-bed universityhospital would produce about 20 Tb of image data peryear [88]. Further, radiologists prefer to see patient studiesappear at display workstations within 1 to 2 s [148]. Allthese practical constraints motivate the search for efficientcompression for economic storage and fast transmission ofradiologic images.B. P e g o m n c e Measure of Image Compression

The performance of radiologic image compression de-pends not only the compression ratio but also the imagequality of reconstructed images. Higher quality imagesshow finer structural or functional information of bodyorgans and support more reliable diagnostic outcomes. Inmedical imaging, the engineers, the manufacturers, and theclinicians measure image quality differently.The instrumentation engineer characterizes the digitalimage generated by an imaging equipment by three phys-ical parameters: density resolution, spatial r esolution, and196

Avg. Number of Images per Exam 1 Avg. Mbytes Per Exam3050 1 :20 I 2o6244

23232

signal-to-noise ratio (SNR) [69]. The density resolution isthe total number of discrete gray level values in the digitalimage. The gray level is specified by the analog-to-digital( A D ) onversion during the film digitization or by the dataformat of the digital modality used. The spatial resolutionmeasures the number of pixels used to represent the objects.For computed radiographs, the pixel number is depended onthe spot size and sampling pitch of the digitizer. The spotsize is the diameter of a laser beam that scans the image andthe sampling pitch corresponds to the distance between thecenter of two adjacent spots. Clearly, N and IC of image bitsize are proportional to the spatial and density resolutions.For two images of fixed density and spatial resolutions,a high signal-to-noise ratio means that the image is verypleasing to the eyes. Typically, a power spectrum is used tostudy the noise of reconstructed images. The relationshipsbetween compression ratio and the three parameters, i.e.,spatial resolution, density resolution, and the digitizer noiseare discussed in [69].

The equipment manufacturers consider the image qualityin an imaging chain or system, including not only theimaging instrument but also other components, such asdisplay stations and film printers, in two categories: 1)the measurement of image unsharpness which is inheritedfrom the system design, and 2) the measurement of imagenoise arises from various sources which include photonfluctuations from the energy source and electronic noiseaccumulated through the imaging chain. The manufacturersuse the requency representation of an image to measure thequality of its sharpness. This leads to the notions of pointspread function, line spread function, edge spreadfunction,and modu lation transfer function [69], which measure thesharpness of points, lines, and edges, as well as the systemresponse at a spatial frequency, w , espectively. The spatialfrequency is measured in the direction perpendicular to theline pairs.

The modulation transfer function provides a certain in-dication of the system capability to reproduce fine detailsand to generate image contrast, but contains no informationregarding the effect of noise which affects detail visibility.

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Fig. 1. The difference between a digitized X-ray chest imagebefore and after it has been averaged (figures from Chapt. 2, [69]).

High modulation transfer values do not necessarily entaila good diagnostic quality image if the noise level is high.Power spectrum is used to study the image noise whicharises from quantum statistics, electronic noise, and filmgrain in the imaging chain. Averaging many images ofthe same object is a common method used to reduce theimage noise. Fig. 1 illustrates such an example using adigitized chest X-ray image. Fig. l(a) shows the originalimage while Fig. l(b) the image obtained after sixteen timesof averaging. Fig. l(c) exhibits the difference image of thetwo, indicating that the noise in the imaging system is notrandom.The images of interest to the clinicians are complexanatomical objects. Simulated measures resulting from theengineers and the manufacturers experiments do not al-ways correlate well with human subjective testing andWONG er al. : RADIOLOGIC IMAGE COMPRESSION-A REVIEW

perception. To remedy this situation, numerical statisticalanalyses based on the receiver operating characteristic(ROC) curves are used to examine medical image qualityfor individual applications [62], [ l l l l , [1471, 11191, [1501,[81], [35], [48]. In such a ROC study, the radiologists areasked to review the reconstructed images after compression,which either did or did not possess an abnormality andto provide a binary decision, i.e., abnormality present ornot, along with a quantitative value for their degree ofcertainty, usually a number from 1 to 5. The diagnosticaccuracy of these images then are compared with that ofthe original plain films. Since the viewers rated diagnosticusefulness rather than general appearance or simply lineor edge patterns, these studies related diagnostic accuracyto compression level. Certain statistical model, such as thebivariate binormal distribution [121], would be used to testdifferences between ROC curves based on correlated datasets.ROC analyses are used to quantify the compression levelsin a specific medical application that can be used without astatistically significant change in diagnostic accuracy. Theyare, however, expensive and time-consuming to perform.A typical ROC study would require over 300 images toobtain a reasonable statistical confidence level, five or moreradiologists to view these images, and a full-time statisticianto coordinate and analyze the data.

111. IMAGECOMPRESSIONRAMEWORKThis section describes the general framework for radi-ologic image compression. Similar to other digital com-pression fields, the framework includes three major stages:image transformation, quantization (irreversible compres-sion only), and entropy encoding [124], [84]. The relativeimportance of each stage varies from one technique toanother, and not all stages are necessary included in aparticular scheme. All reversible compression techniques

do not involve the stage of quantization.The image transformation, sometimes also referred asdecorrelation, is used to reduce the dynamic range of thesignal, to eliminate redundant information, and to providea suitable representation for efficient entropy coding. Atransformation should satisfy three conditions. First, alltransform coefficients become statistically independent. Fora stationary and Gaussian-distributed pixel ensemble, thetransform functions approximate the eigenvectors of theautocorrelation matrix of the pixels. Decorrelation withconcomitant entropy reduction is important so that thetransformed outputs are suitable for entropy encoding.Second, the energy of the transformed image is compactedinto a minimum number of coefficients. Efficient energycompaction requires good localization of the sampling func-tions in both the spatial and the frequency domains. Third,the transform coefficients are concentrated in minimumfrequency or transform scale regions.Quantization is fundamentally lossy, i.e., pertaining toirreversible compression only. It achieves compression byrepresenting transform coefficients with no greater precision

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than is necessary to achieve desired image quality. Thefirst desirable condition of transformation, i.e., statisticallyindependent coefficients, is less important for lossy com-pression than for lossless; as the former method can attainadditional entropy reduction in the quantization stage. Onthe other hand, the second transformation condition is morecrucial for lossy compression to simplify the quantizationprocess. The transform coefficients are quantized accordingto a quantization table, which must be specified by theapplication, or user, as an input to the encoder.Entropy encoding achieves additional compression loss-lessly by encoding the transform coefficients (quantizedand non-quantized) more compactly based on their non-random statistical characteristics. It is useful to considerentropy encoding as a two-step process. The first step uses astatistical model to convert coefficients into an intermediatesequence of symbols. The second step converts the symbolto a data stream in which the symbols no longer haveexternally identifiable boundaries [1551. The entropy codingmay be as simple as using fixed-length binary code words todescribe the outputs from the previous stage, or it may usea variable-length code to achieve higher compression rates,such as HufSman coding [76] and arithmetic coding [122].The same code tables used to compress an image are neededto decompress it; these code tables may be predefined oradaptive.

A promising approach of image compression for clin-ical use is progressive transmission (PT) that transmitsimage data in stages [46], [47] and, at each stage, anapproximation to the original image is reconstructed at thereceiver. The reconstructed images progressively improveas more image data is received. In general, PT techniquesorganize the image data in multi-resolution hierarchieswith data at each hierarchy corresponds to a reconstructedimage at a particular resolution or level of quality. The PTtechnology finds use in teleradiology or similar applicationswhere a radiologist or a physician is accessing remotelystored images of patient images and associated diagnosticstudies via a low-bandwidth wide area network (it is,however, less important for PACS applications, as PACSlocal area networks are generally operated at much higherbandwidths). In such a case, the radiologist may have tobrowse through a few images before locating the particularimages of interest. The highly compressed image can serveas a guide for the initial selection process with significantsavings in time and bandwidth. If further information isneeded, the difference image can then be transmitted toprovide a completely lossless reconstruction.

The choice of a radiologic image compression schemeis a complex tradeoff of system and clinical requirements,including 1) image characteristics and contents, such as sizeof pixel matrix, digitization resolution, average correlationlength, signal-to-noise ratio, and entropy; 2) adaptability tosecondary applications, such as multi-resolution represen-tation, teleradiology, and PACS; 3) information loss andartifacts caused by the compression; 4) pre-processing stateand post-processing requirements of the images; 5) ease ofimplementation and speed of execution; 6) availability of198

hardware and software; and 7) the cost of implementationand maintenance [161.A radiologic image compression algorithm that providesmulti-resolution image representation offers many advan-tages. Such an algorithm facilitates the extraction of alow-resolution image to create a pictorial index of a patientfolder or a teaching slide, the delivering of a medium reso-lution radiograph to a hospital ward without transmitting thefull-resolution image first, and the reduction or decimationoperation in computers to simplify spatial filtering or featureextraction, as well as to emulate the channel properties ofhuman visual perception. It will be most suitable to progres-sive transmission techniques in medical telecommunicationapplications [16]. The adaptability of a coding scheme toimportant applications, such as PACS and teleradiology,adds value to the medical imaging system. If a compressionalgorithm requires costly pre-processing or post-processingoperations, it is unlikely to be used in practice. Furthermore,reliable implementation of a compression technique usingexisting software and hardware is essential both from thesystem and legal views of medical imaging.

IV. REVERSIBLEMAGECOMPRESSIONDirect coding of medical images using an entropy en-coder does not achieve any considerable degree of com-pression. Some form of prior decorrelation is warranted.Thus, all the different coding techniques and their variantsappeared in medical imaging literature today use eithera predictive model [151], [91], [64], a multi-resolutionmodel [135], [15], [157], or both [41], [24], [26] to reducethe statistical redundancy at the stage of image trans-formation, and then encode the residuals using certainentropy encoder. Popular coding schemes used for suchresidual encoding, such as Huffman, arithmetic, run-lengthencoding (RLE), and LZW, are well explained in textbooks[84], [149] and are in routine software use, e.g., theUNIX COMPRESS program uses LZW coding while itsearlier version COMPACT program is based on adaptiveHuffman coding [162]. Of these schemes, Huffman codingand RLE are by far the most predominantly used codesfor medical image compression [15], [91]. FUE is bestsuited for image areas with low variation in pixel values,such as soft tissue regions in CT images [129], [loll,[lo21 and Huffman coding is efficient in coding the imagedifferences with highly peaked histograms [1241, [98]. Rel-atively few academic explorations of LZW and arithmeticcoding with medical images have been published [15],[ W .This section outlines major advanced lossless techniques:differential pulse code modulation (DPCM), hierarchicalinterpolation (HINT), difference pyramid (DP), bit-planeencoding (BPE), and multiplicative autoregression (MAR).All these techniques can be made into lossy ones byincluding the quantization stage, but with moderate gainin compression ratios. Thus Section V presents anotherset of approaches for lossy compression of radiologicimages.

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Fig. 2. The general framework for image data compression.

Fig. 3. A general block diagram of DFCM. For lossless compression, there is no quantizationstage and e, = e.A. Differential Pulse Code Modulation

Differential pulse code modulation (DPCM) is a simpleand popular predictive coding method [7], [120], [84]. Itexploits the property that the values of adjacent pixels inan image &e often similar and highly correlated. Fig. 3illustrates a general block diagram of DPCM. Suppose anoriginal image has M rows and N columns and x(m,n)denotes the pixel value at the m th row and the n th columnfrom the origin located at the top-left comer. In DPCM, animage is typically encoded one pixel at a time across a rasterscan line, from left to right for two consecutive raster lines.The value of a pixel is predicted as a linear combination ofa few neighboring pixel values which have been previouslyreconstructed. The predicted value of a pixel, x e s t ( m ,n), is

xest(mrn) = a( i , j )xT(m- , n - ) (1)[i,j]ROS

where a ( i , j ) are known as the prediction coeficients orweighting factors specified by the user. For the purpose ofcoding, the region of summation or support (ROS) is chosensuch that the set, {x,.(i,j)}, includes only those pixelswhose values have been already decoded or reconstructed atthe receiver. For example, the predicted value of the pixel,x(m,n), can be expressed using three adjacent neighbors asxest(m,n) = a(0,1 ) ~ - ( m ,- 1)+ a ( l , O ) x v ( m- 1,n )

(2)a(1,)xr(m- 1,n- 1).WONG et al.: RADIOLOGIC IMAGE COMPRESSION-A REVIEW

The prediction error given by e(m,n) = x(m,n)xes t (m rn ) is then entropy-coded and transmitted to thedecoder. The motivation for this is that the differentialimage typically has a much reduced variance and can thusbe encoded more efficiently. In the case of lossy compres-sion, the quantization is introduced, and the compresseddata would consist of the quantized errors, denoted byeq(m, ) (see Fig. 3). From the quantized prediction error,the decoder reconstructs the pixels as follows (let us ignorethe entropy encoding part in this case):

It can be easily shown that the reconstruction error ~ ( m ,)= x (m,n)- T(m, ) s the same as the quantization error,

DPCM has been researched extensively in medical imag-ing regarding its design, operation, and performance [21],[18], [124], [91]. The extension of the two-dimensional (2-D) DPCM method to a three-dimensional (3-D) one is alsostraightforward [1371. For lossless compression of medicalimages, DPCM generally achieves average compressionfactors that range from 1.5 to 3. Variable-length coding,such as Huffman coding and arithmetic coding, is preferredto fixed-length coding [21], [22] because the histogram ofthe difference values in lossless DPCM is highly peakedaround zero.

e(m,n)- eq(m,n) .

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Notably, Rabbani and his colleagues at Eastman KodakCompany have demonstrated on a set of CT and MR imagesthat the use of adaptive Huffman coding in DPCM providesa slightly higher compression ratio than fixed Huffmancoding [124], [125]. Yeh, Miller, and Rice have proposedthe Rice data compression algorithm [166], [1671 whichalso uses lossless DPCM for decorrelation and adaptiveHuffman coding for entropy coding [43]. Ramabadran et al.at Iowa State University have attempted lossy DPCM onseveral MRI, US, and X-ray medical images and achievedabout twofold increase of compression performance withrespect to medical images compressed using lossless DPCMwith the same image quality [126], [127], [36]. In general,higher compression ratios are difficult to achieve usingthe DPCM method, as granular and contouring distortionsbegin to appear when the fairly uniform regions of animage are coarsely quantized to take advantage of theirgreater compression potential. Also, since DPCM requiresthe majority of the image to be reconstructed to achieverecognition and permits only a single reconstructed imageof fixed quantity, it therefore does not support progressivetransmission.B. Hierarchical Interpolation

The hierarchical interpolation (HINT) method is avariable-resolution pyramid coding scheme based onsubsampling [135], [136]. It starts with a low-resolutionversion of the original image, So , and successivelygenerates the higher resolutions, SL, 1 5 L 5 n, usinginterpolations. The image data at the lowest resolutionlevel, SO , s entropy-coded and transmitted first. After that,in a hierarchical manner, an interpolation scheme is used togenerate estimates of the unknown pixel values at a higherresolution level by calculating the average of its four nearestneighbors at the immediate lower level. The estimates arerounded to their nearest integers and then subtracted fromthe true pixel values. The difference signals relating to eachof the higher resolutions in the image hierarchy are alsoentropy-coded and transmitted.More formally, the set of low-resolution 2-D imageindexes upon which the HINT decomposition is based isdefined asSL = { ( 2 L ~ , 2 L ~ ) } , E { 1 , 2 , . . . R(log,(N - 1 ) ) )

(4)where r , s = 0,1,. . ,N - 1 , 0 5 2 L r , 2 L s 5 N - 1 andthe function R returns the largest integer not greater thanlog,(N - 1).The set of indexes S L - ~t the next higherresolution level then isSL-1 = SL U {2L( r + 1 / 2 ) , 2L( s + 1 / 2 ) }

U { p L ( r + 1 / 2 ) , 2%) ) U {pLr , y s + 1 / 2 ) ) }= SL UHL1 U H L 2 ( 5 )

where H L ~ {ZL(r + 1 / 2 ) , 2 L ( s + 1 / 2 ) } and H L Z ={ ( 2 L ( r + 1 / 2 ) , 2Ls ) } U { ( 2Lr , 2L ( s + 1/2))}. Each non-boundary element of H L ~s surrounded symmetrically byfour elements of SL .Thus, we can estimate the pixel values200

. + . 0 . + . 0 . + . 0

. . . . . . . . . . e .. x . + . x . + . x . +. . . . . . . . . . e .. + . 0 . + . 0 . + * 0. . . . . . . . . . . .. x . + . x . + . x * +. . . . . . . . . . . a

. + . o . + . o . + . o

Fig. 4.pyramid. Symbolic representationof the construction of a 1-DHINT

belongs to H L ~y interpolating the values correspondingto these four nearest elements. Each nonboundary elementof H L ~as also equal distance to four neighbours of{SLUH L ~ }nd can be interpolated in a similar fashion.Fig. 4 provides an illustration of this construction of a 2-DHINT pyramid. The indexes of S1 is the union of those ofSp (represented by o), H11 ( x signs), and H22 (+ signs).The dots represent the remaining indexes (- signs) forwhich the original image is defined. The complete set ofindexes, SO,can be written as

Roos et al. have shown that the 2-D HINT decorre-lation gave compression ratios ranging between 1.4 for12-b 256 x 256 MR images to 3.4 for 9-b 512 x 512angiographic images [135]. Ramabadran et al. enhancedthe HINT by coding decorrelated medical images using anadaptive statistical model [1271 and obtained about 16%to 26% increase in compression ratios for several MRI,US, and X-ray images. The use of 2-D HINT technique,however, provides no significant improvement for time-series of 2-D images, because the temporal decorrelation(interframe) destroys the spatial correlation of the individ-ual frames (intraframe) [138], [160], i.e., too much noisebetween frames causes poor correlation. To circumvent thisproblem, a 3-D HINT technique, which is based on the3-D first order 6-point estimator and a 2-D equidistant 4-point filter, has recently been proposed [137]. In addition,the HINT method commonly uses only one codebook forcoding all the residual errors. A variant of it, HINTS,uses separate codebooks to encode the residual errors.Although HINTS requires more computation, it is expectedto perform better than HINT.C . Difference Pyramid

Diference pyramid (DP) is another kind of compressionmethod based on the variable-resolution model. It consistsof two parts: the construction of a mean pyramid andthe calculation of a difference pyramid that contains thedifferences between successful levels of the mean pyramid[1571. For an image X N of size N xN , he mean pyramid is



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Fig. 5. Difference pyramid composition.

constructed by computing the following values (see Fig. 3):zmean = ( 1 / 4 ) ( z ( k , i , j ) + z ( k , i , j + 1 ) +z(k,i+ 1 , j )+ z ( k , + 1 , j+ 1)) ( 7 4

andz ( k - 1, i+ 1) / 2 , ( j+ 1) / 2 ) = Nearest(z,,,,) (7b)

where k 5 N , refers to a hierarchical image level, i and jrefer to the row and column positions of the image matrix,and the round-off function, Nearest, returns the nearestinteger of z The difference pyramid at level k isformed as follows:

d(k,i,j)= z ( k - 1, i + 1) / 2 , ( j+ 1) / 2 )d(k,i,j+ 1 ) = z ( k - 1, i + 1) / 2 , ( j + 1) / 2 )d(k,i+ 1 , j ) = z ( k - 1,(i + 1) / 2 , ( j + 1) / 2 )

d ( k , + 1 , j+ 1) = z ( k - 1, i + 1) /2 , ( j + 1) / 2 )

- x ( k , , ) (8 4- ( k , i , j + 1 ) (8b)- z ( k , i + l , j ) (8c)- ( k , + 1 , j+ 1). ( 8 4

The difference pyramids are entropy-coded and trans-mitted. The d s calculated from (8a-d) represent differentvalues between adjacent pixels and are stored as the addi-tional information needed to reconstruct the z ( k , , ) romz ( k - l , ( i + 1 ) / 2 , ( j + 1) /2) . A variant of DP, calledreduced diflerence pyramid (RDP) [157], forms the meanpyramid by first calculating the differences between theneighboring nodes (all at the same level), i.e.,d(k,i,j) z ( k , i , j ) z ( k , i , j + l ) ( 94

(9b)

(9c)

d ( k , i , j + l ) = z ( k , i , j + l ) - z ( k , i + l , j + l )d(k,i+ 1 , j ) = z(k,i 1 , i+ 1 ) - z(k,i+ 1 , j ) .

Then these three differences are entropy-coded and trans-mitted. RDP is generally lossy, but it can be turned intoa lossless method. That is, at each construction stage, thex ( k , z , j ) values can be losslessly reconstructed if p b areWONG et al.: RADIOLOGIC IMAGE COMPRESSION-A REVIEW

LSB planew ) t..2nd MSBplene(anP -2)

MSB plane(BnP-1)

DescendingBit positions

Fig. 6. The bit-plane decomposition.

used to represent z(k-1, (2+1) /2 , ( j+1) /2) a n d p + l bareused to represent ds, where p is the number of bits/pixel inthe original image. These extra bits would also increase thebit rate substantially. Since the histogram of the differencevalues, as in lossless DPCM, is highly peaked around zero,variable-length coding is thus used to take this advantage.Another pyramid approach to decorrelation is the S-transform [107], [15], which constructs the mean pyramidat each stage using (7a-b) and the following differenceformulas:d ( k , i , j ) = ( 1 / 2 ) ( z ( k ,Z , j ) +x(k,i,j + 1)

d(k,i,j+ 1 ) = ( 1 / 2 ) ( z ( k , i , j ) - ( k , i , j + 1 )d(k,i+ 1, j )= z ( k , i , j )- ( k , i , j+ 1 ) +z(k,i+ 1 , j+ 1 )

- z ( k , i + l , j + l ) - z ( k , i + l , j ) ) (loa)- z(k,i 1 , j+ 1 ) + z(k,i 1 , j ) ) (lob)+z(k,i+ , j ) .

The S-transform method is slightly more efficient thanthe RDP method at the expense of an increased number ofcomputations (compared with (9a-c)).I

D. Bit-Plane EncodingCompared to the HINT and DP of variable-resolution

modeling, Bit Plane Encoding (BPE) partitions the hi-erarchies of images into fixed resolutions, that is, thereconstructed image is of the same size as the source image,and the value at any particular pixel location is refined asone moves up the image hierarchies. Consider an image ofsize N x N x k b. By selecting a single bit from the sameposition in the binary representation of each pixel value, anN x N binary image (1 or 0 value) called a bit plane canbe formed [1431, [92]. For instance, the most significant bit(MSB) plane is an N x N binary image that contains themost significant bits of pixel values of the image. Repeatthis process for the other bit positions of each pixel, theoriginal image can be decomposed into a set of p , N x Nbit planes, numbering 0 for the least significant bit (LSB)plane through p-1 for the MSB plane as shown in Fig. 6.BPE facilitates progressive transmission by transmittingthe bit planes in a sequence, with the MSB plane first andLSB plane last. The image reconstructed from the data fromMSB plane is a binary image, and additional gray levels areadded as more bit planes are received. BPE is lossless if

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,+stimation ,&, 0 pixel to be predicted0 pixel in the supprotFig. 8. Support regions of NSHP 3 x 3) (figure from [41]).Fig. 7. A block diagram of the predictive2- D MA R method.

all bit planes are used in the scheme. Lossy images withhigher compression ratios can also be attained by sendingonly the first few MSB planes, which normally containmost of the structural information of the image and providea larger compression. The amount of compression due toredundancy reduction is usually the largest for MSB imagedata and decreases as one moves down the hierarchy.The designers of bit plane encoders typically take advan-tage of the existence of large uniform areas in each bit planeto achieve compression. The simplest encoding schemes forbinary data of frequent clusters of 0s and 1s is run-lengthencoding (RLE) [75], which is being used routinely forcoding binary text and documents in the field of facsimiletransmission [79]. In medical imaging, RLE is best suitedfor image areas with low variation in pixel values, suchas soft tissue regions in CT images [129], [loll or indigital subtraction angiograms outside the vessels whichwere acquired at radiographic exposure levels. Rabbani etal . [124] experimented with a more elaborated techniquebased on adaptive arithmetic coding [94]. Although BPEcompression ratios may not be as high as those of reversibleDPCM, the differences are usually small. In addition, BPEprovides competitive compression ratios to RDP and S-transform, as well as the added PT capability. These twoproperties make bit plane encoding a worthy candidate forlossless coding of radiologic images.

E. Multiplicative AutoregressionMultiplicative autoregression (MAR) is a 2-D com-pression method introduced recently in [24], [26]. It hastwo versions: 2-D MAR and 2-D multi-resolution MAR(MMAR) [25]. In 2-D MAR, the digital image is firstsubdivided into several smaller, M x M , blocks. Overeach block, let {x( i , j ) , l 5 i , j 5 M} denote the 2-Dpixel data sequence obtained from this block, the imagedata is assumed to be locally stationary and representableby a 2-D linear stochastic model [41].

where w ( i , j ) denotes a zero-mean white noise sequence, bthe mean value of { x ( i , ) } , nd { g ( i , ) } he correspondingzero-mean sequence. The 2-D operator, a(q1,qz) . is apolynomial in qT 1 and qT 1 with q; and qT 1 denoting theunit backward shift operators along the rows and columns.Fig. 7 illustrates a block diagram of MAR encoder.202

A MAR encoder consists of a parameter estimator, a2-D MAR predictor, a rounding operator, and a losslessencoder for the residuals. First, { y ( i , j ) } is constructed bysubtracting an estimated value, best, from {x(z, ) } . Next,the coefficients of a(q1, q2) is estimated, and the predictedof y( i , j ) is calculated and rounded off as follows.Y p ( i , d = P ( Q l , 4 2 ) x Y ( i , j )

(12a)Y r ( i , j ) = R ( Y P ( i 1 d ) . (12b)

= (1- a e s t ( ~ 1 , 4 2 ) ) ~ ( i , j )

The residual signals, d ( i , j ) , are obtained fromd ( i l j ) = Y ( i , . d - r(i,j). (13)

The residual sequence, { d ( i , ) } , s entropy-coded usingHuffman coding or arithmetic coding. The coded residuals,the model coefficients, and the mean value pertaining toeach block are transmitted in MAR. At the receiver end,x ( i , j ) s exactly reconstructed by first synthesizing yr ( i , j )from (12a-b), as well as d ( i , j ) and best, that is

x(i , j) = ~ r ( i , j ) d ( i , j ) +best. (14)The choice of a(q1 42) is a tradeoff between predictor per-formance and the implementation complexity. The numberof model parameters is typically limited to three or four. Amodel with a nonsymmetric half-plane (NSHP) ROS is

a (q 1 , 4 2 ) = (1+ a1q;l) x (1+ a 2 4 1 7x (1+ a3qL142) (15)

where the numbers within the parentheses represent thesupport regions; also shown diagrammatically in Fig. 8.MMAR models are merely adaptations of the MARstructure to multi-resolution image representations [24].The MMAR coding method consists of filtering and sub-sampling the original image into three resolutions, andcoding them in an interpolative manner. Das and Burgettshowed that MAR performs better than HINT, DPCM,DP, and RDP using six digitized radiographs and eightnoisy MRI images [24], [25], [41]. More studies, however,are needed for other kinds of radiologic images. Otheradvantages of using 2-D MAR models, as opposed togeneral 2-D models, is the ability to guarantee stabilityof the predictive coder for NSHP support regions [41],and the support of progressive transmission of medicalimages (MMAR). The tradeoff here is that the MAR codingtechniques are more difficult to implement and slower incompression than the other lossless techniques.

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V . IRREVERSIBLE MAGECOMPRESSIONAs compared to reversible compression, the irreversibletechniques present an order of magnitude of higher com-pression ratios. Owing to this big jump in performance,

most of the research activities, as well as recent advances,in image coding have taken place in the area of irreversiblecompression. The current popular lossy methods understudy in the medical imaging area include the 2-D discretecosine transfonn (DCT) [113], [4], [128], [155],fuZZ-fiameDCT [103], [104], [32], [33], [65], [128], Zapped orthog-onal transform (LOT) [112], [113], [29], [80], subbandcoding [164], [165], [161], [3], [146], vector quantization[39], [108], [511, 1611, quadtrees [139], [581, [591, andadaptive predictive coding schemes [93], [84]. The firstfour techniques are based on the linear, discrete transforms(DT) that decorrelate the pixel data f(xi) and representthem compactly in a spatial-frequency-like domain (in onedimensional notation):

where a is a scale parameter related to frequency. Itis generally desirable, but not mandatory, that the basisfunctions h(v , , a) are orthogonal. Then the basis functionsare identical to the sampling functions and the number oftransform coefficients is equal to the number of pixels.From the viewpoint of algorithmic complexity, the adap-tive predictive coding techniques, such as adaptive DPCM[127], [96] and MAR [25], are simpler to implement thanthe other techniques, but they can only achieve mod-erately good compression ratios. For low-bit-rate lossycompression applications, the other techniques, e.g., DCT,full-frame DCT, LOT, subband coding, vector quantization,and quadtrees are thus preferable. We describe these othertechniques in the following.

A . Discrete Cosine TransformThere are many kinds of transform coding techniques[84], [149]. Among them Karhunen-Loeve transform (KLT)[159], [68] is the most compact in terms of decorrelation.The KLT constructs the image-specific set of basis functionsthat correspond to the normalized eigenvalues of the co-variance matrix of the image and, thus provides maximumdecorrelation and entropy reduction. However, the KLT isseldom in practice as the required matrix inversion for theKLT, is difficult to compute and a fast algorithm doesnot exist for it. For a great variety of images, the DCTis a transform among the other transform techniques thathas decorrelation properties very close to the KLT. TheDCT was first introduced by Ahmed in 70's [4] and hassince been used for lossy image compression more thanany other techniques. It is also included in the recent JointPhotographic Experts Group (JPEG) and Moving PictureExperts Group (MPEG) compression standards for general-purpose still-image [1231 and video image applicationsW l.WONG et al.: RADIOLOGIC IMAGE COMPRESSION-A REVIEW

Horizontal frequency0-1 5-6 14-15 27-282/ / / / / / /

I / / / / / / / I/ / / / / / /10 19 23 32 39 45 52 54

' 20 22 33 38 46 51 55 60I / / / / / / / I21- 34- 37 47 50 56 59 61

35-36 48-49 57-58 62-63/ / / / / / /Fig. 9.encoding (figure from [123]).Zigzag ordering of the DCT coefficients for entropy

The 2-D DCT for an N x N block is given byF(u ,v)= (4/N2)c(u)c(v)

x [.t.yx(m,n)os((7r(2m+ l ) u ) / 2 N )1m=O n=O ( 1 7 4x cos((7r(2n+ l ) v ) / 2 N )

N-1N-1x (m,n )=Ec (u )c (v )F(u ,) o s ( ( r ( 2 m+ 1 ) U ) / 2 N )

m=On=Ox cos((7r(2n+ l ) v ) / 2 N ) (17b)where c(w)= 2-l" for w = 0; c(w)= 1 for w = 1 , 2,... , N - 1 . In many applications of the DCT for imagecompression, the original image is divided into adjacentblocks, e.g., 8 x 8 submatrices as in the JPEG compressionstandard. The DCT is then computed for each block and aquantizer is applied to the transform coefficients. Becausethe pixel value distribution is generally not stationary, thequantizer may have to be regionally adapted. Small blocksizes of, e.g., 8 x 8 pixels have the advantages that thecomputational and memory requirements are very moderateand can be implemented on the fly, but may be too smallto cover correlated regions.The best known example for block DCT image com-pression is the JPEG Standard [123] for compression ofcontinuous-tone still images. This standard specifies lossyand lossless codec processes. The lossy coding is basedon an 8 x &block DCT. To simplify the entropy coding,after quantization, the 64 DCT coefficients are scannedin a zigzag order (see Fig. 9) , beginning with the DCcoefficient of zero frequency. This zigzag ordering helps to

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1 o

0.0 0 8 1 6 24 40 48Zigzag indexFig. 10. Typical probability distribution of the AC DC T coefficients after zigzag ordering (from [123]).facilitate better entropy coding by placing low-frequencycoefficients, which are more likely to be nonzero, beforehigh-frequency coefficients. After the scanning, a spec-trum of coefficients like the one in Fig. 10 may beobtained. While the JPEG standard offers quantizationtables modeled according to human contrast sensitivity,there is complete freedom in choosing the quantization. Thequantization table may be altered within an image.The large and quickly growing volume of radiologicimage data has prompted significant interest in the feasibil-ity of applying the lossy DCT to medical images. Recentstudies have demonstrated no statistically significant differ-ence in diagnostic accuracy with 20:l DCT compressionratio for hand and thorax radiographs [140], [141], [ l ] . Inanother investigation at Northwestern University and theUniversity of Chicago by Kostas et al. [89], promisingresults with JPEG compression were also obtained afteroptimizing the quantizer tables for the specific radiographsdifferently from the Standards default tables. Extendedsequential JPEG with Huffman coding was applied to 2K x 2 K x 12-b radiographs. With compression ratiosof 33:l to 50:1, the radiologists in that study judged theloss in image quality to be quite subtle. In one of the chestradiographs, a very subtle pneumothorax was clearly visibleon the 50:1 compressed image. In another chest radiograph,fine interstitial infiltrates in the lung base were judged to bealso clearly visible in the 50:l compressed image. In two204

mammograms with mass and clustered microcalcifications,both abnormalities were visible at compression ratios largerthan 55:l.Radiologic image compression with the DCT workswell if the important clinical information of an imagecan be represented within a relatively narrow frequencyrange. Many details of medical images, however, are quitesingular and nonstationary and demand a wide spectralrange, i.e., many transform coefficients, for their represen-tation. If one is not careful in quantizing the coefficients,the decoded image will have fringes parallel to edges.Thus, ideally, transforms for radiologic image compressionshould have the space-frequency localization attribute [161.Furthermore, the shortcomings of the block structure ofthe transform manifest themselves by block boundariesthat appear in the decoded image; particularly, when edgeenhancement must be employed after the codec operation.The full-frame DCT, the lapped orthogonal transforms(LOT), the concept of dividing or splitting the image[105], [106], the combined transform coding scheme [170],[169], and various linear filtering techniques [9] have beenproposed to overcome this problem.B. Full-Frame Discrete Cosine Transform

In block transform coding, the image is divided intoblocks of 8 x 8 or 16 x 16 pixels, with a subset of the trans-form coefficients of each transformed block transmitted and

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used in image reconstruction. However, for compressionratios greater than about l O : l , the 2-D DCT, such as inthe P E G standard, introduces noticeable tiling artifacts.The blocking artifacts visible in the reconstructed imagerender block coding unacceptable for medical applications.The fill-frame iscrete cosine transform (FF-DCT) [103],[32], [33] has been developed to remedy this situation andis therefore more suitable for radiologic image compres-sion. The full-frame coding compresses the entire imageas a block, thereby avoiding the problem of blockingartifacts at the expense of an increased computationalburden. Compared with the block DCT, the full-frameDCT can generally maintain better image quality at highcompression even though the quantization table cannot beadapted regionally to adjust image quality and compressionratio. It also simplifies spatial filter processes and providesfast compression to transmit images for real-time PACSand teleradiology applications.Templeton et al . (University of Kansas) [152] com-pared full-frame DCT image compression with extendedsequential JPEG using Huffman coding: Clinical studiesshowed that 2 K x 2 K x 10-b computed radiographscould be compressed 35:l with full-frame DCT withoutobservable loss of diagnostic information while the errorof JPEG compressed images at that compression rate ismore noticeable. The most significant published effort inexploring FF-DCT for lossy medical image compressionwas undertaken by H. K. Huangs group formerly at UCLA[W , W , WI, [331, 1651, [661, [701, [1401, HI . TheUCLA group also developed dedicated hardware capable ofexecuting a compression of a 1 K x 1 K image in 1 s [66],[73]. They reported that, in general, higher compression isachieved for higher resolution image [104].More recent studies of the UCLA group treat all frequen-cies as being almost equally important [32]. The quantizedcoefficients &(U, U) re obtained from the DCT coefficientsF(LL,v)by

where R denotes the round-off function as before, p is aglobal constant, and k is a compression parameter. For agiven p, a large value of k means more coefficients arekept to extra precision. The quantized transform imageis divided into a large number of rectangular zones. Withineach zone, the coefficient with the largest absolute valuedetermines how many bits are allocated per coefficient inthat zone. The coefficients are then packed into a bit-streamin a predetermined order and all zones are concatenated intoa single data set. A large ROC study at UCLA with 2 K x2 K x 12-b thorax radiographs demonstrated that, at about20: 1 compression-produced with two-zone quantizationand bit-allocation, no significant difference existed in thedetection of any thorax abnormalities between original andcompressed images [11.WONG t al.: RADIOLOGIC IMAGE COMPRESSION-A REVIEW

(C)Fig. 11. An example of using the full-frame DCT compressionhardware (a) a digital chest image, (b) the compressed and recon-structed image with a 20: 1 compression ratio, and (c) the subtractedimage between those in (a) and (b).

In Fig. 11, we show an example of the compressionresults with a chest image using the FF-DCT hardware.The compression ratio is about 20: 1. The difference image(Fig. ll(c)) from the original image (Fig. ll(a)) and thereconstructed image (Fig. 1 (b)) indicates no noticeablestructural noise. Fig. 12 shows another example of using

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the full-frame compression hardware in hand radiographswith evidence of subperiosteal resorption (see arrows).Recognition of subperiosteal resorption on a radiographis a sensitive indication of the required level of imageresolution versus the desirable compression ratio. Suchfindings are difficult to detect in most patients and requirehigh-resolution radiography. A related ROC study findsno decrease in performance among the radiologists onconventional radiographs, digital laser printed radiographs,or compressed and reconstructed images [1401. Individ-ually or collectively, the radiologists performed equallywell with all types of images at 20:l compression ra-tio.Villasenor, also at UCLA, has recently shown that the fullframe DCT or 2-D DCT of large block size, such as 16 x 16or higher, is outperformed by the discrete Fourier transform(DFT) [20] and discrete Hartley transform (DHT) [191 for aset of images obtained using positron emission tomography(PET) and MRI [154]. This difference occurs because PETand MRI images are characterized by a roughly circularregion, R, with nonzero intensity inside and zero intensityoutside. Clipping R to its minimum extent can reduce thenumber of low-intensity pixels. The DCT requires to storeimages on a rectangular grid and thus retains a significantregion of zero intensity, useless information, in compressedimages. With this constraint imposed, the FF-DCT loses itsadvantage over the DFT and DHT. Nevertheless, whetherthis result holds for the DCT of smaller block size or othertypes of images is arguable.C . Lapped Orthogonal Transform

An attractive compromise in computational complexityand elimination of block artifacts has been found in theLapped Orthogonal Transform (LOT) [112], [113], [29],[go]. Fig. 13 illustrates the process of the LOT in one-dimensional notation, where each block has 2M samplesand neighboring blocks overlap by M samples [23], [17].The LOT implementation maps the 2 M samples of eachblock into M transform coefficients. The basis functionswhich extend over 2 M samples consist of subsets of evenand odd functions (seeFig. 14) [112]. Each function decaystoward zero at the boundaries of the block. The first evenfunction has a positive mean so that a DC level can beconstructed by the overlapping of these functions fromconsecutive blocks. The energy compaction capability ofthe LOT approximates that of an ordinary block transformwith 2 M samples.The reduction of boundary artifacts with the LOT isdue to two properties: The overlapping of the samplingfunctions causes that the information for an M-size blockis represented by functions and their coefficients which aredetermined by a 2M-size block symmetrically surroundingthe M-size block (see Fig. 13). In particular, the DC andvery low-frequency components of one block affect alsothe coefficients of the neighboring blocks and vice versaso that quantization effects are spread. Further, the decaytoward zero of the basis functions at the 2 M boundariesand the fact that the right boundaries of one block are206

(C)Fig. 12. An example of using the FF-DCT compression hard-warein hand radiographs with evidence of subperiosteal resorption(ariows). (a) The 2048 x 2048 x 12-b digital laser printed imageof an analog original, (b) compressed and reconstructedimage witha compression ratio 20:1, and (c) the subtracted image betweenthose in (a) and (b).

immediately adjacent to the left boundaries of the secondnext block helps eliminating artifacts in the center of theM-size blocks.PROCEEDINGS OF THE IEEE, VOL. 83, NO. 2, FEBRUARY 1995

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UU

U

U

U

U

UU

U

11U U

Fig. 13. The lapped orthogonal transform (LOT) process (from 23]).

D . Subband Coding represents the low-frequency components which can beviewed as either a minified or blurred copy of the original.sary edge infomation cm be added to the low-fiequencycomponents to reproduce the sharpness of original image.

A subband coder perfoms a set Of Operations Successive higher spectral bands that contain the neces-on an mage to divide it into spectral components or bands.For example, an image might have a small subimage thatWONG et al.: RADIOLO GIC IMAGE COMPRESSION-A REVIEW 207


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(a) (b)Fig. 14. The even and odd basis functions of a 32-tap LOT (fromU121).Fig. 15 illustrates the decomposition of a hand phantomimage into four components according to the horizontal andvertical spatial frequencies. One can see that most energyof the original image is localized in the low horizontal andvertical frequency components.The requirements for an image compression system dis-cussed earlier, hierarchical image decomposition as wellas space-frequency localization, can be accomplished witha wide range of orthogonal and nonorthogonal transformschemes of which subband coding with wavelet transformsare a broad category 1271, [1611, [164], [1651, [31, [381,[8], [571, [421. The subband transforms can generically berepresented (in one-dimensional notation) by

NWf(V,3) = Cf(Z2)x * v , s ( z z ) . (19)

The f(z,) epresents discrete pixel values of a square-integrable one-dimensional function f E L 2 ( R ) and s isthe scale parameter related to frequency.Fig. 16 illustrates the principle of subband decompo-sition for the one-dimensional case [133]. The signal isdecomposed into a low-pass and a high-pass band of equalbandwidth. Assuming the ideal filtering, the decomposedsignals would have half the bandwidth of the original andcan be subsampled by a factor of 2. The process of band-splitting and decimation by two can be applied to both thehigh- and the low-pass bands of a preceding decompositionand a subband jilterbank tree is obtained. If we follow,for example, the lower branch, we can easily see thatthe basis functions are self-similar or scaled versions ofeach other. In other words, the basis or filter functionshave scale invariance and come in many sizes (calledscales) and thereby provide space-frequency localization.Generally speaking, the 1-D analysis is used for speechand audio analysis, and the 2-D and 3-D decompositionsare appropriate for image and video analysis (see Fig. 17[86]). It is assumed that the filterbanks used for thesedecompositions satisfy the requirements on reconstructionerror, processing delay, and interband interference.Wavelets of the type concerned in our 1-D case are afamily of orthonormal functions:6v ,s ( z , ) ( s - ~ ' ~ ) 6((z - ) / s ) s ,u E Rea1,s> 0

(20)

z=o

208

that are employed with dilation of the real-value scale sand translation by U of 6. An example of three continuousbasis functions is shown in Fig. 18 [lo]. Just as in ordinarysubband coding, projection of the signal onto differentscales is equivalent to bandpass filtering with a bank ofconstant-Q filters (ratio of bandwidth and center frequency,A f / f , is constant). Further, another important class ofwavelet filters are biorthogonal. These biorthogonal filtershave the further advantage of allowing linear phase inall filters, which is not possible for the orthogonal filters;excepting the trivial Haar basis.Although not overly crucial for lossy data compression,if, after reversing the coding process, alias-free recon-struction of the original is achieved, the subband filter isa quadrature-mirror jilter (QMF). One can show that aQMF requirement, is equivalent to the requirement thata band-splitting transform has an orthogonal transformmatrix. Thus, wavelet transforms form QMF pyramids. Thewavelet theory emphasizes the differentiability or regularity[133], [57] of the basis functions for N 4 00. Waveletregularity implies a flat frequency response for the waveletfilters at normalized frequencies w = 0 and w = T. Thisregularity feature, however, is of little importance for imagecompression where the decomposition is applied only a fewtimes in succession.Wavelets per se do not offer features or advantagesfor image data compression and signal decomposition thatcould not be obtained by the wider class of subbandtransforms. Moreover, when a one-dimensional QMF isapplied separately in two dimensions, an image is dividedinto four subimages: a low-pass, and three high-frequencysubimages-of the vertical, horizontal, and diagonal detailcomponents. Fig. 19 presents the corresponding partitioningin frequency space [146]. Cascading the operation, alwaysusing the low-pass image from the prior level, leads to anefficiently computed self-similar image pyramid.

The first publications on QMF pyramids and wavelettransforms for data compression began to appear after 1984.Work especially worth mentioning is by Vetterli [161] andAdelson, Simoncelli, and Hingorani [3]. In recent years, aflurry of activities in subband and wavelet coding for medi-cal image compression has also occurred. In addition to thecommercial marketing of this technology by Aware Inc.[77], [78], we comment on two other notable applications.In one application, Rompelman [1341 used a QMF bankplus vector quantization. He formed 16-dimensional vec-tors with corresponding pixels of all 16 images froma full second-order subband picture decomposition. Withcodebook sizes of 4096 and 1024 vectors, 512 x 512x 12-b CT images were coded with compression ratiosof 16:l and 19.2:l without statistically significant lossof information based on checklist and RO C analyses. Inthe other application, Manduca [1151, [1141 employed analgorithm and a 9-tap wavelet developed by Simoncelli andAdelson [1461. The quantized transform coefficients wererun-length and Huffman encoded. Regions of interest ofprojection radiographs (512 x 512 x 12-b pixels) and MRIimages (8-b pixels) were compressed with compression



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Fig. 15. An example of subband coding images.

ratios of 37.5:1 (0.32 bits per pixel (bpp)) and 8: l ( 1bpp), respectively. Manduca compared his scheme with thebaseline JPEG for the same compression ratios and statedthat the JPEG-compressed images had larger root meansquare errors and more noticeable artifacts.Wavelet transform is a promising tool for radiologicimage compression and applications of it are also beginningto emerge. What is still lacking, however, is a thoroughunderstanding of what wavelets can do for medical imagecompression that other existing techniques cannot. More-over, in applying wavelet tools for low-bit-rate coding ofradiologic images, we must also pay attention to the yet-untouched problems of uncancelled aliasing as well as thehigh computational cost of a signal-adaptive filterbank.E. Vector Quantization

Vector quantization (VQ) is an extension of scalar quan-tization to a higher dimensional space and is based on thefundamental result of Shannon's rate-distortion theory [1451that better coding performance can always be achieved bycoding vectors instead of scalars. VQ is asymptoticallythe optimal structure for block source coding when thevector dimension increases to infinity. Gray and Nasrabadipresent excellent reviews of VQ for general-purpose imageprocessing [54], [1081. Formally, a vector quantizer can bedefined as a mapping of k-dimensional Euclidean space R k

into a finite subset Y of Rk,.e.,

where Y = {y 2 1 1 5 z 5 N } . The subset Y is called aVQ codebook and its elements {yL} are called reproductionvectors. Fig. 20 shows a block diagram of VQ method [54].The encoder views the k-dimensional input vector ofdescriptor components and searches through the codebookto find the address of a reproduction vector, y2, that re-produces the input vector as closely as possible. It thentransmits the index address i of the reproduction vector tothe decoder which replaces it with y1 as the approximationxeS t of x.The compressed data thus contain the indices ofthe reproduction vectors corresponding to different inputvectors. The decoder uses the address to recreate thereproduction vector. The distance (or distortion) measurethat is commonly used is d ( z . y , ) = 112 - ~ 1 1 ~ .he sizeof a VQ codebook is typically at the power of 2, i.e.,N = 2', so that the index of a reproduction vector canbe represented as a b-bit quantity. The goal in designingan optimal VQ is to obtain a code-book of N reproductionvectors that minimizes the average distortion. The codebookmay be generated from training images using, for example,statistical clustering techniques [99].The encoding complexity fo r full search schemes, wherean input vector is compared with every vector of the

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.. .

Fig. 16. Subband coding scheme. (a) Two subsampledapproxi-mations, one corresponding to low and the other to h ighfrequencies,are computed. The reconstructed signal is obtainedby reintep-lating the approximations and summing them. Thefilters on theleft from an analysis filterbank, while, on theright is a synthesisfilterbank (b) Filter bank tree of asubband coder (figure fromt1291).

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codebook, increases linearly with the number of vectorsand exponentially with vector dimension. Consequently, theperformance of VQ is largely constrained by the availablecomputer power. In practice, vectors are often formed froma sub-block of, for example, 4 x 4 pixel squares, i.e., ofrelatively low dimension compared to the typical range ofspatial correlation.

Tree-structured encoders with a sequence of binarysearches have been developed to reduce the search effort[28]. The coding complexity then increases proportionalto the logarithm of the number of vectors N . A varietyof unbalanced, pruned trees have been designed withwhich, for a given average data rate, a lower distortioncan be achieved by devoting more bits to high distortionevents than with balanced trees [131], [39], [ S I . Riskinand Gray [130], [132], [131], [55] developed several tree-growing algorithms for the design of variable rate vectorquantizers and applied them to MRI. his work at StanfordUniversity has recently been extended to lossy compressedimages of CT chest scans and thoracic images [39], [401.210

Their results indicated that there was no significantdifference in diagnostic accuracy of image assessmentat compression ratios of up to 9:l; i.e., 12 bpp CT imagecan be compressed to between 1 bpp and 2 bpp with nosignificant changes in diagnostic accuracy. VQ also mixesother coding techniques. For example, the work of Sezan,Rabbani, and Jones [ l a ] combines VQ with a Knowltonhierarchy to achieve progression transmission. Studies inother digital imaging field also integrated the subbandcoding into VQ to yield significant size reduction [91].This notion has yet to be explored in medical imaging.The published results indicate that VQ is a promisinglossy compression technique for radiologic images. Itsmajor limitation is the high implementation complexityof the compressor both in terms of the codebook storageand search time [6]. Also, most of the reported workdid not mention the suitability of VQ for preserving theedge information. VQ is extremely effective in compressingreasonably uniform regions of an image at low bit rates withhigh quality. However, regions with sharp transitions, e.g.,edges, present difficulties. High fidelity coding of edges iscrucial in medical diagnosis and interpretation. This wouldmean that the higher bit rates and larger codebooks have tobe used to compress such sensible regions, which inevitablyincrease the implementation complexity.F. Quadtrees

Quadtree-based image compression [139], [116], similarto vector quantization image compression, is a schemeconceptually differs little from transform coding. It exploitsredundancy and correlation of pixels within an image byordering or matching transform coefficients. In medicalimaging, both quadtrees and VQ schemes have been usedin conjunction with other decorrelation models [134], [5],[170].A quadtree data structure is constructed by linking afinite set of nodes such that each non-terminal node isrelated to four disjoint offspring nodes, as illustrated inFig. 21 [139]. Throughout the tree, the offsprings of everynode subdivide the region represented by the parent nodeinto four equal quadrants of the image. The leaf nodesrepresent a pixel or pixels with the same gray level,and the root note of the tree corresponds to the entireimage. The goal for data compression is to make theregions associated with a leaf as large as possible, using acertain split and merge algorithm. As shown in Fig. 21, theshaded areas correspond to merged nodes (black boxes).In lossy compression, resolution relaxation and contrastrelaxation (coarser quantization) are often employed inlossy compression to increase the compression factors.As a representative example of quadtree-based medicalimage compression, the work of Halpern et al. is mentionedwho applied this method to 512 x 512 x 8-b abdominal CTimages [SI-[60]. Compression ratios of up to 1O:l wereobtained without statistically significant loss of clinical sen-sitivity according to ROC studies, although a general trendof decreasing clinical accuracy with increasing compressionwas apparent already at low compression ratios. Quadtrees



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Fig. 18. Left: continuous basis functions of the short-space Fourier transform (SSFT) or itstemporal equivalent, the STFT, which are frequently used for transformation of nonstationarysignals. These transforms have space or time localization properties, but do not provide frequencylocalization. Right: Wavelets with space-frequency localization (figure from [lo]).

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Fig. 21. A region, its maximal blocks, and the correspondingquadtree (figure from [139]).acceptable diagnostic quality [1411, 111, 1891, [1031, [391,[401, 1691.In recent years there has been a marked increase in thenumber of medical image communication and storage de-vice that use data compression as a means to reduce storagespace and transmission time. This increase is prompted bythe immediate need to store large volumes of accumulatingdigital images and the shift towards the digital radiologyenvironment, especially the widespread use of PACS andteleradiology applications. To a certain extent, this is alsoinfluenced by the formation of industrial data interchange212

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and communication standards, such as the ACFUNEMA[2] and DICOM (Digital Imaging and Communication inMedicine) [43].Product comparison in the literature also evidently showsthe increase in the availability of medical devices thatimplement lossy compression. For example, Medical Equip-ment and Electronic News recently published a PACS prod-uct survey on fifteen companies [1181. Of these sampledproducts, twelve provide compression for data transmissionwith 8 of them lossy, and 11 use compression for datastorage with 6 lossy. A summary of premarket notificationsreviewed by the Center for Devices and Radiological Health(CDRH) of FDA in 1992 [168] indicated that most PACSdevices submitted for marketing clearance are all newproducts or significant modifications of existing products.Of the nineteen products reviewed, 15 implement someform of compression and 6 incorporate lossy compression,some even has a compression ratio as high as 80: 1.The availability of lossy compression has raised newregulatory and legal questions for the manufacturers, users,and the FDA. The regulatory policy, however, concernsless about patents and copyright matters as in commercialsoftware systems, but more on the safety and the qualityof medical devices that incorporate compression software,including: the indication for use and labeling, a suitablemeasure of compression that properly characteristics thedegree of information, and the effects of compression onimage post-processing [1681. The legal questions frequentlyasked are: Is there any possible legal standards for imagecompression? what is the guideline of product liability? Allthese pertinent questions and issues raised are interrelated.For transferring lossy compression technology into themarket place, the researchers, as well as the developers,must properly understand the technical implications andchallenges derived from these issues.A. Use of Irreversible Compression

Should the lossy coding techniques be restricted to usesother than primary diagnosis? Lossy techniques are beingused for teaching files, reviewing reports, general archivesPROCEEDINGS OF THE IEEE, VOL. 83, NO. 2, FEBRUARY 1995


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with known diagnosis, and presenting research conclusions.It is at the primary diagnosis where the radiologists areskeptical that the use of lossy compression might causelose of fine details or subtle information of original imagesand result in incorrect diagnosis or interpretation, as wellas any possible malpractice suits following the event. Sinceprimary diagnosis is the important activity that makessignificant impact on the health care service, excluding theuse of lossy coding to it hinders the move towards the dig-ital radiology environment. Thus, another regulatory issueneeded to undertake is to decide whether lossy compressioncan be used for specific primary diagnoses which do notrequire high resolution. One more issue of worthy study isto tailor the degree of lossy compression for different kindsof radiological applications.B. Measure of Image Compression

Although there exist many methods of evaluating imagequality, such as subjective ratings, paired comparisons, freeresponse ROC, sensitivity and positive predictive value,signal-to-noise ratio, classical ROC analyses are still themost credible and acceptable way to measure the imagequality by the radiologists. A great deal of work hasbeen done to determine ROC curves for different specificradiological asks using images reconstructed under variousdegrees of lossy compression [141], [lll], [121], [150],[81], [35], [42]. It, however, would be almost impossible toattempt this work as the basis of regulation. This is becausethere is a wide variety of diagnostic radiological tasks, andthe acceptable degree of compression is task-dependent.The FDA has chosen to place such a decision in the handsof the user. The agency, however, has taken steps to ensurethe user has the information needed to make the decision byrequiring that the lossy compression statement as well as theapproximate compression ratio be attached to lossy images.The manufacturers also are required to provide a discussionon the effects of lossy compression on image quality in theiroperators manual. Also, the data from laboratory tests isonly asked within a premarket notification when the medicaldevice uses new technologies and asserts new claims.The PACS guidance document from the FDA allows themanufacturers to report the normalized mean square error(NMSE) of their communication and storage devices usinglossy coding techniques [56]. This measure was chosenas it has often used by the manufacturers themselves (seeFig. 1) and there is some objective basis for comparisons.However, as discussed in Section 11-B, the NMSE does notprovide any information regarding the type of loss, e.g.,the spatial location or spatial frequency of the losses, thatcauses the image unsharpness. The developmentof a better,and general, method for characterizing compression lossesis urgently needed and should be a high priority researchtopic in medical imaging.C. Image Post-Processing

The effect of lossy compression on image post-processingsoftware has received little attention. Post-processing im-WON0 et al.: RADIOLOGIC IMAGE COMPRESSION-A REVIEW

age software includes: filtering, such as smoothing, edgeenhancement, and morphological operations; mensurationalgorithms, such as surface and volume determinations;image feature extraction, such as identification of lung nod-ules and breast cancer microcalcifications. For transmittingthe image to a refemng physician at a remote location,the post-processing of lossy images is seldom used asthe physician would not need to apply these techniques.On the other hand, for storing large image data received,such as PACS image database, and for performing certainkinds of examination, such as cine type examinations, thepost-processing is desirable. The basic position of FDAon lossy image post-processing is to have the developersdemonstrate that the software will function with the chosenlevel of compression and submit test data to support theirclaims.

D. egal Standards fo r CompressionPresently there is no legal standards that exist for ra-diologic image compression. Lacking a standard meansthat there is no objective clinical reference for the courtto judge a malpractice case that involves the use of a

medical device which incorporates lossy algorithm. Tobe acceptable, a compression algorithm requires thoroughclinical validation tests. Such test must be carried outon a large number of images and should involve a largenumber of clinicians to assure the diagnostic accuracyis not jeopardized by lossy compression. This approachcould conceivably comprise a reasonable standard be-fore the courts. Such a task would be difficult, thoughnot impossible, to carry out for measuring the imagequality of a wide variety of modalities available. Cur-rently, when a legal trial concerning missed diagnosishappens, the plaintiff and defense radiologists will argueimage quality before the jury, and the judge precedingthe case will give instructions regarding reasonablenessas related to issue of the defendant duty owed to theplaintiff as well as the quality of image. We then let thejury to decide if there was a breach of duty to providereasonable image quality [53]. The obvious question is:should courts dictate compression schemes? Our positionis that it is the clinical and engineering professionals whoshould dictate clarity in legal compression standards, notthe court.The regulation of the federal government shifts the re-sponsibility to the user. The aim is to reduce the chance ofmis-interpretation of lossy images by ensuring the imagingequipment has the desired features and by providing theuser with the information to make a decision. But, therelacks a clear specification for the user to formulate anobjective judgement of using lossy schemes. The standardis also important for teleradiology applications, where thereis lesser control of medical devices used at both ends thana single site. The derivation of a legal standard should notdepend on the courts decision, but should a task, albeitdifficult, requires the expertise of the medical imagingprofessionals.

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E. Product LiabilityA plaintiff who feels that he has been injured due tosome degradation of image quality during a radiologicaloperation may bring a suit against a vendor under product

liability theory [53]. This legal theory has been in placefor a number of years and founds its origin in California.Under this theory the vendor is liable for any physicalharm caused by a defective product which is unreasonablydangerous to the user even if the seller has used allpossible care in preparation of the product. This situationis even more complex in teleradiology, when an imageis subjected to lossy compression on one system, thentransmitted to another for reconstruction; yet the third forviewing. There is the unsettled question of who should bearthe responsibility, the company whose device applies thecompression, the manufacturer of reconstruction software,or the developer of the viewing workstation. The currentfederal policy, which requires that images which have beensubject to lossy compression be labeled with a caution, canhelp only to some extent. To this, the manufacturers anddevelopers must invest time to examine the response oftheir imaging processing algorithms with respect to lossycompression.

VII. SUMMARY AND RESEARCH DIRECTIONSDespite rapid progress in mass-storage density and com-puter network performance, the demand for transmission

bandwidth and storage space in the digital radiology envi-ronment continues to outstrip the capabilities of availabletechnologies. To overcome these two stumbling blocks, theresearch in radiologic image compression aims to achievea low bit rate in representing digital images of variousmodalities while maintaining an acceptable image qualityfor clinical use.Many studies done in the field of medical imagingindicate that it is conceivable to compress a radiologicimage to 10 : 1 or even higher without losing its diag-nostic quality. Due to the legal and medical implications,reversible compression is the current acceptable way tocompress medical images. Nevertheless, the promise ofusing high performance irreversible compression to solvedata storage and transmission problems has enticed themedical imaging researchers and developers for years.The recent formation of certain industrial standards, suchas ACWEMA [2] and DICOM [43], and the emergingmarket for PACS and teleradiology help to trigger a markedincrease in the development of medical devices that uselossy coding algorithms.In this review, we have described the key characteristicsof radiologic images and provided a general framework forradiologic image compression. Based on this framework,we examined a host of advanced reversible methods: dif-ferential pulse code modulation, hierarchical interpolation,difference pyramid, bit-plane encoding, and multiplicativeautoregression, as well as several leading, or experimen-tal, irreversible coding techniques: 2-D discrete cosinetransform, full-frame DCT, lapped orthogonal transform,

subband coding and wavelets, vector quantization, andquadtrees. Huffman, adaptive or fixed, and run-length en-coding are popular entropy encoders used in the surveyeddecorrelation techniques, whereas relatively few reportedthe use of LZW and arithmetic coding.An interesting recent development in the image compres-sion area is the fractal image compression technique [111,[121, which is basically the inverse of fractal image genera-tion and has been applied in digital images with promisingresults [83]. Fractal coder is highly asymmetry in thatsignificantly more computing time is required for searchingand encoding than for decoding. This is because the encod-ing process involves many transformations and comparisonsto search for sets of fractals, whereas the decoder simplygenerates images according to the fractal formulas received.Wilhelm et al. compared the performance of DCT, Vectorquantization, and fractal compression methods applied toseveral 1024 x 1024 CR chest images and 512 x 512CT images with reasonable preliminary results [158]. We,however, are not aware of any other effort in applyingthis coding technique for medical images. We feel that theproblem lies in the fact that body organs do not generallyexhibit good fractal-like imaging property.

The choice of a compression scheme is a complex trade-off of system and clinical requirements. For example, all ofthe coding techniques covered in this review support pro-gressive image transmission, with the exception of DPCM;but the latter is simple to implement and achieves relativelyhigh compression performance for lossless coding. Dis-crete cosine transform coding, as in other digital imagingfields, is the most common approach to lossy compressionin medical imaging today. Since the characteristics ofradiologic images vary with modalities and applications,our discussion reveals that there are also many strongcandidates in subband coding techniques, such as QMF-wavelet transforms. On the other hand, vector quantizationand quadtree-based compression algorithms will still beconfined to the research laboratories for a while due totheir implementation complexities.Although significant progress has been made in radio-logic image compression since its beginning in the lastdecade [69], many research challenges remain. First, thecoming of digital radiology environment, especially, PACSand teleradiology, will continue to test the limits of diskstorage and transmission bandwidth [72], [44], [142]. Fur-ther improvement on existing compression techniques isthus necessary.

Second, acquisitions of 3-D and 4-D medical imagesequences are becoming more usual nowadays, especially inthe case of dynamic studies performed with modalities suchas MRI, fast XCT, US , NM, or PET [30], [31], [34]. Thus,another challenge is to enable multi-dimensional medicalimage coding but still provide fast response time and af-fordable disk space. For these new applications, the parallelprocessing technology offers a solution to manipulate andprocess the significant increased data volume. Existingimage compression algorithms are optimized for sequentialcomputing, although sporadic attempts on parallel com-

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