Evaluation of Linear and Nonlinear TomosyntheticReconstruction Methods in Digital Mammography1
Sankararaman Suryanarayanan, MS, Andrew Karellas, PhD, Srinivasan Vedantham, MS, Stephen P. Baker, MScPHStephen J. Glick, PhD, Carl J. D’Orsi, MD, Richard L. Webber, DDS, PhD
Rationale and Objectives. The purpose of this study was to comparatively evaluate digital planar mammography andboth linear and nonlinear tomosynthetic reconstruction methods.
Materials and Methods. A “disk” (ie, target) identification study was conducted to compare planar and reconstructionmethods. Projective data using a composite phantom with circular disks were acquired in both planar and tomographicmodes by using a full-field, digital mammographic system. Two-dimensional projections were reconstructed with both lin-ear (ie, backprojection) and nonlinear (ie, maximization and minimization) tuned-aperture computed tomographic (TACT)methods to produce three-dimensional data sets. Four board-certified radiologists and one 4th-year radiology resident par-ticipated as observers. All images were compared by these observers in terms of the number of disks identified.
Results. Significant differences (P � .05, Bonferroni adjusted) were observed between all reconstruction and planarmethods. No significant difference, however, was observed between the planar methods, and only a marginally significantdifference (P � .054, Bonferroni adjusted) was observed between TACT-backprojection and TACT-minimization.
Conclusion. A combination of linear and nonlinear reconstruction schemes may have potential implications in terms ofenhancing image visualization to provide radiologists with valuable diagnostic information.
Key Words. Breast cancer, digital imaging, mammography, TACT, tomosynthesis.
Breast cancer continues to exert a dominant impact on thefield of radiology. It was estimated that 184,200 new can-cer cases would be detected in the year 2000 (1), and thatbreast cancer would account for 30% of these cases andfor 15% of cancer-related deaths among women in theUnited States. Recent advances in imaging technology
have facilitated the development of digital x-ray mammo-graphic systems and techniques (2–6). Planar digitalmammography possesses various image enhancement andmanipulation features, but it is inherently limited to repre-senting three-dimensional information in two-dimensionalspace. Therefore, it is imperative to develop three-dimen-sional image reconstruction schemes to improve imagevisualization.
Various tomosynthetic reconstruction techniques havebeen explored (7–14), but few of these studies have ad-dressed the application of such techniques to digital mam-mography. In this investigation, we performed a compara-tive study to evaluate the potential of certain linear andnonlinear tomosynthetic reconstruction methods in digitalmammography. In a previous investigation, we studiedthe contrast-detail characteristics of tuned-aperture com-puted tomography (TACT)–backprojection and certainiterative tomosynthetic methods (15–17); however, the
Acad Radiol 2001; 8:219–224
1 From the Department of Radiology (S.S., A.K., S.V., C.J.D.), Division ofNuclear Medicine (S.J.G.), and Department of Academic Computing(S.P.B.), University of Massachusetts Medical School, UMass MemorialMedical Center, Worcester; and the Division of Radiologic Sciences, WakeForest University School of Medicine, Winston-Salem, NC (R.L.W.). Re-ceived August 21, 2000; accepted and revision requested October 23; revi-sion received October 23. Supported by Public Health Service, NationalInstitutes of Health (NIH) grant RO1-CA74106 from the National Cancer In-stitute (NCI). Address correspondence to A.K., Department of Radiology,S2-836, UMass Medical School, 55 Lake Ave N, Worcester, MA 01655.
The contents of this article are solely the responsibility of the authors anddo not necessarily represent the official views of the NCI or NIH.
present investigation focused on evaluating TACT-back-projection and two nonlinear reconstruction methods,TACT-maximization and TACT-minimization, in terms ofa “disk” identification task. Planar images were acquiredand incorporated as controls.
MATERIALS AND METHODS
A prototype amorphous, silicon-based, full-field dig-ital mammographic system (Senograph 2000D; GEMedical Systems, Milwaukee, Wis) was used duringthis investigation (3). The x-ray tube was decoupledfrom the detector, thereby facilitating independenttranslation of the tube, and moved at seven discreteangles in 6° steps while the detecting array remainedstationary throughout the process of data acquisition(Fig 1). The x-ray exposure factors for tomosynthesiswere 26 kVp and 10 mAs for each of the seven views.Planar images were acquired at 26 kVp and 70 mAsand at 26 kVp and 225 mAs. This ensured that the to-tal exposures for tomosynthesis were either approxi-mately equal to or much lower than the exposure pa-rameters of the planar images. A composite phantom(Fig 2) with a nonuniform background encompassing acentrally located contrast-detail insert (MedOptics,Tucson, Ariz) also was designed (15–17) (Fig 3).
TACT-BackprojectionThe process of TACT-backprojection is similar to that
of conventional backprojection, but it does not require theprojection geometry to be fixed before reconstruction(8,12,15–18). With a fiducial marker used as an anchor,multiple two-dimensional projections are shifted propor-tionately toward a convergence point by a preselected
amount as determined on the basis of the desired relativesection thickness. Shifted projections then are summed toyield a three-dimensional image. The process of shiftingand adding is reversible and, hence, can be used to bringany arbitrary plane into focus, whereas unwanted planesare blurred (Fig 3). Tomosynthetic blurring (ie, correlatednoise or streak artifacts) is inherent in TACT-backprojec-tion reconstructed images, as it is in any backprojectiontechnique (15–18). The degree of correlation could influ-ence the visual presentation of the images, and it alsocould have a direct impact on diagnostic quality. Variousmethods such as iterative restoration (19) and filteredbackprojection (20) have been explored, but each has lim-itations in terms of uncorrelated noise buildup and com-putational intensity.
Figure 1. X-ray system geometry for digital tomosynthesis withseven source positions and stationary, full-field, flat panel imager.
Figure 2. (a) Composite phantom with disks embedded in astructured background. (b) Planar radiograph of the contrast-detail insert, without any overlying structures, illustrates the vari-ous disk diameters and depths.
SURYANARAYANAN ET AL Academic Radiology, Vol 8, No 3, March 2001
220
TACT-Maximization and TACT-MinimizationTo circumvent the problem of correlated noise and
associated blurring in reconstructed images, we propose anonlinear reconstruction process. In this technique, thelinear summation process shown in Figure 3a is replacedwith either the maximum (ie, TACT-maximization) or theminimum (ie, TACT-minimization) values of the shiftedpixel elements (Fig 3b) as dictated on the basis of thediagnostic task (21,22). In the TACT-maximization pro-
cess, only those pixels with maximum pixel values (ie,radiolucent) are retained in the reconstructed image,whereas those pixels with relatively lower brightness val-ues (ie, radiopaque) are suppressed. In the TACT-minimi-zation process, minimum pixel values are retained, andmaximum pixel values are suppressed. Both of these pro-cesses could potentially enhance specificity by eliminatingthe blur from out-of-plane structures, although a compro-mise involving sensitivity (ie, signal-to-noise ratio) is in-evitable.
Observation TaskA pilot study involving six observers was conducted to
compare planar and TACT reconstructed images. An esti-mated sample size of five observers, designed to achieve95.9% statistical power at the .05 level of statistical sig-nificance, was obtained from the pilot study by using thePC-SIZE software (23). The methods analyzed in the finalstudy are shown in Table 1. A nominal section thickness(0.453 mm) was used for all tomosynthetic methods, thusensuring that the total exposure with tomosynthesis wasless than or, at most, equal to the planar exposure param-eters.
Note.—Tube voltage � 26 kVp. Target and filter were made ofmolybdenum.
Figure 3. (a) Generalized model of TACT-backprojection shows the shifting and adding process that form tomographic sections.(b) Steps involved in nonlinear (maximum or minimum) reconstruction of tomosynthetic sections. Use of an “Or” scheme, as opposedto an “And” scheme, is evident.
Academic Radiology, Vol 8, No 3, March 2001 TOMOSYNTHETIC RECONSTRUCTION METHODS
221
A training set of 15 images was provided to the ob-servers before each actual observation session. There wasone observation session for each observer, and the ob-servers were asked to review independently all 15 images(five images� three printed copies of each) in a dark-ened room. Images were randomized before each observa-tion session, and they were displayed sequentially on ahigh-resolution, clinical-quality, gray-scale monitor(model M21PCF1RE; Clinton Electronics, Rockford, Ill).Predetermined window-width and window-level settingsthat maximized visualization of the disks were determinedby the authors (S.S., A.K., S.V.) and were used in thisexperiment. Observers began the study with previousknowledge of disk shape and location, and they weregiven the task of counting the total number of disks theycould visualize with confidence in each image. Observersalso were requested to use a constant decision criterionfor all images.
Statistical AnalysesData from each observer were averaged, and a
pooled average was obtained for each method for allobservers. A mixed-model analysis then was performedon the data sets. We obtained 10 pairs of methods forcomparison by using our model. Pairwise multiplecomparisons of the data sets were performed with attest on the estimated least-square means, with Bonfer-roni adjustments for multiple comparisons (24–27)(Table 2).
RESULTS
Planar images acquired at 26 kVp and 80 mAs and at26 kVp and 225 mAs are shown in Figure 4. Tomosyn-thetically reconstructed images are shown in Figure 5.Streak artifacts are evident in the TACT-backprojectionimages, but they appear to be suppressed in the TACT-
Table 2Pairwise Comparison of Planar and Reconstruction Methods
Pair Comparisons P
P(Bonferroniadjusted)
Planar at 80 mAs vs planar at 225 mAs .749 7.49Planar at 80 mAs vs TACT-backprojection .00149 0.0149*Planar at 80 mAs vs TACT-maximization .00099 0.0099*Planar at 80 mAs vs TACT-minimization .00163 0.0163*Planar at 225 mAs vs TACT-backprojection .00139 0.0139*Planar at 80 mAs vs TACT-maximization .00090 0.0090*Planar at 80 mAs vs TACT-minimization .00340 0.0340*TACT-backprojection vs. TACT-maximization .00863 0.0863
TACT-backprojection vs. TACT-minimization .00540 0.0540†
TACT-maximization vs. TACT-minimization .01415 0.1415
Note.—Planar mammographic images were obtained at 26 kVp,80 mAs and at 26 kVp, 225 mAs. Tomosynthetic images wereobtained at 26 kVp, 10 mAs/view, seven views.* Statistically significant at P � .05 (Bonferroni adjusted).† Marginally statistically significant.
Figure 4. Planar images of the composite phantom at (a) 26 kVp and 80 mAs and(b) 26 kVp and 225 mAs. Increasing exposure does not appear to enhance the infor-mation content of the images. A crack was present in the upper right region of thewax structure surrounding the contrast-detail insert. The black dots in the upper cen-tral region and lower right corner of the phantom are fiducial markers that serve aspoints of reference.
SURYANARAYANAN ET AL Academic Radiology, Vol 8, No 3, March 2001
222
maximization and TACT-minimization, reconstructed im-ages. Statistical differences between the methods areshown in Table 2.
The results clearly indicate that the two planar meth-ods did not differ significantly from each other, but thatboth planar methods did differ significantly (P � .05,Bonferroni adjusted) from all tomosynthetic methods. Thetomosynthetically reconstructed images exhibited betterdisk detectability compared with the planar images. Nosignificant difference was found between TACT-maximi-zation and TACT-minimization, but a marginally signifi-cant difference (P � .054) wasobtained betweenTACT-backprojection and TACT-minimization. The aver-age number of disks observed with each method is shownin Figure 6.
DISCUSSION
Blur caused by unregistered details located outside thefocal plane compromises the quality of TACT-backprojec-tion reconstructed images. This also could account for thelarger variance values in the number of disks observedwith TACT-backprojection compared with that observedwith other techniques (Fig 6). In clinical mammograms,blur artifacts could be a concern, especially when lookingfor low-contrast lesions.
Because the objects of interest were radiolucentholes, TACT-maximization eliminated those pixels withlower values, thereby alleviating the blurring artifacts
caused by out-of-plane structural components in thephantom. There is a possibility, however, for loss ofdiagnostic information, because only those pixels withmaximum values are retained. This possibility is sup-ported by the fact that the average number of disksidentified in the TACT-maximized image was lowerthan that in the TACT-backprojection image. At thesame time, TACT-maximization suppressed artifactscaused by the shifting and adding processes. This samerationale could be applied to the process of minimiza-tion, except that minimum pixel values are retained andmaximum pixel values are suppressed. In our particularcase, TACT-minimization could have produced “ring-ing artifacts” due to incomplete suppression of themaximum pixel values, because the objects of interestwere radiolucent disks. The images as such, however,are not indicative of any ringing artifacts, probably be-cause of the low-exposure conditions that were used toacquire the projection data. In a clinical situation, theTACT-minimization scheme may be more appropriateif it is used in conjunction with linear tomosynthesis,because masses and microcalcifications generally areradiopaque.
In this investigation, tomosynthetic methods outperformedplanar mammography. Further, because the projection datawere always available, we could reconstruct the images byusing a combination of tomosynthetic methods for enhancedvisualization of diagnostic information.
Figure 5. (a) TACT-backprojection reconstructed section. Streak artifacts appear to be dominant. (b) TACT-maximization recon-structed section. Note the reduction in artifact blurring with a reduction in signal-to-noise ratio. Suppression of fiducial markers is strik-ing. (c) TACT-minimization reconstructed section. Artifact blurring appears to be suppressed with a reduction in signal-to-noise ratio.Elimination of artifacts because of a crack in the phantom also is noted.
Academic Radiology, Vol 8, No 3, March 2001 TOMOSYNTHETIC RECONSTRUCTION METHODS
223
REFERENCES
1. Greenlee RT, Murray T, Bolden S, Wingo PA. Cancer statistics, 2000.CA Cancer J Clin 2000; 50:7–33.
2. Karellas A, Harris LJ, Liu H, Davis MA, D’Orsi CJ. Charge-coupled de-vice detector considerations and potential for small-field mammo-graphic imaging applications. Med Phys 1992; 19:1015–1023.
3. Vedantham S, Karellas AK, Suryanarayanan S, et al. Full breast digitalmammography with an amorphous silicon-based flat panel detector: phys-ical characteristics of a clinical prototype. Med Phys 2000; 27:558–567.
4. Williams MB, Fajardo LL. Digital mammography: performance consid-erations and current detector designs. Acad Radiol 1996; 3:429–437.
5. Kupinski MA, Giger ML. Automated seeded lesion segmentation ondigital mammograms. IEEE Trans Med Imaging 1998; 17:510–517.
6. Buchbinder SS, Leichter IS, Bamberger PN, et al. Analysis of clusteredmicrocalcifications by using a single numeric classifier extracted frommammographic digital images. Acad Radiol 1998; 5:779–784.
7. Garrison JB, Grant DG, Guier WH, Johns RJ. Three-dimensional roent-genography. AJR Am J Roentgenol 1969; 105:903–908.
8. Grant DG. Tomosynthesis: a three-dimensional radiographic imagingtechnique. IEEE Trans Biomed Eng 1972; 19:20–28.
9. Maravilla KR, Murry RC, Horner S. Digital tomosynthesis: technique forelectronic reconstructive tomography. AJR Am J Roentgenol 1983;141:497–502.
10. Kolitsi Z, Panayiotakis G, Anastassopoulos V, Scodras A, PallikarakisN. A multiple projection method for digital tomosynthesis. Med Phys1992; 19:1045–1050.
11. Kolitsi Z, Panayiotakis G, Pallikarakis N. A method of selective re-moval of out-of-plane structures in digital tomosynthesis. Med Phys1993; 20:47–50.
12. Niklason LT, Christian BT, Niklason LE, et al. Digital tomosynthesis inbreast imaging. Radiology 1997; 205:399–405.
13. Kampp TD. The backprojection method applied to classical tomogra-phy. Med Phys 1986; 13:329–333.
15. Suryanarayanan S, Karellas A, Vedantham S, Glick SJ, D’Orsi C, Web-ber RL. Tomosynthesis reconstruction methods for digital mammogra-phy (abstr). In: Proceedings of the Biomedical Imaging Symposium:visualizing the future of biology and medicine. Bethesda, Md: NationalInstitutes of Health, 1999; 46.
16. Suryanarayanan S, Karellas A, Vedantham S, Glick SJ, D’Orsi C, Web-ber RL. Comparison of contrast-detail characteristics of tomosyntheticreconstruction techniques for digital mammography (abstr). Radiology1999; 213(P):368–369.
17. Suryanarayanan S, Karellas A, Vedantham S, Glick SJ, D’Orsi CJ,Baker SP. A comparison of tomosynthesis methods for digital mam-mography. Acad Radiol 2000; 7:1085–1097.
18. Webber RL, Horton RA, Tyndall DA, Ludlow JB. Tuned-aperture com-puted tomography (TACTTM): theory and application for three-dimen-sional dento-alveolar imaging. Dentomaxillofac Radiol 1997; 26:53–62.
19. Ruttiman UE, Roelf AJ, Webber RL. Restoration of digital multiplanetomosynthesis by a constrained iteration scheme. IEEE Trans Med Im-aging 1984; MI-3:141–148.
21. Webber RL, Underhill HR, Hemler PF, Lavrey J. A nonlinear algorithmfor task-specific tomosynthetic image reconstruction. Proc SPIE MedImaging Phys Med Imaging 1999; 3659:258–265.
22. Suryanarayanan S, Karellas A, Vedantham S, Glick SJ, D’Orsi C, WebberRL. An evaluation of linear and non-linear tomosynthesis reconstructiontechniques for digital mammography (abstr). Med Phys 2000; 27:1399.
23. Dallal GE. PC-SIZE: a program for sample size determinations. AmStat 1986; 40:52.
24. Siegel S. Nonparametric statistical methods for the behavioral sci-ences. New York, NY: McGraw-Hill, 1956.
25. Armitage P, Berry G. Statistical methods in medical research. 2nd ed.Oxford, England: Blackwell Scientific, 1987.
26. Kirk R. Experimental design procedures for the behavioral sciences.2nd ed. Belmont, Calif: Brooks/Coles, 1982.
27. SPSS for Windows, release 8.0. Chicago, Ill: SPSS, 1998.
Figure 6. Column plots show the mean number of disks seen by all five observers.On average, more disks are observed with TACT-backprojection compared with othermethods; however, the standard deviation (vertical bars) with TACT-backprojection isthe largest, indicating the possible influence of streak artifacts.
SURYANARAYANAN ET AL Academic Radiology, Vol 8, No 3, March 2001
