Xiuping Jia, Senior Member, IEEE, and José M. Bioucas-Dias, Member, IEEE
Abstract—In remote sensing image processing, relaxation isdefined as a method that uses the local relationship among neigh-boring pixels to correct spectral or spatial distortions. In recentyears, relaxation methods have shown great success in classifica-tion of remotely sensed data. Relaxation, as a preprocessing step,can reduce noise and improve the class separability in the spec-tral domain. On the other hand, relaxation (as a postprocessingapproach) works on the label image or class probabilities obtainedfrom pixelwise classifiers. In this work, we develop a discontinuitypreserving relaxation strategy, which can be used for postprocess-ing of class probability estimates, as well as preprocessing of theoriginal hyperspectral image. The newly proposed method is aniterative relaxation procedure, which exploits spatial informationin such a way that it considers discontinuities existing in the datacube. Our experimental results indicate that the proposed method-ology leads to state-of-the-art classification results when combinedwith probabilistic classifiers for several widely used hyperspectraldata sets, even when very limited training samples are available.
R EMOTELY sensed hyperspectral image classification hasbeen a very active area of research in recent years
[1]. Although techniques for unsupervised classification and/orclustering have also been used in the literature [2], supervisedclassification has been more popular in many applications [3].Still, there are several important challenges when performingsupervised hyperspectral image classification [4], such as theunbalance between high dimensionality and limited training
Manuscript received February 16, 2015; revised June 08, 2015; acceptedAugust 08, 2015. Date of publication September 13, 2015; date of currentversion February 09, 2016. This work was supported by the Portuguese Scienceand Technology Foundation under Project UID/EEA/50008/2013 and ProjectPTDC/EEI-PRO/1470/2012, and in part by the Chinese National ScienceFoundation under Project 41431178.
J. Li is with the Guangdong Provincial Key Laboratory of Urbanization andGeo-Simulation, School of Geography and Planning, Sun Yat-sen University,Guangzhou 510275, China (e-mail: [email protected]).
M. Khodadadzadeh and A. Plaza are with the Hyperspectral ComputingLaboratory, Department of Technology of Computers and Communications,Escuela Politécnica, University of Extremadura, Cáceres E-10003, Spain.
X. Jia is with the Department of Electrical Engineering, School ofEngineering and Information Technology, University of New South Wales,Sydney, NSW 2904, Australia.
J. M. Bioucas-Dias is with the Instituto de Telecomunicações, InstitutoSuperior Técnico, Universidade de Lisboa, Lisboa 1649-004, Portugal.
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JSTARS.2015.2470129
samples, or the presence of mixed pixels in the data (whichmay compromise classification results for coarse spatial res-olutions). Another relevant challenge is the need to integratethe spatial and spectral information to take advantage of thecomplementarities that both sources of information can pro-vide. Such integration can reduce the negative impact of theaforementioned challenges.
According to the principle that, in remote sensing images,neighboring pixels are likely to have the same contextual prop-erties, spectral–spatial techniques can be effectively exploitedto improve the classification accurary [2]. For example, in [5],simply adding the mean of neighboring pixel values for eachband to the original spectral feature vector of central pixelhas shown better classification performance than conventionalspectral methods. In [6], authors proposed to extract texturalfeatures from the hyperspectral image using efficient imageenhancement algorithms and then combine them with spec-tral information via kernels in a semisupervised graph-basedframework for classification. In other approaches, modelingdifferent kinds of the structural information contained in hyper-spectral images by using morphological filters and integratingwith spectral information have been successfully used forhyperspectral image classification [7]–[9].
The important category of spectral–spatial techniques com-prises relaxation methods which are defined as methods that usethe local relationship among neighboring pixels to correct spec-tral or spatial distortions. As preprocessing, spatial smoothingover the hyperspectral data can remove noise and enhance spa-tial texture information [10]–[12]. For example, in [11], in orderto classify land cover mathematical morphology-based noisereduction filter has been used before the maximum-likelihood(ML) classification algorithm. In [10], authors showed thatanisotropic diffusion algorithm can reduce the spatial andspectral variability of the image, while preserving the edgesof objects, which will improve the classification accuracy ofhyperspectral imagery. On the other hand, as a postprocessingmethod, relaxation-based approaches can be an effective tool toimprove classification accuracies [2]. These normally iterativemethods are broadly referred to as continuous relaxation (CR)or probabilistic relaxation (PR) [13]–[16], which incorporatespatial-contextual information into the obtained probabilisticclassification results. In other words, after a probabilistic pix-elwise classification of the hyperspectral image, the process ofPR is applied to exploit the continuity, in probability sense, ofneighboring labels. Perhaps the most popular PR strategy is
626 IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING, VOL. 9, NO. 2, FEBRUARY 2016
Fig. 1. Flowchart of the proposed method.
Fig. 2. (a) Classes in a synthetic scene with n = 100× 100. (b) Spectral signatures of randomly selected materials from the USGS digital library used in thesimulation. (c) Fractional abundance distributions considered for generating mixed pixels using a fixed window of size 9× 9 pixels.
based on the use of Markov random fields (MRFs) [2], [17]–[20]. Specifically, the MRF has been shown to be a very suc-cessful technique for refining the classification results providedby the probabilistic SVM classifier. For instance, spectral–spatial hyperspectral image classification was performed in[21], given an initial SVM classification map and a final MRF-based relaxation process. This work suggests to incorporate a“fuzzy no-edge/edge” function into the MRF-based relaxationprocedure for preserving discontinuities. An adaptive MRFapproach was proposed, in [22], for hyperspectral image clas-sification. This work introduced a relative homogeneity indexfor each pixel to determine an appropriate weighting coefficient
for the spatial contribution in the MRF-based relaxation proce-dure. In [23], a novel and rigorous framework was proposed forcontextual hyperspectral image classification, which combinesSVMs and MRFs in a unique formulation. More recently, inte-gration of the multinomial logistic regression (MLR) and MRFalgorithms has shown significant performance in hyperspectralimage classification. For instance, in [24], combining MRF-based multilevel logistic (MLL) prior with subspace-basedMLR (MLRsub) algorithm was proposed for hyperspectralimage classification. In another effort to use MRF-based prior,in [25], the hyperspectral classification results were obtainedby maximizing the marginal probability of the posterior
LI et al.: A DISCONTINUITY PRESERVING RELAXATION SCHEME FOR SPECTRAL–SPATIAL HYPERSPECTRAL IMAGE CLASSIFICATION 627
Fig. 3. Impact of parameter λ.
distribution using the loopy belief propagation method, wherethe posterior class probability was modeled as an MLR clas-sifier and an MRF. Very recently, combining sparse MLR(SMLR) algorithm [26] with a spatially adaptive total variation(SpATV) regularization was proposed, which showed signifi-cant performance [27]. However, one of the first approaches toinclude spatial–contextual information in probabilistic classifi-cation was probabilistic label relaxation (PLR), [2], [28], [29].PLR strategies use the probabilities of neighboring pixels itera-tively to update the class probabilities for the center pixel basedon a neighborhood function [2]. It has been observed, quiteoften, the use of spatial information as relaxation, although,on one hand, it clearly improves the classification accuracyin smooth image areas, on the other hand, it degrades theclassification performance in the neighborhood of the classboundaries. Fundamentally, this is a consequence of enforcingsmoothness across the boundaries. Based on this observation,in this work, we develop a new relaxation strategy for hyper-spectral image classification which aims at introducing spatialrelaxation while accurately preserving the edges of class bound-aries. This edge preserving strategy relies on discontinuity mapsestimated from the original image cube. These maps are accu-rate because they are inferred from the many image bands,usually on the order of hundreds, with aligned discontinuities.
The proposed approach can also be used as a preprocessingstep to logically relax the original spectral vectors by consid-ering discontinuities from the data cube. This step is able toreduce noise and improve the class separability while preserv-ing discontinuities by including edge information. However, asa postprocessing, the proposed approach is based on the mainprinciples of PLR-based methods, which can be considered asa form of PR since they iteratively improve the probabilisticoutput of the considered classifier by naturally imposing spa-tial consistency in the final classified image. This is important,as some spatial postprocessing strategies tend to generate anundesired blob-like effect in the final classification results. Inthis regard, our experimental results indicate that the proposedmethodology leads to state-of-the-art classification results whencompared with other widely used PR-based methods (e.g., PLR
TABLE IOVERALL (OA) AND AVERAGE (AA) CLASSIFICATION ACCURACIES (%)
(AS A FUNCTION OF PARAMETER σ) NOISE
and MRF). The probabilistic outputs and the fact that the pre-sented method does not require prior information about thescene are other important features of the proposed approach.
This paper is organized as follows. Section II describes themain stages of the proposed classification framework, includingpreprocessing, classification, and edge-preserving probabilityrelaxation. Section III presents an experimental validation ofthe method, conducted using three well-known hyperspectraldata sets collected by the airborne visible infrared imagingspectrometer (AVIRIS) over the Indian Pines, Indiana, andSalinas Valley, California, and by the reflective optics spectro-graphic imaging system (ROSIS) over the city of Pavia, Italy.Section IV concludes the paper with some remarks and hints atplausible future research.
II. PROPOSED FRAMEWORK
In this section, we first present probabilistic pixelwise clas-sification method, which is applied in this work and then we
628 IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING, VOL. 9, NO. 2, FEBRUARY 2016
Fig. 4. AVIRIS Indian Pines data set. (a) False color composition. (b) Ground-truth. (c) Discontinuity map.
Fig. 5. AVIRIS Salinas data set. (a) False color composition. (b) Ground-truth. (c) Discontinuity map.
Fig. 6. ROSIS Pavia University data set. (a) False color composition. (b) Training data. (c) Ground-truth. (d) Discontinuity map.
describe the proposed relaxation approach which is used in bothpreprocessing and postprocessing methods. The flowchart ofproposed method has been shown in Fig. 1.
A. Probabilistic Pixelwise Classification
Let X = {x1, . . . ,xn} denote the observed data from aninput image, where xi = [xi1, xi2, . . . , xid]
T denotes a spectral
vector associated with an image pixel i ∈ S, d is the numberof spectral bands, and S = {1, 2, . . . , n} is the set of integersindexing the n pixels of an image. In probabilistic pixelwiseclassification, the goal is to make a decision for a pixel xi
regarding a label assignment yi ∈ {1, 2, . . . ,K}. The decisionis made on the basis of the posterior probabilities that the pixelbelongs to each of the K classes, i.e., p(yi = k|xi). With thesedefinitions in mind, and adopting the maximum a posteriori
LI et al.: A DISCONTINUITY PRESERVING RELAXATION SCHEME FOR SPECTRAL–SPATIAL HYPERSPECTRAL IMAGE CLASSIFICATION 629
TABLE IIOA AND AA CLASSIFICATION ACCURACIES (%) OBTAINED BY DIFFERENT METHODS FOR THE AVIRIS INDIAN PINES DATA SET
probability (MAP) classification criterion, we can write thediscriminant function as follows:
yi = k if p(yi = k|xi) ≥ p(yi = c|xi) ∀c �= k. (1)
Various probabilistic classification techniques have been suc-cessfully used for hyperspectral data [24], [30], [31]. In thiswork, we consider an MLR algorithm. MLR-based techniquesexhibit the advantage of modeling directly the posterior classdistributions. In this context, the densities p(yi|xi) can be mod-eled by the MLR, which corresponds to a discriminative modelof the discriminative–generative pair for p(xi|yi) (Gaussian)and p(yi) (multinomial). The MLR model is formally givenby [32]
p(yi = k|xi, ω) =exp
(ω(k)h(xi)
)∑K
k=1 exp(ω(k)h(xi)
) (2)
where h(x) ≡ [h1(x), . . . ,hl(x)]T is a vector of l fixed func-
tions of the input, often termed as features, ω(k) is the set oflogistic regressors for class k, and ω ≡ [ω(1)T , . . . , ω(K−1)T ]T .
Recently, [24] proposed to combine the MLR with a subspaceprojection method called MLRsub. The idea of applying sub-space projection methods to improve classification relies on thebasic assumption that the samples within each class can approx-imately lie in a lower dimensional subspace. Thus, each classmay be represented by a subspace spanned by a set of basisvectors, while the classification criterion for a new input sampleis the distance from the class subspace [24]. In [33], a modifiedversion of MLRsub is proposed, which uses the following inputfunction h(xi) in (2) and is given by
h(xi) = [‖xi‖2, ‖xTiU
(1)‖2, . . . , ‖xTiU
(K)‖2]T (3)
where U(k) = {u(k)1 , . . . ,u
(k)
r(k)}, k = 1, 2, . . . ,K, is a set ofr(k)-dimensional orthonormal basis vectors for the subspaceassociated with class k (r(k) � d).
The fact that hyperspectral vectors tend to live in unions ofsubspaces underlies the input function (3). In the following, wesimply refer to the MLRsub classifier adopted in this work asMLR for simplicity.
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TABLE IIIOA AND AVERAGE (AA) CLASSIFICATION ACCURACIES (%) OBTAINED BY DIFFERENT METHODS FOR THE AVIRIS SALINAS DATA SET
B. Discontinuity Preserving Relaxation
In this work, we introduce a new relaxation method tologically smooth the classification results or the original hyper-spectral image using both spatial and spectral information whilepreserving the discontinuities extracted from the data cube.
Let p = [p1, . . . ,pn] ∈ RK×n, pi = [pi(1), . . . , pi(K)]T
for i ∈ S be the K-dimensional multivariate vector of prob-abilities defined on site i. Let u = [u1, . . . ,un] ∈ R
n×K , fori ∈ S , ui = [ui(1), . . . , ui(K)]T be the final vectors of prob-abilities obtained from the relaxation process. In this work,we implement a relaxation scheme that is the solution of thefollowing optimization problem:
minu
(1− λ)‖u− p‖2 + λ∑i
∑j∈∂i
εj‖uj − ui‖2
s.t.: ui ≥ 0, 1Tui = 1 (4)
where the constraints are justified by the fact that the vec-tors ui represent probabilities 1 is a vector column of K 1s,λ (0 ≤ λ ≤ 1) is a weight parameter controlling the relativeimpact of the both terms in the objective function, ∂i denotesthe eight-neighborhood of pixel i (other types of neighborhood
can be applied), and εj is a value in the site j ∈ S of edge imageε given by
ε = exp
(−
d∑i=1
sobel(X(i))
)(5)
where sobel() denotes the Sobel filter, which detects the dis-continuities in an image and the output at each pixel is 0 or 1.The Sobel filter is applied on each spectral channel in a specificdirection and X(i) denotes the ith band of the original data cubeX. Note that here, to have a better interpretation of the edges,we considered the average of the results obtained by applyingsobel() in two vertical and horizontal directions.
In the proposed relaxation scheme (4), the first term in theobjective function measures the data misfit and the secondterm promotes smooth solutions weighted by the parameterεj , which, according to its definition, is large when thereare no discontinuities between the neighboring pixels it con-nects and small when there are discontinuities. The solutionof (4) corresponds, therefore, to tradeoff between adjustmentto the “noisy” classification, imposed by the first term, andsmoothness imposed by the second term. We stress, however,
LI et al.: A DISCONTINUITY PRESERVING RELAXATION SCHEME FOR SPECTRAL–SPATIAL HYPERSPECTRAL IMAGE CLASSIFICATION 631
Fig. 7. Classification maps obtained by different methods for the AVIRIS Indian Pines scene (PP refers to preprocessing and the OAs are reported in theparentheses).
that due to the presence of map ε, the smoothness is not appliedacross the discontinuities.
At this point, we would like to make reference to edge-preserving image restoration methods such as those based ontotal variation (TV) [16] or based on anisotropic diffusion (AD)[34]. In both cases (i.e., TV and AD), the objective is similar toours: to apply strong smoothing in areas away from edges andavoid smoothing the edges. However, in our case, we know theedges in advance, which is not the case of those methods. Thisis a considerable advantage, which results from the availabilityof many hyperspectral bands.
Problem (4) is strictly convex and, therefore, has a uniquesolution. Herein, we apply a projected iterative Gauss Seidelscheme, which consists in iteratively minimizing the objectivefunction in (4) with respect to each optimization variable ui(k)and, after a complete sweep, project on the probabilities at eachpixel onto the probability simplex. The obtained algorithm isshown in Algorithm 1, where iters is the number of maximum
iterations defined in advance, Err(t+1) = ‖ut+1−ut‖‖ut‖ is an error
parameter and τ is the error threshold parameter controlling thedegree of convergence.
Input: p, ε, λ, iters, Err(1) = ‖p‖, τOutput: ut := 1while Err(t+1) − Err(t) ≤ τ or t ≤ iters do
for k := 1 to K do
u(t+1)i (k) =
(1−λ)pi(k)+λ∑
j∈∂iεju
(t)j (k)
(1−λ)+λ∑
j∈∂iεj
end foru(t+1)i = u
(t+1)i /
∑Kk=1 u
(t+1)i (k)
Err(t+1) = ‖ut+1−ut‖‖ut‖
end while
At this point, we would like to call attention to the fact that,apart from the constraints used in (4) linked to the fact that weare estimating probabilities, the ratione used to carry out PRcan be used to denoise the original bands of the hyperspectralimage X ensuring the preservation of the discontinuities. Thecorrespondent algorithm, which may be used as a preprocess-ing step, is shown in Algorithm 2, where Err:k denotes theerror parameter for the kth band, x̃:k is the processed image ofthe kth band, which corresponds to the original kth band, i.e.,x:k = [x1k, . . . , xnk]. Finally, we empirically find out that bothalgorithms converge very fast, say, less than 20 iterations.
Input: X, ε, λ, iters, Err(1) = ‖X‖, τOutput: X̃for k := 1 to d do
t := 1Err
(1):k = Err(1)
while Err(t+1):k − Err
(t):k ≤ τ, or t ≤ iters do
x̃(t+1)ik =
(1−λ)xik+λ∑
j∈∂iεj x̃
(t)jk
(1−λ)+λ∑
j∈∂iεj
Err(t+1):k =
‖x̃t+1:k −x̃t
:k‖‖x̃t
:k‖end while
end for
III. EXPERIMENTAL RESULTS AND DISCUSSION
In this section, we use both simulated and real hyperspectraldata to evaluate the proposed approach. The main goal of usingsimulated data set is to evaluate the performance of the algo-rithm in a fully controlled environment, while the experimentswith real experiments are intended to provide a quantitative
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Fig. 8. Classification maps obtained by different methods for the AVIRIS Salinas scene (PP refers to preprocessing and the OAs are reported in the parentheses).
Fig. 9. Probability image of the class Soybean min-till resulted from the proposed methods.
evaluation of the method in real-analysis scenarios. For sim-plicity, in this section, we refer to spatial preprocessing as“pp,” while “MLL” and “pr” denote MLL-based [35], [36] andPR-based spatial relaxation, respectively.
A. Experiments With Simulated Data
In our first experiment, we use a simulated image with eightclasses and 100× 100 pixels, in which the spatial distribu-tion is extracted from a real image and the spectral signaturesare selected from the U.S. Geological Survey (USGS) digital
spectral library.1 The ground-truth image and the spectral sig-natures of eight randomly selected mineral signatures allocatedto the main classes are shown in Fig. 2. We considered the fol-lowing linear mixture model for generating a simulated mixedpixel:
xi =∑j∈∂i
m(j)γj + ni (6)
where m(l), l = 1, . . . , 8 are spectral signatures obtained ran-domly from the USGS spectral library, and γj , which follows a
LI et al.: A DISCONTINUITY PRESERVING RELAXATION SCHEME FOR SPECTRAL–SPATIAL HYPERSPECTRAL IMAGE CLASSIFICATION 633
Fig. 10. Bands of numbers 50, 100, and 150 of the original hyperspectal image (a–c) before and (d–f) after preprocessing.
random distribution with 0 ≤ γj ≤ 1 and∑
j∈∂iγj = 1, deter-
mines the abundance of the signatures which contribute to themixture model. Note that, here, the maximum abundance valueof γj is assigned to the objective class according to the ground-truth image. ∂i is a neighborhood with a specific size around thecentral pixel i over the considered ground-truth image. ∂i deter-mines a set of class labels to contribute in the mixture. So thatthe pixels near the borders of the regions are generated by mix-tures of different class labels and the pixels far from the bordersare considered pure.
In our simulations, we set the size of the neighborhood to9× 9 pixels. For illustrative purposes, Fig. 2(c) shows an exam-ple of the abundance maps associated with the eight classesof the simulation image. In each pixel of the scene, the frac-tional abundances vary from 0% (black color) to 100% (whitecolor) and sum to unity. Note that, using the suggested proce-dure, signature abundance is not constant over class regions andthe pixels closer to the discontinuities are more heavily mixed,as expected in real scenarios. Zero-mean Gaussian noise withcovariance σ2I, i.e., ni ∼ N (0, σ2I), is finally added to thegenerated synthetic image. For each class, we randomly chose10 samples (in total 80 samples) from the ground-truth imagein Fig. 2(a) for training purposes.
We have conducted different experiments with the simulatedhyperspectral image described earlier. These experiments havebeen carefully designed to analyze several relevant aspects ofour proposed method in a fully controlled environment. All ofthe results reported in this paper with the simulated data setswere obtained after 30 Monte Carlo runs in which we ran-domly select eight different materials and also randomly selectdifferent training sets.
B. Impact of Parameter λ
In our first experiment, we analyze the impact of the tun-able parameter λ intended to control the relative impact ofboth the terms in the proposed relaxation scheme. It shouldbe noted that, if λ = 0, only the first term is considered andthe method remains as the original MLR algorithm. If λ = 1,only the smoothing term is used. Fig. 3(a) plots the obtainedOA results as a function of λ, with σ = 0.1 and the maximumnumber of iterations as 20. From Fig. 3(a), we can concludethat the relaxation performance indeed depends on the settingof λ. However, even with 0.7 ≤ λ ≤ 0.9, the proposed relax-ation method leads to significant classification results for theconsidered problem. Fig. 3(b) shows convergence of the pro-posed PR method with different values of λ parameter. As canbe observed, the proposed approach converged very fast, i.e.,less than 20 iterations, for all cases with different value of λ.Hence, in this paper, we set the parameter λ = 0.9 and the max-imum number of iterations as 20 for the remaining simulatedexperiments.
C. Impact of Noise
In the other experiment with simulated data, we evalu-ate the impact of noise on the proposed relaxation method.Table I shows the classification results obtained by the proposedapproach using different values of noise standard deviation σ.Several conclusions can be obtained from Table I. First andforemost, it is remarkable that the proposed approach, whichcarefully uses the local relationship among neighboring pix-els, has improved the performance of MLR-based classification
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TABLE IVOA AND AA CLASSIFICATION ACCURACIES (%) OBTAINED BY DIFFERENT METHODS FOR THE ROSIS PAVIA UNIVERSITY SCENE
accuracy. Clearly, the performance of the proposed relaxationmethod decreases as σ increases. When the noise is low, usingthe proposed method as PR shows better performance than pre-processing, however, in high noise images, relaxation methodas preprocessing shows significant improvements. Note thatthe results obtained using both preprocessing and PR, i.e.,ppMLRpr, are always superior.
D. Real Experiments
Three different hyperspectral images were used for the exper-iments. These data sets have different characteristics and con-texts (two agricultural areas and an urban area, with differentspectral and spatial resolutions).
1) The first one is the well-known AVIRIS Indian Pinesscene [see Fig. 4(a)], collected over Northwestern Indianain June 1992 [3]. The scene is available online2 and con-tains 145× 145 pixels and 220 spectral bands between0.4 and 2.5 µm. The spatial resolution of the scene is20 m/pixel. A total of 20 spectral bands were removedprior to experiments due to noise and water absorptionin those channels. The ground-truth image displayed inFig. 4(b) contains 10 366 samples and 16 mutually exclu-sive classes having from 20 to 2468 samples. These dataare widely used as a benchmark for testing the accuracyof hyperspectral data classification algorithms, mainlybecause it constitutes a challenging classification problemdue to the presence of mixed pixels in available classes,and also because of the unbalanced number of availablelabeled pixels per class.
2) The second image considered in experiments is theAVIRIS Salinas image, collected over the Valley ofSalinas, Southern California, USA, in 1998. It contains217× 512 pixels and 204 spectral bands and is charac-terized by 3.7 m/pixel spatial resolution. Fig. 5(a) showsthe ground-truth map with 16 mutually exclusive classes.Due to the spectral similarity of most classes, this data setalso represents a very challenging classification problem.
3) The third image used in our experiments was collectedby the ROSIS instrument. These data were acquired overthe urban area of the University of Pavia, Pavia, Italy. Theflight was operated by the Deutschen Zentrum for LuftundRaumfahrt (DLR, the German Aerospace Agency) in theframework of the HySens project, managed and spon-sored by the European Commission. The image size inpixels is 610× 340, with very high spatial resolution of1.3 m/pixel. The number of data channels in the acquiredimage is 103 (with spectral range from 0.43 to 0.86 µm).Fig. 6(a) shows a false color composite of the image,while Fig. 6(c) shows nine ground-truth classes of inter-est, which comprise urban features, as well as soil andvegetation features. In the original data set, out of theavailable ground-truth pixels, 3921 were used for training[see Fig. 6(b)] and 42 776 samples were used for testing.
Moreover, for the three considered hyperspectral images, thediscontinuities maps were generated using (5), which have beenshown in Figs. 4(c), 5(c), and 6(d), respectively.
1) Experimental Setup: Before describing our results, it isimportant to first report the parameters and main considerationsin our experiments. For the experiments with the AVIRIS IndianPines and Salinas images, the training samples were randomly
LI et al.: A DISCONTINUITY PRESERVING RELAXATION SCHEME FOR SPECTRAL–SPATIAL HYPERSPECTRAL IMAGE CLASSIFICATION 635
Fig. 11. Classification maps obtained by different methods for the ROSIS Pavia University scene (PP refers to preprocessing and the OAs are reported in theparentheses).
selected from the available ground truth and the remainingsamples are used for validation. However, for the ROSIS PaviaUniversity image, small subsets of the original training sam-ples were used. Note that we constructed very small trainingsets by selecting only 15 labeled samples per class. Obtaininga good performance of the classifier in the presence of verylimited training samples is very important as labeled trainingdata are often difficult and expensive to be collected in prac-tice. Concerning the λ parameter of the proposed relaxationmethods, we considered λ = 0.9. For the stopping, the max-imum number of iterations in all experiments was set to 20.These settings, although suboptimal, lead to very good classifi-cation performance. Note that, in all the experiments, the resultsreported correspond to the average of the results obtained after20 Monte Carlo runs.
2) Experiments for AVIRIS Images: Tables II and III reportthe obtained classification accuracies for the AVIRIS IndianPines and Salinas images, respectively. The metrics reportedare the individual classification accuracies, as well as theOA, AA, and κ statistic. These tables provide the results foreach step of the proposed spectral–spatial relaxation method.
Moreover, the results have been compared with the recentlyproposed spectral–spatial classification method MLRsubMLL[24]. From the results reported in Tables II and III, we can con-clude that our proposed method exhibits state of the art. Forinstance, Table II reveals that the proposed relaxation method,i.e., ppMLRpr obtained an OA of 91.05% for the AVIRISIndian Pines image, which contrasts with the OA of 64.30%obtained by the MLR-based classifier. Compared to MLR-MLL, the OA achieved by the presented method improved byabout 16% the OA obtained by this method. For the AVIRISSalinas image, we obtained comparable results.
A more detailed investigation of individual class accuraciesis important to assess quantitatively the impact of the pro-posed method on class separability. As indicated in Tables IIand III, the improvement is quite significant for the sets ofsimilar class labels. For example, the classification accura-cies obtained by the MLR method with preprocessing for theclasses Corn-no till, Corn-min till, and Corn in the AVIRISIndian Pines scene were 82.49%, 86.60%, and 94.94%, respec-tively, which are 32.13%, 27.98%, and 25.24% higher thanthose obtained by the MLR algorithm. It is also remarkable
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TABLE VSTATISTICAL SIGNIFICANCE OF DIFFERENCES IN CLASSIFICATION ACCURACIES
TABLE VIOA AND AA CLASSIFICATION ACCURACIES AFTER COMPARING THE PROPOSED ALGORITHM WITH SOME IMPORTANT RELAXATION BASED
ALGORITHMS FOR INDIAN PINES (IP), SALINAS (S), AND PAVIA UNIVERSITY (PU) DATA SETS
that the accuracies for these classes increased in 3.05%, 3.30%,and 2.50%, respectively, when the proposed MLRpr methodwith preprocessing was used. The same conclusion can beobtained after comparing the individual class accuracies forthe sets of Grass/trees, Grass/pasture, Grass/pasture-mowedand Soybeans-no till, Soybeans-min till, Soybeans-clean till.For the AVIRIS Salinas image, it is also possible to considerother sets of similar classes and obtain the same conclusion.For instance, pixelwise classifier MLR obtained low accuraciesfor class Vinyard-untrained, i.e., 63.90%. However, after apply-ing the preprocessing method the accuracy for this class wasincreased by 23.42%. This improvement is significant because,e.g., the MLR+MLL method obtained 71.53% accuracy for thisclass, which is just 7.63% higher than MLR result. It is alsonoticeable that the accuracy obtained by the proposed methodppMLRpr for the class Vinyard-untrained is 90.55%, which is26.65% higher than the result obtained by the MLR algorithm.
For illustrative purposes, Figs. 7 and 8 show the obtainedclassification maps for the AVIRIS Indian Pines and Salinasdata sets. Each of the maps corresponds to one of the 30 MonteCarlo experiments, which were averaged to produce the resultsreported in Tables II and III. From Figs. 7 and 8, it can be seenthat using spatial information (both at the preprocessing andpostprocessing level) can lead to more homogeneous regions inclassification maps, when compared to the pixelwise classifi-cation maps. Most importantly, the proposed method exhibitsvery good performance in the task of delineating the borders ofclasses of interest.
Figs. 9 and 10 illustrate the performance of the proposedrelaxation method in detailed. For example, Fig. 9 shows thechanges of probabilities of class Soybean min-till for all thepixels. We can conclude that our proposed method preserve
discontinuities during relaxation process. Similarly for prepro-cessing (Fig. 10), the proposed method obviously smoothedthe original hyperspectral image while it considered edgeinformation.
E. Experiments for the ROSIS Pavia University Image
Table IV details the classification results obtained for theROSIS Pavia University scene. Several conclusions can beobtained from this table. First and foremost, it is remarkablethat the proposed relaxation approach exhibited very good per-formance using very limited number of training samples. Forinstance, our proposed method obtained an OA of 85.05%,which is 18.05% higher than the one obtained by the MLRalgorithm, whereas the MLR-MLL obtained an OA of 76.50%,which is 9.5% higher than the result obtained by the MLRalgorithm. For illustrative purposes, Fig. 11 shows the obtainedclassification maps for the Pavia University data set.
F. Evaluation of the Statistical Significance
The McNemar’s test [37] is a widely used technique in theremote sensing community for evaluating the statistical signif-icance of the difference in accuracy between two classificationmethods. In this test, a value of |Z| > 1.96 indicates that thereis a significant difference in accuracy between two classificationresults. The sign of Z is also a criterion to indicate whether thefirst classifier compared is more accurate than the second one(Z > 0) or vice versa (Z < 0). Table V reveals the differencesin classification accuracies between the proposed ppMLRprmethod and the other classification methods used in Tables II–IV are statistically significant. The significant differences in
LI et al.: A DISCONTINUITY PRESERVING RELAXATION SCHEME FOR SPECTRAL–SPATIAL HYPERSPECTRAL IMAGE CLASSIFICATION 637
accuracy between the case of using the ppMLRpr method andMLR method were the most for the Pavia University data andthe least for the Indian Pines data. Furthermore, for all the thedata sets, the differences in accuracy between the ppMLRprmethod and ppMLR method were the least significant.
G. Comparison With Other Algorithms
Using the same data sets in Tables II–IV, Table VI providesa comparison of the proposed relaxation algorithm with othersuccessful methods such as probabilistic SVM [38], [39], andLORSAL [40] with multilevel logistic spatial prior (denotedas SVM-MLL and LORSAL-MLL, respectively), LORSALwith segmentation via the constraint split augmented lagrangianshrinkage (SegSALSA) algorithm [15], and SMLR classifier[26] following with SpATV relaxation algorithm [27]. Notethat, for all the tested methods, we carefully optimized therelated parameters. From Table VI, we can conclude thatppMLRpr obtained significant results in terms of OA and AA incomparison with those obtained by the other tested algorithms.Moreover, if we compare the results obtained by MLRpr withthe results obtained by the other tested algorithms in view ofpostprocessing, we can conclude that the proposed PR methodexhibits better performance.
IV. CONCLUSION
In this work, we have developed a new methodology forspectral–spatial classification of remotely sensed hyperspectralscenes. The inclusion of both spectral and spatial informa-tion is an important aspect, as it has been shown that thejoint exploitation of the information in both domains can sig-nificantly improve the final classification results. The mainfeatures of our proposed approach can be summarized as fol-lows. First, it provides spatially homogeneous regions afterprobabilistic classification, thus exploiting the intrinsic corre-lation which exists between neighboring pixels to improve thefinal classification results. Second, it specifically models thepixels at the borders of the regions to provide a better delin-eation of the classified objects. In other words, our proposedapproach is able to provide accurate spectral–spatial classifi-cation while preserving the edges and the boundaries betweenclasses, which is quite important as the inclusion of spatialregularizers tends to blur the class boundaries and providenonsmooth delineations. Our experimental results, conductedusing a variety of (simulated and real) hyperspectral scenes andspectral–spatial classification strategies, indicate that the pro-posed approach provides state-of-the-art classification results.In particular, the proposed method provides high classificationaccuracies when very limited training samples are used, andalso provides accurate delineation of classes at the borders.
V. ACKNOWLEDGMENT
The authors would like to thank the Editors and theAnonymous Reviewers for their detailed and highly con-structive comments, which greatly helped us to improve thetechnical quality and presentation of our paper.
REFERENCES
[1] J. Bioucas-Dias, A. Plaza, G. Camps-Valls, P. Scheunders, N. Nasrabadi,and J. Chanussot, “Hyperspectral remote sensing data analysis and futurechallenges,” IEEE Geosci. Remote Sens. Mag., vol. 1, no. 2, pp. 6–36,Jun. 2013.
[2] J. A. Richards and X. Jia, Remote Sensing Digital Image Analysis: AnIntroduction. New York, NY, USA: Springer, 2006.
[3] D. A. Landgrebe, Signal Theory Methods in Multispectral RemoteSensing. Hoboken, NJ, USA: Wiley, 2003.
[4] A. Plaza et al., “Recent advances in techniques for hyperspectral imageprocessing,” Remote Sens. Environ., vol. 113, pp. 110–122, 2009.
[5] G. Camps-Valls, L. Gomez-Chova, J. Munoz-Mari, J. Vila-Frances, andJ. CalpeMaravilla, “Composite kernels for hyperspectral image classifi-cation,” IEEE Geosci. Remote Sens. Lett., vol. 3, no. 1, pp. 93–97, Jan.2006.
[6] S. Velasco-Forero and V. Manian, “Improving hyperspectral image clas-sification using spatial preprocessing,” IEEE Geosci. Remote Sens. Lett.,vol. 6, no. 2, pp. 297–301, Apr. 2009.
[7] M. D. Mura, J. A. Benediktsson, B. Waske, and L. Bruzzone, “Extendedprofiles with morphological attribute filters for the analysis of hyperspec-tral data,” Int. J. Remote Sens., vol. 31, no. 10, pp. 3747–3762, Oct.2010.
[8] P. Ghamisi, J. Benediktsson, and J. Sveinsson, “Automatic spectral–spatial classification framework based on attribute profiles and supervisedfeature extraction,” IEEE Trans. Geosci. Remote Sens., vol. 52, no. 9,pp. 5771–5782, Sep. 2014.
[9] J. Li, P. R. Marpu, A. Plaza, J. M. Bioucas-Dias, and J. A. Benediktsson,“Generalized composite kernel framework for hyperspectral image clas-sification,” IEEE Trans. Geosci. Remote Sens., vol. 51, no. 9, pp. 4816–4829, Sep. 2013.
[10] Y. Wang, R. Niu, and X. Yu, “Anisotropic diffusion for hyperspectralimagery enhancement,” IEEE Sens. J., vol. 10, no. 3, pp. 469–477, Mar.2010.
[11] I. Yildirim, O. K. Ersoy, and B. Yazgan, “Improvement of classificationaccuracy in remote sensing using morphological filter,” Adv. Space Res.,vol. 36, no. 5, pp. 1003–1006, 2005.
[12] P.-F. Hsieh and D. Landgrebe, “Classification of high dimensional data,”Ph.D. dissertation, School Elect. Comput. Eng., Purdue Univ., WestLafayette, IN, USA, 1998.
[13] J. Richards, D. Landgrebe, and P. Swain, “Pixel labeling by super-vised probabilistic relaxation,” IEEE Trans. Pattern Anal. Mach. Intell.,vol. PAMI-3, no. 2, pp. 188–191, Mar. 1981.
[14] L. Pelkowitz, “A continuous relaxation labeling algorithm for Markovrandom fields,” IEEE Trans. Syst. Man Cybern., vol. 20, no. 3, pp. 709–715, May/Jun. 1990.
[15] J. Bioucas-Dias, F. Condessa, and J. Kovacevic, “Alternating direc-tion optimization for image segmentation using hidden Markov mea-sure field models,” in Proc. IS&T/SPIE Electron. Imag., 2014,p. 90 190P.
[16] L. Sun, Z. Wu, J. Liu, and Z. Wei, “Supervised hyperspectral image clas-sification using sparse logistic regression and spatial-TV regularization,”in Proc. IEEE Int. Geosci. Remote Sens. Symp. (IGARSS), Jul. 2013,pp. 1019–1022.
[17] R. Dubes, A. Jain, S. Nadabar, and C. Chen, “MRF model-based algo-rithms for image segmentation,” in Proc. 10th Int. Conf. Pattern Recog.,1990, vol. 1, pp. 808–814.
[18] S. Z. Li, Markov Random Field Modeling in Image Analysis, 3rd ed.Berlin, Germany: Springer-Verlag, 2009.
[19] X. Jia and J. Richards, “Managing the spectral–spatial mix in contextclassification using Markov random fields,” IEEE Geosci. Remote Sens.Lett., vol. 5, no. 2, pp. 311–314, Apr. 2008.
[20] X. Huang, Q. Lu, L. Zhang, and A. Plaza, “New postprocessing meth-ods for remote sensing image classification: A systematic study,” IEEETrans. Geosci. Remote Sens., vol. 52, no. 11, pp. 7140–7159, Mar.2014.
[21] Y. Tarabalka, M. Fauvel, J. Chanussot, and J. A. Benediktsson, “SVM-and MRF-based method for accurate classification of hyperspectralimages,” IEEE Geosci. Remote Sens. Lett., vol. 7, no. 4, pp. 736–740,Oct. 2010.
[22] B. Zhang, S. Li, X. Jia, L. Gao, and M. Peng, “Adaptive Markov randomfield approach for classification of hyperspectral imagery,” IEEE Geosci.Remote Sens. Lett., vol. 8, no. 5, pp. 973–977, Sep. 2011.
[23] G. Moser and S. Serpico, “Combining support vector machines andMarkov random fields in an integrated framework for contextual imageclassification,” IEEE Trans Geosci. Remote Sens., vol. 51, no. 5,pp. 2734–2752, May 2013.
638 IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING, VOL. 9, NO. 2, FEBRUARY 2016
[24] J. Li, J. Bioucas-Dias, and A. Plaza, “Spectral-spatial hyperspectralimage segmentation using subspace multinomial logistic regression andMarkov random fields,” IEEE Trans. Geosci. Remote Sens., vol. 50, no. 3,pp. 809–823, Mar. 2012.
[25] J. Li, J. Bioucas-Dias, and A. Plaza, “Spectral-spatial classificationof hyperspectral data using loopy belief propagation and active learn-ing,” IEEE Trans. Geosci. Remote Sens., vol. 51, no. 2, pp. 844–856,Feb. 2013.
[26] B. Krishnapuram, L. Carin, M. Figueiredo, and A. Hartemink, “Sparsemultinomial logistic regression: Fast algorithms and generalizationbounds,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 27, no. 6, pp. 957–968, Jun. 2005.
[27] L. Sun, Z. Wu, J. Liu, L. Xiao, and Z. Wei, “Supervised spectral–spatial hyperspectral image classification with weighted Markov randomfields,” IEEE Trans. Geosci. Remote Sens., vol. 53, no. 3, pp. 1490–1503,Mar. 2015.
[28] B. R. Cuenca, J. A. Malpica, and M. C. Alonso, “A spatial contextualpostclassification method for preserving linear objects in multispectralimagery,” IEEE Trans. Geosci. Remote Sens., vol. 51, no. 1, pp. 395–406,Jan. 2013.
[29] A. Rosenfeld, R. Hummel, and S. Zucker, “Scene labelling by relaxationalgorithms,” IEEE Trans. Syst. Man Cybern., vol. SMC-6, no. 6, pp. 420–433, Jun. 1976.
[30] M. Fauvel, Y. Tarabalka, J. A. Benediktsson, J. Chanussot, andJ. C. Tilton, “Advances in spectral–spatial classification of hyperspectralimages,” Proc. IEEE, vol. 101, no. 3, pp. 652–675, Mar. 2013.
[31] V. Vapnik and A. Chervonenkis, “The necessary and sufficient condi-tions for consistency in the empirical risk minimization method,” PatternRecognit. Image Anal., vol. 1, no. 3, pp. 283–305, 1991.
[32] D. Bohning, “Multinomial logistic regression algorithm,” Ann. Inst. Stat.Math., vol. 44, no. 1, pp. 197–200, 1992.
[33] M. Khodadadzadeh, J. Li, A. Plaza, and J. Bioucas-Dias, “A subspacebased multinomial logistic regression for hyperspectral image classifica-tion,” IEEE Geosci. Remote Sens. Lett., vol. 11, no. 12, pp. 2105–2109,Dec. 2014.
[34] P. Perona and J. Malik, “Scale-space and edge detection using anisotropicdiffusion,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 12, no. 7,pp. 629–639, Jul. 1990.
[35] Y. Boykov, O. Veksler, and R. Zabih, “Fast approximate energy mini-mization via graph cuts,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 23,no. 11, pp. 1222–1239, Nov. 2001.
[36] S. Bagon. (2006, Dec.). MATLAB Wrapper for Graph Cut [Online].Available: http://www.wisdom.weizmann.ac.il/~bagon/matlab.html
[37] G. M. Foody, “Thematic map comparison: Evaluating the statistical sig-nificance of differences in classification accuracy,” Photogramm. Eng.Remote Sens., vol. 70, no. 5, pp. 627–633, May 2004.
[38] J. Platt, “Probabilities for support vector machines,” in Advances in LargeMargin Classifiers. Cambridge, MA, USA: MIT Press, 2000, pp. 61–74.
[39] T.-F. Wu, C.-J. Lin, and R. C. Weng, “Probability estimates for multi-class classification by pairwise coupling,” J. Mach. Learn. Res., vol. 5,pp. 975–1005, Dec. 2004.
[40] J. Bioucas-Dias and M. Figueiredo, “Logistic regression via variablesplitting and augmented lagrangian tools,” Instituto Superior Tecnico,Lisbon, Portugal, Tech. Rep., 2009.
Jun Li (M’13) received the B.S. degree in geographicinformation systems from Hunan Normal University,Changsha, China, in 2004, the M.E. degree in remotesensing from Peking University, Beijing, China, in2007, and the Ph.D. degree in electrical engineer-ing from the Instituto de Telecomunicações, InstitutoSuperior Técnico (IST), Universidade Técnica deLisboa, Lisbon, Portugal, in 2011.
From 2007 to 2011, she was a Marie CurieResearch Fellow with the Departamento deEngenharia Electrotcnica e de Computadores and the
Instituto de Telecomunicações, IST, Universidade Técnica de Lisboa, in theframework of the European Doctorate for Signal Processing (SIGNAL). Shehas also been actively involved in the Hyperspectral Imaging Network, a MarieCurie Research Training Network involving 15 partners in 12 countries andintended to foster research, training, and cooperation on hyperspectral imagingat the European level. Since 2011, she has been a Postdoctoral Researcherwith the Hyperspectral Computing Laboratory, Department of Technologyof Computers and Communications, Escuela Politécnica, University of
Extremadura, Cáceres, Spain. Currently, she is a Professor with Sun Yat-SenUniversity, Guangzhou, China. Her research interests include hyperspectralimage classification and segmentation, spectral unmixing, signal processing,and remote sensing.
Dr. Li is an Associate Editor for the IEEE JOURNAL OF SELECTED TOPICS
IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING. She has beena Reviewer of several journals, including the IEEE TRANSACTIONS ON
GEOSCIENCE AND REMOTE SENSING, the IEEE GEOSCIENCE AND REMOTE
SENSING LETTERS, Pattern Recognition, Optical Engineering, Journal ofApplied Remote Sensing, and Inverse Problems and Imaging.
Mahdi Khodadadzadeh (S’10) received theB.S. degree in electrical engineering from SadjadUniversity of Technology, Mashhad, Iran, in 2008,and the M.Sc. degree in electrical engineering andcommunications from Tarbiat Modares University,Tehran, Iran, in 2011, and the Ph.D. degree intechnology of computers and communications fromEscuela Politecnica, University of Extremadura,Caceres, Spain, in 2015.
His research interests include remote sensing, pat-tern recognition, and signal and image processing,
with particular emphasis on spectral and spatial techniques for hyperspectralimage classification.
Mr. Khodadadzadeh has been a Manuscript Reviewer for the IEEETRANSACTIONS ON GEOSCIENCES AND REMOTE SENSING, IEEE JOUR-NAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE
SENSING AND IEEE GEOSCIENCES AND REMOTE SENSING LETTERS.
Antonio Plaza (M’05–SM’07–F’15) was born inCaceres, Spain, in 1975. He is an AssociateProfessor (with accreditation for Full Professor)with the Department of Technology of Computersand Communications, University of Extremadura,Badajoz, Spain, where he is the Head of theHyperspectral Computing Laboratory (HyperComp),one of the most productive research groups work-ing on remotely sensed hyperspectral data processingworldwide. He has been the Advisor of 12 Ph.D. dis-sertations and more than 30 M.Sc. dissertations. He
was the Coordinator of the Hyperspectral Imaging Network. He has authoredmore than 500 publications, including 152 journal papers (more than 100 inIEEE journals), 22 book chapters, and over 240 peer-reviewed conferenceproceeding papers (94 in IEEE conferences). He has edited a book on High-Performance Computing in Remote Sensing (CRC Press/Taylor & Francis) andguest edited 9 special issues on hyperspectral remote sensing for different jour-nals. He has reviewed more than 500 papers for over 50 different journals. Hisresearch interests include hyperspectral data processing and parallel computingof remote sensing data.
Dr. Plaza served as an Associate Editor from 2007 to 2012 an AssociateEditor for IEEE Access, and was a member of the Editorial Board of theIEEE GEOSCIENCE AND REMOTE SENSING NEWSLETTER (2011–2012)and the IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE (2013).He was also a member of the Steering Committee of the IEEE JOURNAL
OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE
SENSING (JSTARS). He served as the Director of Education Activities for theIEEE Geoscience and Remote Sensing Society (GRSS) from 2011 to 2012,and is currently serving as a President of the Spanish Chapter of IEEE GRSS(since November 2012). He has served as a Proposal Evaluator for the EuropeanCommission, the National Science Foundation, the European Space Agency,the Belgium Science Policy, the Israel Science Foundation, and the SpanishMinistry of Science and Innovation. He is currently serving as the Editor-in-Chief of the IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
JOURNAL. He was the recipient of the recognition of the Best Reviewers of theIEEE GEOSCIENCE AND REMOTE SENSING LETTERS (in 2009), the recog-nition of Best Reviewers of the IEEE TRANSACTIONS ON GEOSCIENCE AND
REMOTE SENSING (in 2010), the 2013 Best Paper Award of the JSTARS jour-nal, and the most highly cited paper (2005–2010) in the Journal of Paralleland Distributed Computing. He was also the recipient of the best paper awardsat the IEEE International Conference on Space Technology and the IEEESymposium on Signal Processing and Information Technology and the BestPh.D. Dissertation Award at the University of Extremadura.
LI et al.: A DISCONTINUITY PRESERVING RELAXATION SCHEME FOR SPECTRAL–SPATIAL HYPERSPECTRAL IMAGE CLASSIFICATION 639
Xiuping Jia (M’93–SM’03) received the B.Eng.degree from the Beijing University of Posts andTelecommunications, Beijing, China, in 1982, andthe Ph.D. degree in electrical engineering from theUniversity of New South Wales, Sydney, NSW,Australia, in 1996.
Since 1988, she has been with the School ofInformation Technology and Electrical Engineering,University of New South Wales, Canberra Campus,Canberra, BC, Australia, where she is currently aSenior Lecturer. She is also a Guest Professor with
Harbin Engineering University, Harbin, China, and an Adjunct Researcher withChina National Engineering Rsearch Center for Informaiton Technology inAgriculture, Beijing, China. She is the coauthor of the remote sensing textbooktitled Remote Sensing Digital Image Analysis (Springer-Verlag, 1999, 3rd edand 2006, 4th ed.). Her research interests include remote sensing and imagingspectrometry.
Dr. Jia is an Editor of the ANNALS OF GIS and an Associate Editor of theIEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING.
José M. Bioucas-Dias (S’87–M’95) received theE.E., M.Sc., Ph.D., and “Agregado” degrees fromthe Instituto Superior Técnico (IST), TechnicalUniversity of Lisbon (TULisbon, now University ofLisbon), Lisbon, Portugal, in 1985, 1991, 1995, and2007, respectively, all in electrical and computerengineering.
Since 1995, he has been with the Department ofElectrical and Computer Engineering, IST, where hewas an Assistant Professor from 1995 to 2007 and anAssociate Professor since 2007. Since 1993, he has
been also a Senior Researcher with the Pattern and Image Analysis Group,Instituto de Telecomunicações. He has authored or coauthored more than 250scientific publications including more than 70 journal papers (48 of which pub-lished in IEEE journals) and 180 peer-reviewed international conference papersand book chapters. His research interests include inverse problems, signal andimage processing, pattern recognition, optimization, and remote sensing.
Dr. Bioucas-Dias was an Associate Editor for the IEEE TRANSACTIONS
ON CIRCUITS AND SYSTEMS (1997–2000) and the IEEE TRANSACTIONS
ON IMAGE PROCESSING and he is an an Associate Editor for the IEEETRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING. He was a GuestEditor of the IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
for the Special Issue on Spectral Unmixing of Remotely Sensed Data, of theIEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS
AND REMOTE SENSING for the Special Issue on Hyperspectral Image andSignal Processing, of the IEEE SIGNAL PROCESSING MAGAZINE for theSpecial Issue on Signal and Image Processing in Hyperspectral RemoteSensing, of the IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PRO-CESSING for the Advances in Hyperspectral Data Processing and Analysis,and of the IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE for theSpecial Issue on Advances in Machine Learning for Remote Sensing andGeosciences. He was the General Co-Chair of the 3rd IEEE GRSS Workshopon Hyperspectral Image and Signal Processing, Evolution in Remote sensing(WHISPERS’2011) and has been a member of program/technical committeesof several international conferences.
