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Optical Engineering 45�2�, 023604 �February 2006�

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Multipixel anomaly detection in noisymultispectral images

E. OhelBen-Gurion University of the NegevElectro-Optics UnitP.O. Box 653Beer-Sheva, 84105, IsraelE-mail: [email protected]

S. R. Rotman, MEMBER SPIE

Ben-Gurion University of the NegevDepartment of Electrical and Computer

EngineeringP.O. Box 653Beer-Sheva, 84105, Israel

D. G. BlumbergBen-Gurion University of the NegevDepartment of Geography and Environmental

DevelopmentP.O. Box 653

Abstract. Basing ourselves on a novel segmentation algorithm for mul-tispectral images, we consider how to detect multipixel anomalous ob-jects in image cubes where spectral information is available. In particular,we have developed several morphological filters to compensate for noisethat may be present in the initial cube. We show that for different types ofnoise �Gaussian and speckle�, a modification of our morphology tech-nique allows us to better detect targets without an enhanced false-alarmresult. © 2006 Society of Photo-Optical Instrumentation Engineers.�DOI: 10.1117/1.2166639�

Subject terms: anomaly detection; speckle noise; Gaussian noise; spectral data;morphological operation; AVIRIS; hyperspectral imaging.

Paper 040400RR received Jun. 22, 2004; revised manuscript received May 29,2005; accepted for publication Jun. 21, 2005; published online Feb. 7, 2006.

Beer-Sheva, 84105, Israel

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1 Introduction

Images for which spectral signatures for the pixels areavailable contain a wealth of information that can be usedfor anomalous-pixel detection. Hopefully, objects thatwould naturally blend into the background can be made tostand out with the addition of the spectral information.Such data come with a price: a major increase in the vol-ume of the data taken. Every image is now a cube with twospatial and one spectral dimension; if such cubes need to besaved in real time, any realistic system would be over-whelmed. Thus, a method to concisely save such data isneeded. One possible approach that has been used is byderiving and saving the principal components present in thedata. This reduces the dimensionality of the data and allowsthe noise to be discarded. In recent papers, we showed howprincipal components can be used to segment cubes intotheir components; the resulting segmented images werethen analyzed to find anomalous objects of particulardimensions.1–4 Good results were obtained, and successfulanomaly detection was performed. One weakness to themethod is that the presence of strong noise will severelylimit the ability to detect the suspect areas. It is the purposeof the present research to make our algorithm more robustto the presence of noise.

Standard methods of known target detection use tech-niques �spectral angle mapping, spectral correlation map-ping, and orthogonal subspace projection� that assume thatwe have a reference signature for the target �e.g., a libraryof signatures�. In anomaly detection algorithms, we usemethods that estimate the background using such models as

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Optical Engineering 023604-1

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he local normal model, the Gaussian mixture model, andhe linear mixture model.5 In this paper, we conceptuallyollow this second approach, developing our own methodor anomalous-object detection in the presence of differentypes of noise.

The basic approach is as follows: After segmenting theube, we assume that the largest segments belong to theackground; in this case, we are specifically limiting ourarget acquisition capability to anomalous areas muchmaller than the image background. Certain segments areefined as background; the average signatures of these seg-ents are defined as the background endmembers. No at-

empt is made to relate these signatures to those from pureaterials; the signatures are empirically those that came

rom the largest segments. We then return to the originalata set; we reexamine every pixel, determining its distancerom these background endmembers. Pixels far from allackground endmembers are given a high score. Then mor-hology operations are performed to detect targets of anown size.

The main point of this paper is the examination of howur algorithm compares to the standard Reed-Xiaoli �RX�lgorithm, both on original data and on data corrupted byoise. To cope with noise, we have implemented flexibleorphology filters that exhibit rugged behavior in noise.Our paper is organized as follows: we start with a dis-

ussion of two anomalous detection algorithms in Sec. 2.e then review the morphological approach that was used

n this algorithm, followed by its modification, in Sec. 3. Inec. 4 we give a short overview of noise. A description of

he data set and our simulation to test our modification isiven in Sec. 5. Discussion and conclusions are presented
n Sec. 6.
February 2006/Vol. 45�2�

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Ohel, Rotman, and Blumberg: Multipixel anomaly detection…

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2 Anomaly Detection Algorithms

2.1 Silverman-Rotman-Caefer AlgorithmThe Silverman-Rotman-Caefer �SRC� algorithm2–4 for thedetection of anomalous objects as described as follows.Figure 1 is a synthetic data cube �300 rows by 300 col-umns, 200 bands�, with Gaussian noise. The algorithmsteps are as follows:

1. Produce a two-dimensional histogram where the val-ues on the two axes are determined by the first twoprincipal-component images.

2. Find the peaks in this image, and then associate eachof the possible combinations of principal-componentvalues to one of these peaks. At this point, the origi-nal cube is segmented. Note that this algorithm hasno particular minimum size of the existing clusters.

3. Define the largest segments to be background; chooseenough segments so that roughly 90% of the area iscovered �minimum value�.

4. Each cluster that contributed is averaged separatelyover its constituent pixel members; the resulting end-members are defined to be the endmembers of thebackground.

5. Every pixel in the original data set is now reevaluatedby its minimum distance—either angular distance�using the spectral angle mapper �SAM�� or Euclid-ean distance—to any of these endmembers �theminimum-angular-distance result can be seen in Fig.2�a��. The distinguishing characteristics of the targetare often not found in the first few principal compo-nents. That is not a problem for this algorithm; theprincipal-component analysis is used only for thesegmentation process. After the definition of the seg-

Fig. 1 Synthetic data cube: 300 rows by 300 columns, 200 bands,14 synthetic areas with Gaussian noise.

mented areas, both the background endmembers and a



the reexamination of the individual pixels are doneon the original data cube.

6. An analog morphological operation is next performedto eliminate objects that are either too small or toolarge to fit the target criteria.6,7 Results can be seen inFig. 2�b�. The details of this operation are discussedin Sec. 3.

7. The results are analyzed by producing receiver oper-ating characteristic �ROC� curves relating the numberof false alarms to the number of targets detected.

How this would work on a real image is shown in Fig. 3.igure 3�a� is an RGB image taken from an airborne visible

nfrared imaging spectrometer �AVIRIS� cube �224 bands:00 to 2500 nm, 180 by 180 pixels, Moffett field, CA,SA�. We use only 197 bands, because corrupt bands were

emoved �corrupt bands are totally black or too noisy�. Inhis cube, bands 1 to 3, 108 to 113, 153 to 167, and 222 to24 are corrupt. In addition, a small set of pixels appear toe anomalous in the lower quarter of the image; we haveot done any particular operation to eliminate them.

.2 Reed-Xiaoli Algorithmhe RX algorithm has been described as similar to how auman operator would search for targets in a single bandmage, by looking for bright or dark pixels. In multidimen-ional space, the well-known Mahalanobis distance is usedo identify pixels that lie far from the mean.8,9 The basicX algorithm is given in the equation �taken directly fromef. 8�

ig. 2 Results for synthetic data cube. �a� Minimum angle betweenach pixel and the average background vectors after applying theRC algorithm. �b� Fitted areas after the morphology process.

ig. 3 AVIRIS image �RGB� of Moffett field, CA, U.S.A. �a� RGB ofhe original image. �b� Segmentation of the AVIRIS image. �c� Seg-entation of the AVIRIS image, defining 90% of the pixels as back-round. �d� Minimum angle distance between each pixel and the
verage background vectors.


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�RXD�r� = �r − ��TKL�L−1 �r − �� , �1�

where r is the pixel spectral vector, � is the mean spectralvector for the region of interest �the mean of each spectralband; we assume that the entire cube is one region of in-terest�, L is the number of spectral bands, and K is thespectral covariance matrix. Figure 4 shows the RX algo-rithm result on the data cube in Fig. 3�a�. This algorithm iscompared with our algorithm throughout the paper. A studyof the SRC algorithm compared to the RX algorithm indi-cates that, on average, the SRC algorithm takes 1.3 timesthe amount of time the RX algorithm does �the computingenvironment was: IDL 6.0, ENVI 4.0, Pentium 4�2.00 GHz, 1 Gbyte of RAM� with WinXP pro�.

A previous paper4 has discussed the efficacy of the SRCalgorithm compared to other alternatives; in our paper, weare interested in the use of the RX and SRC algorithms forthe detection of targets in noisy environments. Both the RXalgorithm and the SRC algorithm can use morphology tobest choose the target. A flexible way to implement such analgorithm is given in the next section.

3 MorphologyIn our algorithm as stated, we eliminate objects both thatare too small and that are too large, i.e., that do not satisfyour size criteria. We consider in detail how such morpho-logical operations are done.6,7 Let us go back to our syn-thetic image after we find the SAM result �Fig. 2�a��. Theelimination of the smaller objects is done through an ero-sion followed by a dilation; we refer to this filter as theminimum frame filter. The erosion replaces any particularpixel value with the minimum value of any of the neigh-boring pixels; for the example shown, the neighborhood isdefined as the 5-by-5 window centered on the pixel. Thesubsequent dilation replaces a pixel with the maximum of

Fig. 4 RX result of the AVIRIS image.

its surrounding neighbors. The effect of these two opera- M



ions is to eliminate any objects that are less than 5 by 5.his morphological operation is called opening. It isouble-edged; if the object was really of proper size butad one bad pixel �perhaps due to noise�, then we have losthe target.

Objects that are too large can be eliminated in a similarashion. Assume that we wish to eliminate objects largerhan 9 by 9 pixels. We start with the same operations herehat we used to eliminate the small objects, i.e., we concep-ually apply an erosion based on a 9-by-9 window followedy a similar dilation. The new picture will have only areashat are larger than 9 by 9. Then we subtract the originalmage from this image. This will preferentially leave ob-ects that are less than 9 by 9. In practice, in the filteringystem that we implemented, the goal was to retain onlytems that fit inside a maximum frame �M by M� and toompletely fill an inner frame �N by N�. The order of theltering is as follows: The overall system first eliminates

he areas that are larger than both an M-by-1 frame and a-by-M frame. We refer to this filter as the maximum framelter. This morphological operation is called white top hatWTH�. Then we eliminate those areas less than N by N.he resulting bright areas are those that fit into the framess desired �Fig. 2�b��.

As stated, in the presence of noise, the algorithm can beawed. The erosions and dilations assume that the data areot corrupted in any way. As Fig. 5 shows, if noise isresent, then large sections of the object �or even the entirebject� can be eliminated. We wish to consider how tovoid this problem, by making our dilations or erosionsore flexible. For example, consider the same algorithm as

escribed, but suppose, when executing the filter to elimi-ate the small targets, our erosions were performed byhoosing the second to last minimum in the window ratherhan the minimum. In this case, one low-valued pixel in theindow would not cause a reduction of the central pixelalue. This change would have two effects. On one hand, itould lower the effect of noise on the true targets. On thether hand, it might introduce noise by allowing targetsnder the minimum size to slip through. Thus, false alarmsould ensue, while the probability of detection would rise.Effectively, two types of filters are applied to our im-

ges: those designed to detect and eliminate objects greaterhan a maximum size �the maximum frame filter�, and thoseesigned to detect and eliminate those less than a minimumize �the minimum frame filter�. There are actually two fil-ers to eliminate objects larger than M by M, viz., the

ig. 5 Morphology of target with noise: �a� Target with noise: oneixel damaged by speckle noise. �b� Fitted area after morphology:ot perfect discovery. �c� Fitted area after flexible morphology: per-ect discovery.

-by-1 and 1-by-M filters, but we assume that these filters



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will operate identically. The minimum and maximum filterswill each have an associated dilation and erosion. Let usdenote our overall filtering scheme by A-B-C-D, where:

A is the minimum chosen for the erosion in the minimumframe filter.B is the maximum chosen for the dilation in the minimumframe filter.C is the minimum chosen for the erosion in the maximumframe filter.D is the maximum chosen for the dilation in the maximumframe filter.

For example, in the filter 0-0-0-0, the minimum chosenin the erosion of the N-by-N minimum frame filter is theabsolute minimum within the frame. This can be comparedwith the 1-0-0-0 filter, where the minimum chosen is thesecond to last minimum when the pixels in the window areput in value order. The 2-0-0-0 filter would be for the thirdto last minimum, etc. Similarly, the 0-1-0-0 filter uses thesecond from the top maximum when dilating the image inthe minimum frame filter.

Figure 6 shows the ROC results obtained from severaldifferent versions �1-0-0-0, 2-0-0-0, and 0-1-0-0� of the fil-ter on the minimum distance image, when using an angularcriterion on the synthetic data cube. Figure 6�a� representsthe results from the 0-0-0-0 filter where we have deliber-ately used a method of presentation of the data that empha-sizes the residual noise. It can be seen that different areasare more or less susceptible to the noise in the cube, de-pending on the exact signatures. Given that these changesshould make our algorithm more immune to noise, yet atthe same time more susceptible to false alarms, we need totest our algorithm on real data.

4 NoiseIn most images, we can find two types of noise. One type isthe standard noise, which comes from the background. Thisnoise generally can be assumed to be Gaussian; in infraredimages it will often be proportional to the overall bright-ness of the region under examination. On the other hand,the detection instrument itself can introduce noise. In theextreme case, this noise can consist of bad pixels, whichgive brightness values totally unrelated to the image or tothe neighboring pixels. We refer to this noise as speckle

Fig. 6 ROC results for several filters �morphology of Fig. 2�a��.

noise. In this paper, we examine the ruggedness of the vari- p



us algorithms as a function of the amount and type ofoise present.

It is important to define the signal-to-noise ratio for eachase. For the speckle noise, we simply use the percentagef pixels, randomly selected, that will have their signatureshanged to match the background. When we add controlledaussian noise �additive zero-mean white noise with vari-

nce �2�, the statistics of the added noise depend on thearget average �based on ground truth� and the backgroundverage �adjacent to the target� from the original cube. TheNR for this Gaussian noise was calculating by using

NR =s2

�2 =�avg�target� − avg�adjacent � background��2

�2 .

�2�

hus, at low SNR, the Gaussian noise will tend to mergehe target and the adjacent background, and the detectionill be more difficult, even if the noise is assumed to bencorrelated with the target signatures.

The noise assumed in Eq. �2� is additive, zero-mean, andhite. As in Ref. 10, we approach the problem by assuming

his simple type of noise, while remembering that moreomplicated noise models can be converted to this case. Inarticular, the noise is assumed to be uncorrelated with thearget signature and also to be a zero-mean decorrelatedi.e., the noise covariance matrix is an identity matrix� ran-om process. These two assumptions are not crucial andan be relaxed by data preprocessing.10 The assumption ofdditivity can be rendered valid by using an estimationechnique such as least squares11–13 to remove any correla-ion between target signal subspace and noise subspace.he assumption of zero-mean white noise can be renderedalid by using a prewhitening process, a widely used tech-ique in communications and signal processing.14

Simulated Experimenteveral filters, listed in Table 1, were used on each of theata sets at the morphological stage. The ROC curves wereerived in the following way: We count the total number of

Fig. 7 AISA image �RGB� of desert area in Israel.

ixels on targets �ground truth�, thus obtaining the total




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Fig. 8 Ground truth of the military vehicles for the AISA image.

Fig. 9 PCA result for the AISA image. �a� Band 1. �b� Band 2.

Fig. 10 �a� Classification of the scatterplot based on minimum Eu-clidean distance from each point to the local peaks. �b� Segmenta-
tion of the AISA image, based on the classification from �a�.
Fttwith threshold=mean+5�s.d.

Fig. 11 �a� Classification of the scatterplot based on minimum Eu-clidean distance from each point to the local peaks, with 90% of thepixels defined as background. �b� Segmentation of the AISA image,
based on the classification from �a�.


ig. 12 Results for minimum angle distance between a pixel andhe average background vectors: �a� Without threshold. �b� Afterhresholding with threshold=mean+3�s.d. �c� After thresholding



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number of target pixels �NT�. For each anomaly image at agiven threshold, we determine a point on the ROC curve byusing

Pd = Npanel/NT, �3�

Pfa = Nnonpanel/Nscene, �4�

where the numerators are the numbers of panel �target� andnonpanel pixels above threshold, and Nscene is the totalnumber of pixels in the scene that are not part of the targets.

5.1 Real Data Cube (Field Test Data)We tested the algorithm on real hyperspectral data, from theAISA sensor �airborne imaging spectrometer�, with 180bands �from 403 to 2364 nm� and dimensions of 300 by200 pixels, showing a mountainous region in Israel �Fig. 7is an RGB image�. Several military vehicles were placed inthe scene �Fig. 8 is the ground truth�. The principal-component images can be seen in Fig. 9. The resultingtwo-dimensional histogram shows that most of the pixelsfall in one central region due to the nature of the scene �Fig.10�, as can seen also in the principal-component images.The background was segmented into two big segments�Fig. 11�. The resulting anomaly distance image, using thespectral angle metric, is seen in Fig. 12�a�. Figure 12�b� and12�c� show the pixels that pass the threshold calculated as

Fig. 13 Result of applying RX to the AISA image.

Fig. 14 ROC for RX and SRC algorithm resunoise. �b� Image with artificial Gaussian noise �



he mean plus 3 and 5 standard deviations �s.d.�, respec-ively. As can be seen, there is a strong correspondenceetween the ground truth and the results.

Figure 13 shows the result of the standard RX algorithm.igure 14 is the ROC curve of these algorithms, withoutny morphology. Figure 14�a� is without artificial noise,nd Fig. 14�b� is for artificial Gaussian noise of SNR30:1. We find that the SRC algorithm compares favor-bly, with a slightly higher value of the probability of de-ection for any specific false-alarm probability. When mor-hology is performed, we still find a small advantage to ourlgorithm. In addition, we tested several of the morphologylgorithms listed in Sec. 3—in particular, the 1-0-0-0, 2-0--0, and 1-0-1-0 filters—and compared them with the 0-0--0 filter �Fig. 15�. The 0-0-0-0 filter behaves well, andhere appears to be no need to use more advanced filters.

The best morphology filter changes as noise is added tohe images. We altered the original data cube and producedix different cubes by adding noise in two different ways.n the first three cubes, we add speckle noise to 1%, 3%, or% of the pixels randomly in the cube; in the last threeubes, we add varying Gaussian noise. In the cube cor-upted with speckle noise, we assumed that the noise classs in the background. We deliberately chose the spectra ofhe speckle pixels to look like background pixels, so thathey will interfere with our target detection, i.e., if thepeckle pixel is located within the target, the standard mor-hology will reject that area as a target �see Fig. 5�a� and�b��. The 1-0-0-0 algorithm coupled with a 5-by-5 mor-hology transformation definitely helps the target detectionerformance. The 0-0-0-0 algorithm is considerably worse,s would be expected �Fig. 16�.

When the cubes corrupted with Gaussian noise are con-idered, we see that the results are even more striking. Firstf all, the SRC algorithm is better than the RX algorithmhen morphology is not employed; this trend consistently

thout morphology�: �a� Image without artificial0:1�.

Table 1 List of the filters used.

Filters

0-0-0-0 0-1-0-0 0-0-0-1

1-0-0-0 1-1-0-0 1-0-1-0

2-0-0-0 0-0-1-0 0-0-1-1

lts �wiSNR=3




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Fig. 15 ROC for RX and SRC algorithm results �morphology is performed by selected filters�: �a�
SRC. �b� RXD.
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Fig. 16 ROC for SRC algorithm result with image damaged byspeckle noise �morphology is performed by selected filters�: �a�
Speckle noise 1%, �b� 3%, �c� 5%. S


ig. 17 ROC for SRC algorithm result with image damaged byaussian noise �morphology is performed by selected filters�: �a�
NR=10:1, �b� SNR=20:1, �c� SNR=30:1.


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continues even when morphology is used. When morphol-ogy is used, the best filter is 1-0-0-0. The corruption ofindividual pixels can be corrected and a better detectionresult obtained �Fig. 17�. We note that this changes as afunction of noise. The more drastic filters �where we gofurther from the maximum and/or minimum when makingour choice� are appropriate at the higher noise level.

6 Discussion and ConclusionsIn this paper, we have reviewed a method to automaticallysegment hyperspectral cubes and detect anomalous pixels.These pixels are then passed through a morphological stagein order to find suspect objects. When looking for targets offixed shape and without any interference from noise, thesystem works very well. To avoid problems when the tar-gets are not exactly the expected shape, we can use mini-mum and maximum frame filters to control the size of thesuspected target. As shown, noise can have a major effecton the morphological process. A single bad speckle pixel orstrong fluctuation can knock out an entire section of thetarget, due to the way the erosion-dilation �opening andWTH� process works. Our suggestion is to make the mor-phological process more flexible, thus not being unduly in-fluenced by the presence of noise. We note that while mak-ing the filter more flexible we overcome most missescaused by noise without introducing too large a number offalse alarms.

AcknowledgmentsWe would like to thank Dr. Jerry Silverman and Mrs. Char-lene Caefer of AFRL/SNHI for useful conversations con-cerning this work. This work is partially funded by a MilgatEshkol student stipend to one of the authors �E.O.� from theIsraeli Ministry of Science, and by the Paul Ivanier Centerfor Robotics and Industrial Production, Beer-Sheva, Israel.We would also like to thank the two anonymous reviewers,who considerably strengthened the quality of the manu-script.

References

1. J. Silverman, C. E. Caefer, J. M. Mooney, M. M. Weeks, and P. Yip,“An automated clustering/segmentation of hyperspectral imagesbased on histogram thresholding,” Proc. SPIE 4480, 65–75 �2002�.

2. J. Silverman, S. R. Rotman, and C. E. Caefer, “Segmentation ofhyperspectral images based on histograms of principal components,”Proc. SPIE 4816, 270–277 �2002�.

3. J. Silverman and S. R. Rotman, “Segmentations of hyperspectral im-agery: techniques and applications,” Proc. SPIE 4820, 334–349�2003�.

4. J. Silverman, S. R. Rotman, and C. E. Caefer, “Segmentation ofmultidimensional infrared imagery from histograms,” Infrared Phys.Technol. 45, 191–200 �2004�.

5. D. W. J. Stein, S. G. Beaven, L. E. Hoff, E. M. Winter, A. P. Schaum,and A. D. Stocker, “Anomaly detection from hyperspectral imagery,”IEEE Signal Process. Mag. 19�1�, 58–69 �2002�.

6. J. F. Rivest and R. Fontin, “Detection of dim targets in digital infra-



red imagery by morphological image processing,” Opt. Eng. 35�7�,1886–1893 �1996�.

7. L. Vincent, and H. Lange, “Advanced gray-scale morphological fil-ters for the detection of sea mines in side-scan sonar imagery,” Proc.SPIE 4038, 362–373 �2000�.

8. C.-I. Chang, S.-S. Chiang, and I. W. Ginsberg, “Anomaly detection inhyperspectral imagery,” Proc. SPIE 4383, 43–50 �2001�.

9. I. S. Reed and X. Yu, “Adaptive multiple-band CFAR detection of anoptical pattern with unknown spectral distribution,” IEEE Trans.Acoust., Speech, Signal Process. 38�10�, 1760–1770 �1990�.

0. C.-I. Chang, “Orthogonal subspace projection �OSP� revisited: acomprehensive study and analysis,” IEEE Trans. Geosci. RemoteSens. GE–43, 502–518 �2005�.

1. C.-I. Chang, Hyperspectral Imaging: Techniques for Spectral Detec-tion and Classification, Kluwer, New York �2003�.

2. C.-I. Chang, X. Zhao, M. L. G. Althouse, and J.-J. Pan, “Least-squares subspace projection approach to mixed pixel classification inhyperspectral images,” IEEE Trans. Geosci. Remote Sens. GE–36,898–912 �1998�.

3. T. M. Tu, C.-H. Chen, and C.-I. Chang, “A posteriori least-squaresorthogonal subspace projection approach to weak signature extractionand detection,” IEEE Trans. Geosci. Remote Sens. GE–35, 127–139�1997�.

4. H. V. Poor, An Introduction to Signal Detection and Estimation,Springer-Verlag, New York �1994�.

Eran Ohel received his BSc in communica-tion system engineering and his MSc inelectro-optics engineering in 2001 and2004, respectively, from the Ben-GurionUniversity of the Negev �BGU�, Beer-Sheva, Israel. Now he is a PhD student atthe Electro-optics Unit, BGU. Since May2002 he has been with Earth and PlanetaryImage Facility, BGU. His main research in-terest is anomaly detection in hyperspectraldata and mathematical methods in imageprocessing.

Stanley R. Rotman received his BS, MS,and PhD degrees in electrical engineeringfrom the Massachusetts Institute of Technol-ogy in 1979, 1980, and 1985, respectively.His present position is as a full professor atBen-Gurion University of the Negev, Depart-ment of Electrical and Computer Engineer-ing, Beer-Sheva, Israel. His main researchareas are target detection and digital signalprocessing. He is a member of SPIE, IEEE,and OSA.

Dan G. Blumberg received his PhD fromArizona State University in 1993. Blumberghas been an investigator at the SpaceborneRadar Laboratory and a PI for the IsraelSpace Agency, and currently directs theEarth and Planetary Image Facility �EPIF� atBen-Gurion University of the Negev. Hismain research has been on the use of radarremote sensing together with optical sens-ing for studying biogeophysical phenomena.



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