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Signal Processing

Signal Processing 124 (2016) 115–131

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journal homepage: www.elsevier.com/locate/sigpro

A spectral-spatial based local summation anomaly detectionmethod for hyperspectral images$

Bo Du a, Rui Zhao b,n, Liangpei Zhang b, Lefei Zhang a

a School of Computer, Wuhan University, PR Chinab The State Key Laboratory of Information Engineering in Surveying, Mapping, and Remote Sensing, Wuhan University, PR China

a r t i c l e i n f o

Article history:Received 23 June 2015Received in revised form5 September 2015Accepted 29 September 2015Available online 17 October 2015

Keywords:Hyperspectral imageryAnomaly detectionSpectral-spatial integrationLocal summation strategy

x.doi.org/10.1016/j.sigpro.2015.09.03784/& 2015 Elsevier B.V. All rights reserved.

work was supported in part by the Natof China (973 Program) under Grants

719905, the National Natural Science Found1471274 and 41431175, the Natural Sciencee, China under Grants 2014CFB193 and the Fuor the Central Universities under 211-274175esponding author.

a b s t r a c t

Anomaly detection is one of the most popular applications in hyperspectral remote sen-sing image analysis. Anomaly detection technique does not require any prior features orinformation of targets of interest and has draw the increasing interest in target detectiondomain for hyperspectral imagery (HSI) in the recent twenty years. From hyperspectraldata, the approximately continuous spectral features which are attributed to the highspectral resolution of hyperspectral image can be achieved. Unfortunately, most conven-tional anomaly detectors merely take advantage of the spectral information in hyper-spectral data and rarely give the consideration to spatial information within neighboringpixels. With the development of remote sensing technology, the high spatial resolutioncan also be acquired by the hyperspectral airborne/spaceborne sensors. Then, furtherimprovement in algorithmic performance may be achieved if both the spectral and spatialinformation is combined. This article proposes a novel local summation anomaly detec-tion method (LSAD) which combines the multiple local distributions from neighboringlocal windows surrounding the pixel under test (PUT) with spectral-spatial feature inte-gration. Some other detection performance enhanced operations such as feature extrac-tion and edge expansion are also used. The proposed local summation anomaly detectionmethod makes allowance for exploiting more sufficient local spatial neighboring rela-tionship of local background distribution around the test pixel considered in detectionprocessing. Moreover, summated local background statistics can get better performance insuppressing background materials and extruding anomalies. Feature extraction enablesLSAD with robust background feature statistics and edge expansion can ensure no loss ofedge detection information. Experiments are implemented on a simulated PHI data andtwo real hyperspectral images. The experimental results demonstrate that the proposedanomaly detection strategy outperforms the other traditional anomaly detection methods.

& 2015 Elsevier B.V. All rights reserved.

ional Basic Research2011CB707105 and

ation of China underFoundation of Hubeindamental Research.

1. Introduction

Recent years have witnessed the quick development ofimage processing theory [1–8]. One newly developedimaging technique, IMAGING SPECTROSCOPY, which isalso known as hyperspectral imaging, draws great inter-ests of researchers in image processing field [9–11]. It is atype of remote sensing imaging technology concernedwith the extraction of information about objects lying onthe Earth ground surface, based on radiant signal acquired

B. Du et al. / Signal Processing 124 (2016) 115–131116

by spaceborne or airborne sensors [9,10]. Hyperspectralimaging sensors are passive sensors that simultaneouslyattain images with hundreds of continuous and narrowregions of the electromagnetic spectrums [11]. Approxi-mately continuous spectral characteristics of ground sur-face materials can be achieved from hyperspectral imagebecause of its high spectral resolution which is usually lessthan 10 nm [12–15]. This is the most different trait ofhyperspectral images, compared with the traditionalpanchromatic and multispectral remote sensing images[16]. Then a hyperspectral image “cube” can be establishedby combining two spatial dimensions (width and height)and a spectral dimension together [17]. By means ofapproximately continuous spectral curves of ground sur-face materials, adequate spectral information can be pro-vided for hyperspectral applications such as classification,target detection etc. [18]. For current hyperspectral prac-tical application domains, spectral information is animportant essential factor which is still mainly underconsideration. Thus, significant attention in the field ofhyperspectral remote sensing research is devoted todevelop algorithmic techniques to detect, classify, identify,quantify, and characterize objects and features of interestin the captured data [19].

Two types of target detection techniques are usuallyinterested in target detection domain: known andunknown with target spectra. If target spectra are knownin the processing of target detectors, it is also namedspectral matching detection algorithms refer detectorsthat require the spectral information about the targets ofinterest, and they try to identify pixels whose spectrumexhibits a high degree of correlation to the expected sig-nature [20]. However, in most cases it is difficult to obtainthe spectrum of ground surface objects in hyperspectralimages. The absorption and scattering of the atmosphere,the subtle effects of illumination and the spectral responseof the sensor must all be considered in measuring thespectral properties of a material through the atmosphere[21]. Moreover, spectral variability also needs to beaddressed in this kind of target detection [22].

The multiplicity of possible spectra associated with theobjects of interest and the complications of atmosphericcompensation have led to the development and applica-tion of target detection without target spectra which iscalled anomaly detection. Anomaly detection algorithmsare more practical in actual applications. Anomaly detec-tion technique which does not require any prior featuresor information of targets of interest has been of greatinterest in hyperspectral imagery processing in recenttwenty years [23–26]. Hyperspectral anomaly detectiontechnique has been successfully applied in many applica-tion domains such as mineral reconnaissance, bordermonitoring, search-and-rescue etc. in recent years [27].Thegoal of anomaly detection is to detect a small quantity ofpixels in the hyperspectral image whose spectral char-acteristics differ significantly from those of a large pro-portion of pixels in the hyperspectral data cube, and thenthe hyperspectral image is segmented into two parts:anomaly targets and backgrounds [28]. Anomaly targetsare usually inclined to be small man-made objects ofminor quantity of pixels whose spectra are distinctly

different with other major pixels in the images. Forexample, for those entrusted with search-and-rescuemissions anomalies may be downed-aircraft or adven-tures lost in the wilderness. With national defense,anomalies may be tanks, aircraft, surface-to-air missilelaunchers, command bunkers, and other objects of militarysignificance scattered across a battlefield. And for civilianapplications, anomalies may be vehicles located in anurban or natural field.

Anomaly detection methods mainly extract the knowledgefrom backgrounds and use the differences between anomalytargets and the backgrounds to detect the anomalies [29].According to the different ways of making use of informationin hyperspectral images, anomaly detection methods aremainly classified into two kinds: spectral information basedand spectral-spatial based. Some conventional anomalydetectors think hyperspectral image as a whole sample data-set and extract the background statistical features from it.These detectors can be called global anomaly detectors [30].Global anomaly detection algorithms only utilize the spectralinformation in hyperspectral images. However, the globalanomaly detector will not find an isolated local target whosesignature is similar to that of global background material [31].For example, consider a scene containing the isolated trees ona grass plain. Each separate tree may be seen as a localspectral anomaly even if the image contains a separate regionwith many pixels of trees. The global spectral anomalydetection algorithms are susceptible to this type of clutter andwould generate false alarms. Moreover, although the spectralfeature vector contains a lot of information about the spectralproperties of the pixels, the spectral-vector-based HSI analysisjust process each pixel independently, without consideringthe spatial relationship of neighboring pixels [32].

Most traditionally common used detectors or classifiersare mainly using the spectral information in the “hypercube”.They only deal with a set of first-order data as input, i.e., thevector representation, which is commonly used to representthe spectral feature of a certain pixel in HIS [33–35]. With thedevelopment of airborne/spaceborne remote sensing tech-nology, spatial resolution of hyperspectral image increasedgradually. Airborne/spaceborne hyperspectral sensors such asAirborne Visible/Infrared Imaging Spectrometer (AVIRIS) [36]and Hyperspectral Digital Imagery Collection Experiment(HYDICE) [37] can reach a spatial resolution of 1–10m. Thislevel of spatial resolution can make ground surface materialsin hyperspectral images contain a wealth of spatial infor-mation. And then if the spatial information is joined intohyperspectral applications, better performance can bepotentially achieved. Some research on spectral-spatial inte-gration has been implemented in hyperspectral image pro-cessing algorithms. Endmember extraction methods such asAbundance-Constrained Endmember Extraction (ACEE) [38]and Automatic Morphological Endmember Extraction(AMEE) [39] algorithms join spectral and spatial informationand obtain improved performance than conventional meth-ods. Some researchers also use spectral information as wellas spatial information to achieve further improvement inclassification [40,41]. Anomaly detection algorithms mainlyutilize two ways to integrate spectral and spatial informa-tion: model based methods and window filtering. Anomalydetectors such as Gaussian Markov Random Field (GMRFAD)

B. Du et al. / Signal Processing 124 (2016) 115–131 117

based [42–44] and wavelet domain GARCH random fieldbased [45] anomaly detection methods take on differentspatial models to extract spatial features in hyperspectralimage and detect anomalies that do not submit to thesemodels. Nevertheless, most current spectral-spatial infor-mation based target detectors are more inclined to be thewindow filtering methods which extract adjacent localbackground spatial feature. For example, dual window hasbeen employed by Kernel-RX [46] anomaly detector. Sto-chastic Spatial Filtering has been implemented in targetdetection (SSFTD) [47]. Other examples include WhiteningSpatial Correlation Filtering has been utilized inWSCFAD [48]and Nested Spatial Window-based Anomaly Detector(NSWAD) [49]. Multiple-Window Anomaly Detector(MWAD) [50] also get significant performance by employingdifferent windows statistic methods. Hence, spectral-spatialintegration is a tendency in anomaly detection domain. Themeaning of setting a chosen-size window in this kind ofdetection methods is to establish a profitable local back-ground statistics estimation which utilizes adequate back-ground information and meanwhile try to reduce the influ-ence of the anomaly information. Then, the window sizeshould not be too large or too small to obtain considerablebackground estimation. Most window filtering-basedanomaly detection algorithms usually set only one slidingwindow to acquire neighborhood background statistic for thepixel under test (PUT). This kind of window detection strat-egy may contain anomalies in the test pixel centered windowso that local background statistic will possibly be con-taminated by some anomaly targets seriously. If the localdistributions of some windows are most occupied byanomaly pixels then it is difficult to detect this kind of multi-pixel anomaly target because the background statistic will becontaminated seriously by anomaly pixels. Moreover, it is notconvincing to set only one window to represent the localbackground information for the tested pixel concentrated inthe center of window because the quantity of pixels inwindow filter is often so small that they can’t represent the

Fig. 1. Window filter of size 3�3 in spectral-spatial integrated local-RX d(b) simulated 3�3 window. (For interpretation of the references to color in thi

local background distribution. Supposing that the multiplewindows containing pixels under test are chosen to repre-sent the local background distribution, it will be moreeffective to detect multi-pixel anomaly target. This paperproposes a novel anomaly detection method based on themultiple adjacent windows which also consider about thelocal summation strategy to integrate both the spectral andspatial information.

The rest of the paper is organized as follows: In Section 2,problems in conventional spectral-spatial integrated meth-ods will be presented. Section 3 provides implementation oflocal summation anomaly detector. Section 4 demonstratesthe experiments of the proposed algorithm compared withsome traditional anomaly detection algorithms. Finally, Sec-tion 5 draws our conclusions.

2. Spectral-spatial integration

Some anomaly detection algorithms not only usespectral information but also spatial information toachieve further improvement in detection performance. Inthe following, Section 2.1 takes local-RX anomaly detec-tion algorithm as an example to demonstrate how spectraland spatial information can be integrated in anomalydetection domain and Section 2.2 demonstrates someproblems in window-based spectral-spatial integratedanomaly detection algorithms.

2.1. Spectral-spatial integrated local-RX anomaly detector

In order to dig spatial information in hyperspectralimage, some anomaly detectors exploit a window filter tointegrate the spectral and spatial information in a smaller“window-data cubes”. In anomaly detection domain, RXalgorithm proposed by Reed and Yu is acknowledged to bea benchmark anomaly detection algorithm and has beenwidely applied in multispectral and hyperspectral images

etector. (a) Hyperspectral image with sliding local window filter ands figure, the reader is referred to the web version of this article.)

B. Du et al. / Signal Processing 124 (2016) 115–131118

[51]. The classic RX algorithm can be considered as a globalanomaly detector because the covariance matrix is com-puted by all the pixels of the image and the background isdefined with reference to the full image. Due to integratespectral and spatial information, a single window-basedlocal-RX algorithm has been proposed. The local-RX algo-rithm [52] can be considered as a local anomaly detectorbecause it just considers a small set of neighboring pixelsaround the pixel under test. This implementation uses theconcept of a sliding local window filter for every pixel inthe image [53]. For each pixel r, the local-RX detector isusing a square window of size k� k pixels, centered atpixel r. Then, a covariance matrix Σ is calculated for everypixel r based on its own local window. It is important toemphasize that, in the local implementation the covar-iance matrix is computed using the local window insteadof the full image. In other word, for each pixel under testthe algorithm it applies the RX filter using the local spatialinformation. As a result, local-RX can be considered as aprocess over each pixel of the image, using local spatialinformation provided by the data of the sliding windowfilter and applying the RX detector in the local area. Thisvariance considers a local spectral-spatial integratedapproach estimation to determine whether the imagepixels are anomalous or not. An example of 3�3 windowsize spectral-spatial integrated local-RX detector is shownin the following.

For local-RX anomaly detector, a window of the selectedsize should be chosen firstly. Then the fixed window filterwill slide line by line in the detection implementation oflocal-RX in a hyperspectral image as shown in Fig. 1(a) andthe red window represents a 3�3 window filter that slideson the hyperspectral image. As the window is sliding, thecentral pixel of the window is defined as the pixel underdetection. Fig. 1(b) illustrates a sliding window filter of size3�3 and every “X” represents a pixel vector in the window.The central red pixel is the pixel under detection and allblue pixels represent adjacent background distribution of

Fig. 2. Disadvantage of single window filter utilized by local-RX algorithm. (a) Agiven window for PUT and (c) ideal local distribution for PUT. (For interpretationversion of this article.)

the test pixel. For every window, detection result will beacquired with the background statistic.

Suppose that L is the number of spectral bands of ahyperspectral image and r is an L� 1 column central pixelvector in a sliding window. Then the local-RX detectorimplements a filter specified by

δLRX ðrÞ ¼ ðr�uÞTΣL�Lðr�uÞ ð1Þ

where μ is the local sample mean of adjacent backgroundpixels of the pixel under detection and ΣL�L is the back-ground sample covariance matrix of the local window. Theform of δLRXðrÞ in Eq. (1) is actually the well-knownMahalanobis distance.

Local-RX anomaly detector employs a sliding windowfilter to integrate spectral and spatial information. Thesmaller “window-data cube” generated by every windowfilter of local-RX detector contains the spectral and spatialfeatures of local background surround the pixel underdetection simultaneously. Though there is a manuallydetermined parameter of sliding window size which inter-feres the automation of detection processing, the perfor-mance of local anomalies detection will be enhanced bytaking advantage of local spatial information in local-RXdetector. By means of choosing an appropriate windowsize, an optimal detection results of spectral-spatial inte-grated local-RX detector will be achieved. Enhanced perfor-mance by spectral-spatial integration in anomaly detectionwill be demonstrated in subsequent experiments.

2.2. Problems in window-based spectral-spatial integratedanomaly detection methods

Even if anomaly detectors with window filter basedspectral-spatial integration bring benefit for detectionperformance, some problems exist in this kind of anomalydetection methods. These problems will be stated in thefollowing.

hyperspectral image with 3�3 local window filter, (b) local distribution ofof the references to color in this figure, the reader is referred to the web

B. Du et al. / Signal Processing 124 (2016) 115–131 119

2.2.1. Penurious and unitary representation of local windowdistribution

The above-mentioned local-RX algorithm only utilizesone single window filter of a specified size for every pixelunder test. Then the local background distribution of everylocal window for pixel under test (PUT) is so penuriousand unitary that will not achieve the most ideally repre-sentative local distribution for PUT. Then detector may benot capable of obtaining the best detection performance.

Though anomaly targets usually take a minor section ofpixels in hyperspectral image, the form and shape ofanomaly targets is not determinate in a unified pattern.For some anomaly pixels of the small object such asvehicles and rare mineral stones that occupy only one orless than one pixel. This kind of anomaly targets are calledsingle-pixel target. At the same time, some anomaly tar-gets which are more than one pixel gathered together, canbe called multi-pixels targets. In the case of multi-pixelstarget detection, local-RX algorithm which only utilize asingle window may get an unsatisfactory local distributionin the local window filter.

Here, an example is provided in Fig. 2 to demonstratethe disadvantage of penurious and unitary local distributionfor single window-based local RX detector. As the exampleshown in Fig. 2(a), a local-RX detector utilizes a 3�3 slidingwindow filter (red square box in Fig. 2(a)) to detect theprobable anomaly targets in a hyperspectral image.Anomalies in this hyperspectral image are some aircraftswhich are multi-pixel targets that park on an airportpavement which is considered as the background materials.When the window filter slides on the specific locationshown in Fig. 2(a), we simulate the background distributionof the local window in Fig. 2(b). Fig. 2(c) shows a simulatedbackground distribution of a local window which is thesame window in Fig. 2(b) moving a pace of one pixel to theright-bottom direction. Both in Fig. 2(b) and (c), black pixelsrepresent a part of an aircraft target in the window. Yellowpixels stand for the background materials of airport pave-ment and the black pixels with red shadow represents thepixels under test. It can be found that the local window inFig. 2(b) contains the equivalent number of anomaly pixelsand background pixels. Then the detection result of the

Fig. 3. Simulated example of edge detection result's deficiency. (a) Simulated exfilter and (c) region of no detection result. (For interpretation of the referencesarticle.)

current pixel can’t be highlighted because of the unsa-tisfactory distribution for anomaly detection in the localwindow. On the contrary, if we utilize the local spatialneighboring information of the window in Fig. 2(c), we canget a better detection performance due to the sufficientbackground pixels contained in this window. Hence, thepenurious and unitary distribution represented by a localwindow that is centered on PUT may not be the optimalchoice for spectral-spatial integrated local window-basedanomaly detector when the anomaly targets contain mul-tiple pixels.

Moreover, if there are more anomaly pixels than back-ground pixels in a local window that is centered on abackground pixel, the background pixels under test islikely to be detected as an anomaly target pixel and falsealarms will generate. As a result, penurious and unitarydistribution represented by local pixels under test cen-tered window which is utilized in local-RX and otherspectral-spatial integrated anomaly detectors may poten-tially generate false alarm and detection ratio decrease.

2.2.2. Absence of edge detection informationBecause of sliding window filter, pixels on the edge of

the hyperspectral image will not be in the detection pro-cessing because theses pixels won’t be central pixel of anywindow filter. If so, detection ratio may descend ifanomalies appear on the edge of image. A simulatedexample will show how this kind of detection ratio declineis produced.

In the simulated example shown in Fig. 3, the 7�7 gridgraphic in Fig. 3(a) represents a hyperspectral image of7 lines multiplied by 7 rows. Cyan and yellow square lat-tices stand for some background materials and red onesdenote anomaly targets. For a local-RX detector functionedon the image, we choose a 3�3 window filter indicated bythe blue pane in Fig. 3(a). Fig. 3(b) shows the detectionresult of the simulated example detected by the local-RXdetector. It can be found that pixels in the outermost layerof the image are not incorporated in the detection range.Then no detection result will be received for these pixelsamples which are demonstrated with red shadow regionin Fig. 3(c). The anomaly in the top layer is not detected

ample of a 7�7 grid graphic, (b) detection result map with 3�3 windowto color in this figure, the reader is referred to the web version of this

B. Du et al. / Signal Processing 124 (2016) 115–131120

and this generates a detection rate decline. Detectedresults absent with one outermost layer for 3�3 window.Similarly to that, the detection results of w outermostlayers will absent for 2 �wþ1ð Þ � 2 �wþ1ð Þ window.More detection results will absent with a larger size win-dow and then more potential detection rate decline maybe generated if some anomaly targets are seated on theedge of image. Hence, potentially depressed detection ratewill appear in the spectral-spatial integrated localwindow-based anomaly detector.

2.2.3. Imprecise local covariance matrix estimateEssentially both the global and local RX algorithms are

Mahalanobis distance based detection schemes. Then theyneed to obtain mean vector and covariance matrix fordetection filters. However, usually the true values of themean and covariance matrix are not known and must beestimated from background samples. The mean is typicallyestimated by the sample mean m¼ 1

N

PN

i ¼ 1xi, where xi is

sample from background samples X ¼ x1; :::; xNð Þ and N isthe number of background samples. The covariance matrixis typically estimated by the maximum likelihood covar-iance matrix estimate

Σ ¼ 1N

XN

i ¼ 1

xi�mð Þ xi�mð ÞT ð2Þ

For the high dimensional data, the sample covariancematrix estimate is singular, if fewer than pþ1 backgroundsamples are available. It is a poor estimate of the truecovariance matrix unless many more than pþ1 samplesare available [54]. For the local spectral-spatial integratedRX anomaly detector, there are often a large number offeatures available in hyperspectral data, but the number ofbackground samples is limited due to that the size k� kpixels of sliding local window filter is usually less than thebands number L of hyperspectral image. So the detectionscheme is not optimal when the number of the back-ground samples in the local window filter is small [55].The local-RX detector's performance can be degradedwhen the number of dimensions is large compared to thebackground sample set size due to the instability of cov-ariance matrix estimate. In particular, the sample covar-iance estimate becomes highly variable and may even be

Fig. 4. Hyperpectral manifold in simplified 3-bands space for anomaly detectmeasured feature of anomalies. (For interpretation of the references to color in

singular [56]. Since inaccurate estimates of the covariancematrix lead to the poorer detection performance, too fewbackground samples in local window filter can be animportant impediment in using spectral-spatial integratedlocal window filter detection strategy.

On the other hand, the statistics of the background inlocal-RX detector is actually computed from the pixelssurrounding the observed pixel and then the definition ofthe number of surrounding background pixels can be cri-tical. The number of background samples can increasewith a larger local window size. If in this way, the numberof surrounding pixels can be large enough to contain morepixels than the number of bands so as to implement morestable local covariance estimate, negative influencebrought by the above-mentioned Problem (b) will poten-tially decreased.

Above-mentioned Problem (a)–(c) all potentially dropthe performance of spectral-spatial integrated windowbased anomaly detector. LSAD proposed in this article willtake some measures to overcome these problems.

3. Local summation anomaly detector

The objective of hyperspectral anomaly detection is toidentify the anomalous ground surface objects with sig-nificantly different spectra relative to the major spectralfeatures in hyperspectral dataset. Then anomaly targetpixels are usually seen as outliers in the manifold ofhyperspectral data. Fig. 4 illustrates data distribution foranomaly detection in the hyperspectral manifold with asimplified 3-bands feature space. Blue and red dotsrepresent the major background samples and anomalytargets in hyperspectral dataset respectively. It can befound from Fig. 4(a) that anomalies usually deviate faraway from the major background samples which cluster inthe center distribution of dataset and anomaly targetsgenerally present a significantly large Euclidean distancemeasured feature relative to background samples. Fig. 4(b) takes two anomalous examples of Fig. 4(a) and theyellow arrows demonstrate the largest Euclidean Distanceof each anomaly targets to background samples. Thesesanomalies' Euclidean distances to the specific sample are

ion. (a) Significantly deviation of anomalies and (b) Euclidean distancethis figure, the reader is referred to the web version of this article.)

B. Du et al. / Signal Processing 124 (2016) 115–131 121

much larger than that of the other background samples.Then this characteristic can be seen as a special feature ofanomaly targets.

However, only first-order statistical feature is consideredin Euclidean distance. Sufficient and varying information ofspectral and spatial features should be contained in hyper-spectral image due to its high spectral and increasing spatialresolution. In order to take a fuller advantage of character-istics in hyperspectral image, the proposed anomaly detectorexploits the second-order Mahalanobis distance statisticalfeature and multiple local window filters to establish a localsummation anomaly detection strategy. Moreover, someother operations for dealing with the problems discussed inSection 2.2 are included in the detection strategy.

3.1. Summation of multiple local background statistics

The traditional Local-RX algorithm exploits only onelocal window to estimate the local background statistics.However, Problem (a) in Section 2.2 shows the dis-advantages of this detection method. Fig. 5 illustrates thatsummation of multiple correlated Gaussian distributionswill concentrate the major of the data. Similarly, multiplecorrelated local background statistics can also be sum-mated to suppress the major background.

The proposed LSAD algorithm considers the spatialinformation in hyperspectral image into detection pro-cessing by exploiting a multiple-window sliding filterwhich can obtain various local spatial distributions withthe neighboring pixels of the pixels under test. A similar

Fig. 5. Summation of multiple corre

Fig. 6. Multiple local window filters option of LSAD. (a) Window 1, (b) Windowfigure, the reader is referred to the web version of this article.)

idea of Fig. 5 is embedded in the local summation anomalydetection strategy. Fig. 6 takes 3�3 size multiple localwindows to demonstrate the implementation of the localsummation strategy. For this strategy, local distributions ofall the selected size local windows which contain thepixels under test are taken into the detection statistics. Asillustrated in Fig. 6, if we choose local window of 3�3,there will be 9 local windows taken for the pixel under testrepresented by yellow pixel. The pixel samples of windows1–9 are used for implementation of second-order Maha-lanobis distance features of the pixels under test. Then allof the Mahalanobis distances are summated as the detec-ted value of the pixel under test. Expression of Mahala-nobis distance feature of pixel x to dataset V is:

disM

x;Vð Þ ¼ x�mVð ÞTX�1

Vx�mVð Þ ð3Þ

Here, mV is the mean vector of V andP

V is the cov-ariance matrix of V .

For k� k size local window, the sliding filter containsk� k local windows for summation. Local pixel samplesdatasets Wi ¼ xi;1; xi;2; :::; xi;k�k

� �; i¼ 1; :::; k� k from win-

dow i are obtained for Mahalanobis distance computation.For pixel under test r, summated detection result is

δLSAD rð Þ ¼Xk�k

i ¼ 1

disM

r;Wið Þ ð4Þ

The local summation strategy exploits the multiplelocal neighboring distributions of the pixel under test. Thevarious local distributions of multiple windows containing

lated Gaussian distributions.

2 and (c) Window 9. (For interpretation of the references to color in this

Fig. 7. Edge expansion.

Fig. 8. Subspace feature projection for robust background features andprecise covariance estimation.

B. Du et al. / Signal Processing 124 (2016) 115–131122

more sufficient local spatial information and may possessmore appropriate background distributions for anomalydetection. Summation of Mahalanobis distances will sup-press background features and further highlight anomalytargets. Furthermore, multiple distributions will enhancedetection performance especially for multiple-pixel targetswhich will be demonstrated in followed experiments.

3.2. Edge expansion

In order to ensure no absence of detection on the edge ofimage, edge expansion is operated as a pre-processing forLSAD. If the local window size is 2 �wþ1ð Þ � 2 �wþ1ð Þ, 2 �w layers of pixels are expanded on the edge of image asshown in Fig. 7. Due to the low probability of anomaly targetsappearance in hyperspectral images, we randomly choosepixels in image for expanded layers. Edge expansion mayprevent potential detection ratio decrease on the edge ofimages.

3.3. Subspace feature projection for the stable local covar-iance estimation

Owing to a small amount of pixels in local windows,imprecise estimate will appear with the singularity of aninversed local covariance. In order to enhance the robustbackground features and step over the imprecise covar-iance estimate, subspace feature projection is imple-mented for every local window.

In subspace construction procedure shown in Fig. 8, thesubspaces are represented by the eigenvectors corre-sponding to larger eigenvalues of covariance matrix led bythe major background features. Sub-pixel targets featureswhich are compounded with background may also beexcluded by eigenvectors corresponding to several largesteigenvalues. At the same time, the inversion of covariancematrix projected with these eigenvectors will not be sin-gular. Projected covariance's expression is:X�1

PCA¼UΛ�1U: ð5Þ

Λ is a diagonal matrix and only contains several largesteigenvalues which contain more than 99% information ofthe original local covariance matrix. U contains the cor-responding eigenvectors. Then the projected covariance isused in Mahalanobis distance computation.

The complete steps for the proposed LSAD algorithmare as follows and the flowchart of LSAD is shown in Fig. 9.

Step 1: Select the dimensions of the local windows as2 �wþ1ð Þ � 2 �wþ1ð Þ.Step 2: Randomly choose the pixels from hyperspectralimage to expand 2 �w layers of pixels on the edgeof image.Step 3: Implement the sliding filter with multiple localwindows for every pixel under test and exploit subspacefeature projection on every local covariance matrix forMahalanobis distance computation. The selected largesteigenvalues need to retain 99% information of the ori-ginal local covariance matrix.Step 4: Summate all the Mahalanobis distances of everylocal window for pixel under test as detection result.Step 5: Binarize the detection result to a binary detec-tion map with a certain falsealarm ratio.

Fig. 9. Flowchart of LSAD algorithm.

B. Du et al. / Signal Processing 124 (2016) 115–131 123

4. Experiments and analysis

In this section, we evaluate the detection performanceof the Global-RX (GRX), Local-RX (LRX), subspace-basedRX (SSRX) [57], blocked adaptive computationally efficientoutlier nominator (BACON) [58] and the proposed LSADalgorithms on a simulated PHI data and real AVIRIS andHYDICE hyperspectral images. In order to quantitativelyevaluate detection performance of these algorithms,receiver operating characteristic (ROC) curves [59] areused to compare the different algorithms. Based on thetarget references, the ROC curve can plot the relationshipbetween the falsealarm ratio (Fr) and the detection ratio(Dr) by taking all the possible thresholds. Fr and Dr aredefined as

Fr¼ nf

nti;Dr¼ ncd

ntt: ð6Þ

where nf r is the number of false alarm pixels, nti is thenumber of total image pixels, ncd is the number of correctlydetected target pixels and ntt is the number of total realtarget pixels. If the ROC curve illustrates that a detectionalgorithm acquires a higher detection rate than otheralgorithms in the same false alarm rate, it demonstratesthat the detection algorithm outperforms other algo-rithms. Another quantitative index, area under ROC curve(AUC) is also utilized to evaluate algorithms. The detectorwho has a larger area under its ROC curve will obtain alarger AUC value, and then it means the detector get abetter detection performance.

4.1. Data description

Two kinds of data are used to evaluate detection per-formance in our experiments.

1. Simulated data: composed of a real hyperspectral imagewith added spectra of targets in some pixels. This image

was a Pushbroom Hyperspectral Imager (PHI) hyper-spectral image taken of the Changzhou area, China. Atotal of 80 bands of the PHI image (240�240 pixels)were utilized, with a spectral range of 440–854 nm. Forthe convenience of single-pixel and sub-pixel targetdetection, the targets are the typical ground objects inthe same image, and they are added to certain pixelswith a determined percentage. In the experiment, thespectrum of cement is selected as the target's signatureto be added in 100 pixels, and the original signature inthese pixels would be taken as background and thepercentage is reduced accordingly. The anomaly target'sspectrum is a land cover of Andradite acquired from theENVI software library. The 100 pixels are divided into 10groups according to their targets' abundances as shownin Table 1. The 100 targets are placed in 10 columnswith each column of 10 targets at the same position. Thepositions of these targets are shown in Fig. 10 anddenoted by yellow circles.

2. Real hyperspectral images: two real hyperspectral dataacquired by HYDICE and AVIRIS sensors respectively areutilized in our experiments. The HYDICE hyperspectralimage, which consists of a suburban residential area(Fig. 11(a)) with approximately 3 m spatial resolution, ispublicly available [60]. The image contains 8000 pixelsand has 210 spectral channels from 0.4–2.5 mm. Afterremoving the water absorption bands, it contains 169-band. The scene is cluttered with a parking lot and aroadway with 10 man-made vehicles which can beconsidered as anomaly targets in this image and thereference is shown in Fig. 12(a). Another real hyperspectralimage utilized in our experiments is an AVIRIS hyperspec-tral data which is acquired over San Diego airport area.This is a sub-image that has 3600 pixels in size and has189 spectral bands after removing low SNR and waterabsorption bands. We can regard the small aircrafts as

B. Du et al. / Signal Processing 124 (2016) 115–131124

anomaly targets in this image as shown in Fig. 11(b) andthe reference is demonstrated in Fig. 12(b).

The simulated PHI hyperspectral data contains anomalytargets with 10 various types of targets' abundances. All the100 targets are embedded in single pixels. Then this simu-lated data occupies sub-pixel and single-pixel anomaly tar-gets simultaneously. The anomaly pixels of vehicles in theHYDICE hyperspectral image are also a kind of single-pixeltargets and most of these targets only occupy less than onepixel so they are also sub-pixel targets. The differencebetween the simulated and HYDICE hyperspectral data is that

Table 1Anomalies Abundance Details of the PHI Image.

Line of targets Targets type Target abundance (%)

1–9 Sub-pixel, single-pixel 10–9010 Single-pixel 100

Fig. 10. Simulated PHI data in our experiments. (For interpretation of thereferences to color in this figure, the reader is referred to the web versionof this article.)

Fig. 11. Real hyperspectral images in our exp

the PHI data's anomalies spread symmetrically in the imageand then these targets can be considered as local and globalanomaly targets simultaneously, but anomalies in the HYDICEimage only can be thought of global targets because theirspectra are significantly different from other major land coverin the whole image [61–64]. Hence, the simulated andHYDICE data are utilized to evaluate detection performance ofsingle-pixel and sub-pixel targets by the proposed LSADalgorithm relative to several traditional anomaly detectors.The AVIRIS image contains some aircrafts as multiple-pixelanomaly targets. Then the AVIRIS hyperspectral data is usedto evaluate detection performance of multiple-pixel targets.

4.2. Validity estimation of edge expansion and subspaceprojection

First of all, we estimate the validity of the two opera-tions: edge expansion and subspace projection with theAVIRIS data. In this experiment, we set four kinds ofimplementation for LSAD: (1) LSAD with none of the twooperations (LSAD_NEPNSP), (2) LSAD with edge expansionbut without subspace projection (LSAD_EPNSP), (3) LSADwith subspace projection but without edge expansion(LSAD_NEPSP), and (4) LSAD with edge expansion andsubspace projection (LSAD_EPSP). The local window filteris implemented with size of 13�13.

Detection results of the four kinds of implementation forLSAD are shown in Fig. 13. It can be found that the detectionresult of LSAD_EPSP is more capable of highlighting anomalytargets and won’t lose any detection information on the edgeof image. ROC curves and AUC values in Fig. 14 illustrate thatLSAD_NEPSP and LSAD_EPSP which are implemented withsubspace projection can get much better detection perfor-mance than LSAD_NEPNSP and LSAD_EPNSP. Then it can beproved that subspace projection can suppress background ofimage data. In Fig. 13(a) and (c), it can be found that detectioninformation on the edge of image is lost by LSAD_NEPNSP andLSAD_NEPSP but which is not in Fig. 13(b) and (d). This canprove that edge expansion can make anomaly detector notlose any probable anomaly targets on the edge of the image.

eriments. (a) HYDICE and (b) AVIRIS.

Fig. 12. Anomaly targets references of hyperspectral images. (a) HYDICE and (b) AVIRIS.

Fig. 13. Detection results of the four kinds of implementation for LSAD. (a) LSAD_NEPNSP, (b) LSAD_EPNSP, (c) LSAD_NEPSP and (d) LSAD_EPSP.

Fig. 14. Quantized evaluation analysis. (a) ROC curves and (b) AUC values.

B. Du et al. / Signal Processing 124 (2016) 115–131 125

4.3. Detection performance evaluation of single-pixel andsub-pixel target

We utilize the simulated PHI data and HYDICE “Urban”hyperspectral image to evaluate single-pixel and sub-pixeltargets' detection performance. Fig. 15 demonstrates thedetection results of the proposed LSAD algorithm and otherconventional anomaly detectors using simulated PHI data. Itcan be found from the detection result that detectors whichmerely take advantage of spectral information such as GRX,

SSRX and BACON anomaly detection algorithms omit so manylocal anomaly targets in the simulated PHI data that generatesthe low detection rate. Spectral-based anomaly detectorsobtain poor detection performance for local single-pixelanomaly targets. At the same time, spectral-spatial inte-grated anomaly detectors such as the proposed LSAD and LRXacquire excellent detection performance for sub-pixel andlocal single-pixel anomaly targets. Even sub-pixel targets withabundances that are less than 30% can also be detected byLSAD and LRX. In order to obtain the best detection results,

Fig. 15. Detection results of detectors using simulated PHI data. (a) Reference, (b) LSAD, (c) LRX, (d) GRX, (e) SSRX and (f) BACON.

Fig. 16. Quantized evaluation analysis of detection performance using simulated PHI data. (a) ROC curves and (b) AUC values.

B. Du et al. / Signal Processing 124 (2016) 115–131126

the most appropriate window sizes for LSAD and LRX are bothchosen for detection. For this simulated PHI data, LSAD’swindow implementation is 3�3 and LRX's is 13�13. LSADand LRX get similar perfect detection in this simulated PHIdata which has single-pixel and sub-pixel targets simulta-neously due to their integration of spectral and spatial infor-mation detection strategy. However, LSAD utilizes a smallerwindow implementation than LRX to get the best detectionresult which attributes to multiple local background dis-tribution feature statistics summated by LSAD. Moreover,subspace feature projection also helps LSAD for sub-pixel

anomaly target detection. Quantized evaluation analysis withROC curves and AUC values demonstrated in Fig. 16 alsoillustrates that anomaly detectors with spectral-spatial inte-gration have more ability for local single-pixel and sub-pixelanomaly target detection.

Detection results of the evaluated anomaly detectors forreal HYDICE “Urban” hyperspectral image are illustratedin Fig. 17. Binary detection map of LSAD is the most similardetection map to the targets' reference which means LSADcan detect the exact anomalies in this image. Backgroundfeatures of ground surface materials such as parking lot and

Fig. 17. Detection results of detectors using real HYDICE “Urban” hyperspectral image. (a) Reference, (b) LSAD, (c) LRX, (d) GRX, (e) SSRX and (f) BACON.

Fig. 18. Quantized evaluation analysis of detection performance using real HYDICE “Urban” hyperspectral image. (a) ROC curves and (b) AUC values.

B. Du et al. / Signal Processing 124 (2016) 115–131 127

roadway in this image can be excellently suppressed by LSADwhich is contributed to multiple local neighboring back-ground distributions considered by LSAD for every pixelunder test. Detection results of GRX, SSRX and BACON algo-rithms in Fig. 17(d), (e) and (f) are much far away from thetargets reference which declares that the spectral-spatialintegrated LSAD algorithm performs better on the globalanomaly targets in this experimental data. Detection perfor-mances of LSAD are much better than LRX which demon-strates that spectral-spatial integrated local summationdetection strategy can suppress background features moreeffectively. Moreover, some anomaly targets are on the edgein the “Urban” image, and the detection result of LRX showsthat these targets' detection results are absent, but LSADwhich is implemented with edge expansion is robust to these

anomaly targets. Three-dimensional mesh of these detectionresults in Fig. 19 show that LSAD algorithm obtains the mostreliable detection result than the other detectors. ROC curves,and AUC values in Fig. 18 demonstrate that LSAD achieves thebest detection performance using the HYDICE “Urban”hyperspectral image.

Experiments using the simulated PHI data and HYDICE“Urban” hyperspectral image for detection performanceevaluation demonstrate that the spectral-spatial inte-grated local summation strategy based LSAD algorithm caneffectively detect single-pixel and sub-pixel anomaly tar-gets in hyperspectral data and convincingly suppressbackground features, and edge expansion, subspace fea-ture projection and local summation strategy are all con-ducive to improve detection performance for LSAD.

Fig. 19. Three-dimensional mesh of detection results. (a) LSAD, (b) LRX, (c) GRX, (d) SSRX and (e) BACON.

B. Du et al. / Signal Processing 124 (2016) 115–131128

4.4. Detection performance evaluation of multiple-pixel target

The aircrafts in the AVIRIS “San Diego airport” real hyper-spectral image are considered as anomaly targets in this

image and they are the type of multiple-pixels targets. We usethis AVIRIS hyperspectral data to evaluate the multiple-pixelstarget detection performance of the proposed LSAD algorithmrelative to the other traditional detectors.

Fig. 20. Detection results of detectors using real AVIRIS hyperspectral image. (a) Reference, (b) LSAD, (c) LRX, (d) GRX, (e) SSRX and (f) BACON.

Fig. 21. Quantized evaluation analysis of detection performance using real AVIRIS hyperspectral image. (a) ROC curves and (b) AUC values.

B. Du et al. / Signal Processing 124 (2016) 115–131 129

Spectral information based anomaly detectors as GRX,SSRX and BACON can more or less exclude a little portionof anomaly targets' feature as shown in Fig. 20(d), (e) and(f). However, their results are not as satisfactory as LSAD.The proposed LSAD algorithm exploits the implementationof multiple local windows surrounding pixel under test toget various local background distributions for backgroundfeatures suppression. Then the background aroundmultiple-pixel anomaly targets is more robust becausepotential appropriate background distribution will prob-ably be achieved. These multiple-pixels anomaly targets

also contain some targets of sub-pixel, and subspace fea-ture projection in every local window can assist LSADexcluding these targets. Quantized evaluation analysiswith ROC curves and AUC values in Fig. 21 also declaresthat LSAD is superior in multiple-pixel anomalies detec-tion than the other detection algorithms in ourexperiment.

Sections 4.2 and 4.3 demonstrate that the proposed LSADalgorithm is well behaved in detecting single-pixel, sub-pixeland multiple-pixel anomaly targets due to operations such as

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edge expansion, subspace feature projection and local sum-mation anomaly detection strategy exploited by LSAD.

5. Conclusion

This paper proposes an LSAD algorithm for hyper-spectral anomaly detection. This method exploits a localsummation anomaly detection strategy which implementsa series of the local windows which contain the pixelunder test to obtain various local background distributionsto compute background feature statistics for the pixelsunder test. Some other operations such as edge expansionand subspace feature projection are included in thisstrategy to solve some existing problems in the conven-tional single-window based spectral-spatial informationbased anomaly detectors. The experiments have proventhat the LSAD outperforms the state-of-art anomalydetection methods, such as GRX, LRX, SSRX, BACON algo-rithms in detecting single-pixel, sub-pixel and multiple-pixel anomalies. Our future work mainly focuses on theintroducing multi-view, metric learning and manifoldregularization theory into our LSAD algorithm [65–68].

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