Target detection in SAR images via radiometric multi-resolution analysis

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1 Target detecton n SAR mages va radometrc mult-resoluton analyss JngwenHu a,, Gu-Song Xa, Hong Sun* a a School of Electronc Informaton, Wuhan Unversty, Wuhan, 43007, Chna State Key La. LIESMARS, Wuhan Unversty, Wuhan, , Chna ABSTRACT Ths paper presents a target detecton method n synthetc aperture radar (SAR) mages wth radometrc multresoluton analyss (RMA). The dea s that target salency can e effcently computed y comparng the statstcs of targets and those of the local ackground around them. In order to compute relale statstcs of targets, whch usually nvolve a small numer of pxels, RMA s adopted. The RMA preprocessng method performs well n stalzng the statstcal characterstcs of SAR mages. It can effectvely restran the speckle nose whle keep the statstcal characterstcs of the orgnal mage. Based on the computed target salency, adaptve decson thresholds are got y usng the constant lse alarm rate (CFAR) target detecton framework. Our experments on real SAR mages show that the proposed method can acheve etter performance compared wth the tradtonal cell average-constant lse alarm rate (CA-CFAR) method. Keywords: target salency, target detecton, radometrc mult-resoluton analyss (RMA), synthetc aperture radar (SAR). ITRODUCTIO As an mportant approach of actve remote sensng, synthetc aperture radar (SAR) s wdely used, especally n the feld of mltary, for ts alty to work regardless of weather and lght. Wth the development of the manucture of sensors and the mprovement n data processng alty, the resoluton of SAR mages has een greatly ncreased, and the technques of automatc target recognton (ATR) [] ased on SAR mages attract more and more attenton. As the frst step of ATR system, target detecton greatly nfluences the performance of ATR. One of the most wdely used methods n target detecton s constant lse alarm rate (CFAR) [], whch reles on the contrast etween a target and ts ackground. The most challengng part of CFAR s to model the ackground clutter and a varety of parametrc models have een proposed n the lterature. However, one man drawack of parametrc models s that t s not adaptve to the ackground clutter of dfferent knds. The paper presents a non-parametrc model, whch comnes the radometrc mult-resoluton analyss (RMA) [3] wth tradtonal CFAR method to mprove the performance of target detecton n SAR mages. As we shall see, the experments show that the proposed method performs etter (the same detecton rate and lower lse alarm rate) than the tradtonal cell average-constant lse alarm rate (CA-CFAR) approach.. Related works CFAR recognzes targets from ackground y analyzng ther grey level dstruton. The grey level dstruton s decded y ther scatterng propertes. To make a etter use of mage ntensty as well as mprove the detecton effcency, ovak et al. [4] ntroduced the local two-parameter CFAR detecton method. However, ths method s grounded on the assumpton that the ackground clutter can e well descred y a Gaussan dstruton, otherwse the detecton performance wll decrease serously even n hgh-resoluton mages. In order to solve ths prolem, many mproved algorthms have een susequently proposed, such as the CFAR detecton algorthms usng more roust ackground clutter models [5, 6]. In addton, the usng of sldng wndow n the two-parameter CFAR algorthm restrcted the speed of the detecton. The gloal CFAR algorthm [7] and parallel CFAR technques [8] have een developed for speed up the processng. Moreover, n order to solve the nstalty prolem around the clutter edges and n mult-ojectve areas, some other methods have een proposed such as OS - CFAR [9], SO-CFAR, GO-CFAR, VI CFAR [0], etc. The effect of CFAR depends on how the grey level dstruton fts the statstcal model that CFAR uses. Whle almost all statstcal models cannot model SAR mages well. So, ths artcle uses RMA method that s free of statstcal models. MIPPR 03: Automatc Target Recognton and avgaton, edted y Tanxu Zhang, ong Sang, Proc. of SPIE Vol. 898, SPIE CCC code: X/3/$8 do: 0.7/ Proc. of SPIE Vol Downloaded From: on 0/06/07 Terms of Use:

2 RMA s a mult-resoluton statstcal analyss method n the ampltude-frequency doman, whch was frst used to flter or restore whte nose-lke sgnal, such as an SAR mage [3]. RMA s useful n analyzng the mages wth multplcatve correlated nose ecause t can flter the speckle nose and meanwhle stalze local statstcal characterstcs.. Contruton Ths paper frst ulds a fully non-parametrc model va RMA n the CFAR ased detecton method. It can work under all knds of grey level dstruton. Furthermore, t s more sutale for small amount of sample pxels than some other non-parametrc model such as kernel densty estmaton []. The method s n three steps. Frst, the target regon and ts ackground are modeled y RMA va a sldng wndow. Then, the dfference of ther dstruton s computed to e the salency value and for comparson, ths s done n sx knds of dstances. Last, local CFAR s used to get the adaptve threshold that dstngushes the target pxels form ackground. The experments show that n the regon of homogeneous ackground, the new method can get a etter (the same detecton rate and lower lse alarm rate) result when compared wth tradtonal CA-CFAR [] method. The second chapter ntroduces the theory of RMA. The thrd chapter descres the procedure of our method. The forth chapter shows our experments and results. At last, the concluson s gven n the ffth chapter.. The defnton. RADIOMETRIC MULTI-RESOLUTIO AALYSIS (RMA) Consder a dscrete random sgnal xn ( ) wth n as the tme/space varale, p ( ) ( ) xn X s the proalty densty functon (PDF) of xn ( ). Conventonal wavelet analyss n spatal-frequency doman operates correlaton etween the sgnal xn ( ) and dfferent scales of wavelet functon, ( n ) /scalng functon, ( n ),.e. a, a D x( n) x( n), ( n) () a a, A x( n) x( n), ( n) () a Where f, f expresses the correlaton of f and f. a, ( n ) expresses a wavelet functon on scale a and shft, and, ( n ) a s the correspondng scalng functon. a RMA apples wavelet-ased mult-resoluton analyss n ampltude-frequency doman to local statstcs (the PDF p X ) of the random sgnal nstead of the sgnal tself. Therefore, the defnton of RMA s as follows: xn ( ) ( ) D p ( X ) p ( X ), ( X ) (3) a, x( n) x( n) a, A p ( X ) p ( X ), ( X ) (4) a, x( n) x( n) a, Eq. (3) s wavelet transform or detals of the PDF of the random sgnal on scale a shft, whle Eq. (4)s an approxmaton of PDF of the sgnal. We call ths representaton a radometrc mult-resoluton analyss (RMA) [3]. When x( n) n,,, represents dscrete dgtal mage sgnal, s the numer of all the pxels, the PDF p ( ) xn ( ) X s the hstogram of mage n gray-level. Eq. (3) and Eq. (4) represent the approxmaton and the correspondng error of the hstogram. Proc. of SPIE Vol Downloaded From: on 0/06/07 Terms of Use:

3 . The estmaton method Conventonal wavelet transform drectly uses the orgnal sgnal to calculate the correlaton coeffcent accordng to Eq. () and Eq. (). However, the local PDF n RMA (Eq. (3) and Eq. (4)) s often unale to otan drectly. Therefore, we need to study the estmaton algorthm of RMA. Assumng that the random sgnal s ergodc, ased on the generalzed ergodc theorem, a generalzed statstcal average s equal to tme average, whch can e wrtten as: a, x( t) a, T T T T ( X ) p ( X ) dx lm [ x( t)] dt (5) Consderng dscrete tme sgnal and n the case of fnte pxels n an analyss wndow, the rght sde of Eq. (5)can e approxmated y: Thus Eq. (3) can e rewrtten as: For the same reason, Eq. (4) can e rewrtten as: lm [ x( n)] [ x( n)] (6) a, a, n n0 p ( X ), ( X ) [ x( n)] (7) x( n) a, a, n0 p ( X ), ( X ) [ x( n)] (8) x( n) a, a, n0 Thus, we get the estmaton algorthm of RMA from the orgnal sgnal. 3. Preprocessng 3. RMA BASED CFAR Snce man-made targets, especally metal targets have a larger reflecton coeffcent, they are rghter relatve to the natural features n SAR mages []. Thus, we can preprocess the whole mage to get the possle target area and effectvely exclude the natural features n large area. Ths step can greatly reduce the numer of susequent local processng and mprove the effcency of the operaton. For the whole mage, we can use gloal CFAR as the preprocessng to exclude the ovous non-target area. CFAR reles on the great contrast etween target and ts ackground. Accordng to the sgnal detecton theory, the lse alarm rate s defned as the proalty of msjudgng the ackground to e the target, that s: c () (9) r I p z dz P Ic Thus we can fnd the threshold I c accordng to numercal ntegraton. Where pz () s the PDF of the clutter n the whole mage whch can e the normalzed hstogram drectly, so the correspondng cumulatve dstruton functon (CDF)s x pzdz,whch s an ncreasng functon n F x 0 0,. 0 I c By solvng the Eq.(0), we can get the threshold Ic when lse alarm rate P p z dz (0) P s gven. Proc. of SPIE Vol Downloaded From: on 0/06/07 Terms of Use:

4 Consderng the hstogram as a dscrete dstruton functon, we can get the approxmate soluton of the threshold I c y usng the dchotomy. Fnd a postve nteger I whch satsfed the followng nequalty: F I P andf I P () Thus we get the approxmate soluton of the gloal threshold. By comparng the gray value of the tested pxel wth the threshold, we can judge the pxel as possle target f t s larger or as the ackground conversely. 3. Salency computaton After preprocessng, RMA s used to otan the PDF n local ackground wndow and the test wndow respectvely. Then the dfference etween them s calculated as the salency feature. By usng the sldng wndow, we can get all the dfferences n the possle target area. The greater the dfference, the more possle the tested pxel should e classfed as target. Tale lsts the formulas of sx common methods for dfference computaton. Tale. The formulas of sx common methods for dfference computaton methods Eucldean Manhattan Cheyshev JS Hellnger Jeffrey s 3.3 Adaptve threshold y local CFAR formulas d( p, q) ( p q ) d( p, q) p q d( p, q) max ( p q ) (,... ) p d( p, q) dkl( p, m) dkl( q, m), dkl( p, q) p log, m q d( p, q) ( p q) d( p, q) ( p q )(ln p ln q ) p q In order to get the fnal result wth less lse alarms, we can use local CFAR to fnd the threshold adaptvely n the sldng wndow. In ths step, the PDF pz () n CFAR s replaced y the salency values, and the lse alarm rate should e smaller to remove the remanng lse alarms after preprocessng. 4. EXPERIMETS As we use the normalzed hstogram of the whole mage wthout removal of the target area as an estmaton of the PDF, the lse alarm rate should e larger to lower the lse detecton rate. Although the preprocessng result may have a hgh lse alarm rate, they can e removed n the susequent local processng. But f the target s msjudged as ackground, t P ). can t e recovered afterwards. Fg. shows the orgnal mage and the nary mage after preprocessng ( =0. After preprocessng, we use sx methods lsted n Tale to calculate the dstruton dfference. Fg. shows the salency maps of them. The sx salency maps shown n Fg. show that the more ovous the targets, the more ovous the lse alarms n the salency maps, such as Eucldean dstance, Manhattan dstance, Cheyshev dstance and Hellnger dstance; On the contrary, all the targets and the lse alarms are relatvely less ovous n JS dvergence and Jeffrey's dvergence. That P Proc. of SPIE Vol Downloaded From: on 0/06/07 Terms of Use:

5 tl means, the performance of the sx methods cannot e compared only y ther salency maps. Therefore, the local CFAR s used to get the fnal results that are shown n Fg.3..}4 (a) Fg.. The orgnal mage (a) and the nary mage after preprocessng (). () o 9 D (a) () (c) (d) (e) (f) Fg.. The salency maps of dfferent methods: (a) Eucldean dstance () Manhattan dstance (c) Cheyshev dstance (d) JS ( Jensen Shannon) dvergence (e) Hellnger dstance (f) Jeffrey s dvergence. Three quanttatve ndexes are used to compare the performance,.e. () the rght detecton; () the lse alarm; (3) the mssng detecton. Tale shows the statstcs of the three quanttatve ndexes. Tale shows that sx methods have the same numer of rght detecton and the same numer of mssng detecton, ut they have dfferent lse alarms. When usng Jeffrey`s dstance as the salency feature, the lse alarms are the least and the result s the est. Fnally, we conduct three groups of experments adoptng Jeffrey's dstance to calculate dstruton dfferences and compare wth the tradtonal CA - CFAR methods. The statstcs of the results s lsted n Tale 3. Proc. of SPIE Vol Downloaded From: on 0/06/07 Terms of Use:

6 le (a) () (c) (d) (e) (f) Fg. 3. The nary results of dfferent methods: (a) Eucldean dstance () Manhattan dstance (c) Cheyshev dstance (d) JS ( Jensen Shannon) dvergence (e) Hellnger dstance (f) Jeffrey s dvergence Tale. The statstcs of the sx results methods Eucldean Manhattan Cheyshev JS Hellnger Jeffrey s rght detecton lse alarm mssng detecton Tale 3. The comparson etween our method and CA-CFAR Group numer methods rght detecton lse alarm mssng detecton ours CA-CFAR ours 3 0 CA-CFAR ours CA-CFAR 4 0 Tale 3 shows that n the test mages, our method and CA-CFAR oth detect all the rght target, ut our method can get lower lse alarm rate. 5. COCLUSIO RMA can stalze local statstcal characterstcs of the orgnal mage, and reakthrough the lmtaton of parametrc models. Ths paper descres a new RMA ased target detecton method. After preprocessng the whole mage usng gloal CFAR, we uses RMA to model the PDF of the target regon and ackground regon n the sldng wndow respectvely, and calculate the dstruton dfference as the salency feature. The fnal result s otaned y means of local CFAR method. Although our method hasn t reached the expected effect as we theoretcally analyzed, we can see the feaslty of CFAR usng non-parameter model ased on the RMA n contrast wth the tradtonal CA - CFAR method experments. It provdes a new thought for target detecton n SAR mages. Proc. of SPIE Vol Downloaded From: on 0/06/07 Terms of Use:

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