Image Content Dependent Compression of SAR Data

Transcription

1 Image Content Dependent Compresson of SAR Data Ursula Benz, Jens Fscher, Gunther Jäger Deutsches Zentrum für Luft- und Raumfahrt (DLR) e.v. P.O. Box 1116, D Wesslng, Germany Tel: , Fax: , E-mal: Summary: Data rate and amount of SAR data exceed the capacty of usual data lnks and storage devces n most cases. SAR data compresson s necessary to ensure effcent use of acqured data and processed mages. Unfortunately, lossless compresson s not possble for SAR data due to ther hgh entropy. However, t s of major mportance that no SAR applcatons suffer from data compresson. There are several strateges: 1) nearly lossless data compresson wth a very hgh overall and local performance: Quantzaton errors do not exceed a certan (small) value for any objects n the mage, the drawback s, of course, the only small compresson rato; 2) data compresson adaptve to the mage contents a) The coder uses more bts to quantze coeffcents of regons wth hgh actvty compared to those of more homogeneous regons. For example, n SAR mages pont targets and edges are treated separately from the other mage parts. Ths procedure allows a medum overall compresson rato and gves a homogeneous error dstrbuton over the whole mage. b) The coder uses more bts for regons of nterest. Whereas methods 1 and 2a allow any applcaton on the decompressed SAR data wthout loss n performance, method 2b gves the opportunty to adapt compresson to a specfc applcaton and a very hgh compresson rato can be acheved. In ths paper we propose the combnaton of these methods to take optmal advantage of the whole SAR system consstng of the SAR sensor tself, the network of ground statons wth hgh computatonal archvng resources and clents wth usually lmted computatonal power and low capacty lnks. 1 TWO-STEP DATA COMPRESSION The most expensve parts n SAR systems, e.g. spaceborne SAR systems, are sensor development and operaton. A large user communty has to be served to ensure commercal and effcent use of the acqured data. However, storage capacty on board of satelltes s lmted. Data have to be transmtted va specal lnks to ground statons. There has to be data compresson on board whch allows a longer tme of data acquston between down lnks and addtonally a faster down lnk of the acqured data. Of course, no applcaton should suffer from ths data compresson. The requred mage qualty has to be mantaned as well for vsual evaluaton as for automatc classfcaton and further sgnal processng. Examples are DEM generaton and egenvector analyss n polarmetrc mode. To ensure the requred qualty we suggest to measure not only an overall sgnal-todstorton nose rato and rms phase error but also the dstortons n dependence of mage contents. We propose a two-step compresson strategy: In the frst step a nearly lossless data compresson s appled. The very hgh overall and local performance ensures no degradaton of mage qualty for any applcaton. The algorthm has to be fast, no hgh computatonal resources are allowed. We developed a flexble algorthm (FLECS) for SAR data compresson [3]. In our smulaton no object n the mage has a phase error larger than 1 and a sgnal to dstorton nose rato whch s less than 40 db, f the compresson rato s below 4. Ths s vald for all polarmetrc and nterferometrc channels. The compressed data are transmtted to the server network on the ground. There s access to hgh computatonal power and huge storage capactes. Ths equpment can be used to derve most advantage from remotely sensed data. Here the second step of data compresson takes place: Data compresson s closely adapted to the user's requrements: a) For scentfc applcatons complex data are transmtted wthout further compresson. The amount of data sets wll be lmted and thus the hgh data rate can be accommodated by specal lnks. In ths case also hgh computatonal power s usually avalable at the clent. b) For general applcatons wth medum requrements of reconstructon qualty a medum compresson rato s used. Specal algorthms are employed to avod dstortons around edges and pont targets. c) Dfferent treatment of regons of nterest and background realzes a hgh compresson rato to save transmsson costs and storage requrements for the clent. The computatonal capabltes of the server network for classfcaton of the data are used. In addton to the effcent data compresson the preclassfcaton allows mage content query n the database.

2 Ths two-step data compresson requres only hgh computatonal power and storage capacty at the server network, the necessary down lnk capacty from the satellte s reduced by a factor of more than 3 wthout mage qualty degradaton. From the server to the clent only those data are transmtted whch are of nterest for the clent thus savng lots of money and tme. clent sensor hgh capacty lnk ground staton network hgh capacty lnks clent clent STEP 1: nearly lossless onboard data compresson STEP 2: data compresson adaptve to mage contents and user requrements decompresson low computatonal requrements small compresson rato hgh computatonal requrements hgh archvng requrements flexble compresson rato from one up to very hgh low comput. requrements Fgure 1: Two step data compresson 2 ONBOARD DATA COMPRESSION (STEP 1) We employ for onboard data compresson a flexble compresson of SAR data (FLECS)[3]. FLECS s a wavelet based compresson algorthm. The sutablty of wavelets for (SAR) data compresson s shown n many publcatons. Important references are among others [2][15][17]. There s not only a good energy compacton and representaton of hgh and low frequency parts, also possbltes for further sgnal processng are gven. For example n wavelet doman, despecklng s possble [7][13]. FLECS works n polar or cartesan mode. In nearly lossless mode, compresson can be regarded as a lnear algorthm, and can be appled separately on real part and magnary part of the complex SAR data. Therefore here we consder only FLECS workng n cartesan mode. A Daubeches-8 wavelet transform s appled on real and magnary part. Quantzaton takes place n transform doman. In contrary to optc and acoustc data, t s not possble to neglect the hgher frequences of SAR data, f a good mage qualty and post-processng has to be mantaned. Ths s due to the hgh dynamc and the speckle characterstc n the data. However, the subbands already contan dfferent ac energes after one teraton. The ac energes represent dfferent nformaton contents. Ths s used to allocate dfferent numbers of bts for each subband. There exst several approaches for proper bt allocaton. We base bt allocaton on the rato of ac energy between the subbands and optmze the result by teratve tranng on the data of the consdered sensor to gan mnmum quantzaton dstorton. The average bt number b = ( b + b + b + b ) 4 s fxed to LL HH LH HL ensure the desred compresson rato. In our approach, a scalar quantzer s used up to now. For quantzaton the wavelet subbands are dvded nto N blocks q, 1 N. To ensure approxmately constant statstc wthn one block, the block sze s small, e.g. 8 by 8 samples. The quantzer s adapted to the dynamc d = max q - mn q wth range d of each block q : ( ) ( ) max ( q ) and mn ( ) q maxmum and mnmum value wthn quantzaton block q, respectvely. The dynamc range d s dvded nto equally spaced ntervals I m, I,1 m M. The avalable bt number b m for b quantzaton of block q gves the number M = 2. All quantzaton blocks q wthn one wavelet subband are quantzed usng the same bt number. Due to the scalar quantzer, only nteger bt numbers are possble. The quantzer allows a very smple mplementaton but reduces the flexblty. Ths s also the man reason, why we cannot take advantage of more than one teraton of wavelet decomposton. Further studes wll nclude vector quantzaton to be able to deal wth fractonal bt numbers. Decompresson nverts frst the lnear quantzaton usng the header nformaton (btmask and for each quantzaton block q maxmum max ( q ) and mnmum mn ( q )) and secondly, performs an nverse wavelet transform. Up to now we manly tested the performance of our FLECS on arborne SAR data. Data of hgh accuracy (hgh geometrc and radometrc resoluton, polarmetrc

3 and nterferometrc mode) are avalable. Based on prelmnary studes on X-SAR and ScanSAR (RadarSat) data we expect that the results wll be transferable for hgh resoluton SAR data of future spaceborne systems. In dependence of avalable storage, down lnk capacty and requred mage qualty, the compresson rato can be chosen between two and fve. For Step 1 - compresson at the sensor - we suggest a compresson rato of about 3.2 leadng to 20 bts/pxel. Thus a sgnal-to-nose rato of 58 db s acheved and a phase error smaller than 1. Ths s vald for all polarmetrc and nterferometrc channels. SDNR SDNR n db n db complex mage detected mage acheved compresson compresson rato (ncludng rato header) acheved compresson compresson rato rato a) b) rms phase error error Fgure 2: Performance of FLECS (Flexble Compresson of SAR Data); nearly lossless for compresson rato 3 Fgure 2a) shows the sgnal-to-dstorton nose rato of FLECS n dependence of the compresson rato, Fgure 2b) the rms phase error, respectvely. For compresson rato 3 a nearly lossless performance s acheved. Followng our two-step compresson strategy ths approach s sutable for nearly lossless compresson onboard. 3 IMAGE CONTENT COMPRESSION AT THE GROUNDSTATION (STEP 2) Few users need data wthout any dstorton due to data compresson. Only sophstcated scentfc applcatons requre perfect reconstructon. In these cases no further compresson takes place at the server system. The data are transmtted drectly to these clents. In most cases further data compresson s possble savng transmsson tme and costs for clents and provder. Here mage content dependent data compresson gans major advantages: Separate treatment of regons wth hgh or low actvty allows adjustng the bt rate and stll achevng a suffcent mage qualty wth an overall reduced bt rate. In addton to data compresson, dscrmnaton between dfferent actvty zones s necessary. Separate treatment of relevant and rrelevant nformaton allows transmsson of the very nformaton, whch s of nterest for the clent. Huge compresson ratos are possble. In addton to data compresson, a classfcaton map has to be evaluated and transformed to a sgnfcance map n transform doman. 3.1 SEPARATE TREATMENT OF REGIONS WITH HIGH OR LOW ACTIVITY In FLECS, hgher compresson ratos lead to blockng effects around pont targets and edges. The lnear quantzer s well adapted to maxmum dynamc, but does not smultaneously represent small values wth suffcent accuracy. Logarthmc converters do nether solve ths problem n a sutable way. The response of the pont target, e.g. a corner reflector would be dstorted to some degree. However, perfect reconstructon of those targets s mportant for calbraton and geocodng. Only separate treatment of very hgh coeffcents n the wavelet subbands allows perfect reconstructon of both, strong and weak scatterers. A homogeneous sgnal-to-nose rato and equally dstrbuted phase errors can be acheved. Blockng effects vansh. A more detaled descrpton can be found n [8]. A smlar problem arses around edges. They are characterzed by a transton between dfferent statstcs wth a varyng standard devaton. Ths deterorates the performance of the quantzer. Dstorton can be avoded f edge regons are separated from the more homogeneous regons. Fgure 3 shows a SAR ntensty mage wth the correspondng edge map, derved by our fuzzy edge detector (FED) [6]. Other edge detectors can be used, f they detect not only a sngle edge lne, but lke FED the whole transton regon. Fgure 3c f show smulaton results for ampltude and phase error n false colors (Fgure 3c,e wthout separate treatment of edges, Fgure 3 d,f wth an ncreased number of quantzaton bts for those coeffcents belongng to an edge.

4 a) b) c) d) e) f) <=20 SDNR [db] >= >3 Fgure 3: a) SAR mage, b) edge regons derved wth fuzzy edge detecton, c) SDNR map pror e) after edge preservaton, d) phase error pror f) after edge preservaton

5 3.2 SEPARATE TREATMENT OF RELEVANT AND IRRELEVANT INFORMATION The advantages of compresson adapted to mage content are mentoned n several papers of IGARSS 99. Hgh compresson ratos can be acheved wthout degradaton of relevant nformaton. Specal algorthms for ce detecton [11] were presented or for compresson of only non-textured or only textured regons [1]. However, these approaches are ether restrcted to a sngle applcaton or cannot be further adapted to dfferent applcatons. In our approach we overcome ths problem. We combne a flexble classfcaton algorthm wth data compresson. Classfcaton delvers a classfcaton map, whch can be used to separate relevant from rrelevant nformaton, to dvde background from regons of nterest. The classfcaton map can be derved usng any supervsed approach. We suggest a fuzzy approach to gan maxmum robustness and gather the uncertanty n SAR data themselves and n class assgnment A Fuzzy Approach for Generaton of Classfcaton and Sgnfcance Map We derve a classfcaton map for basc classes, e.g. urban, hgh vegetaton (forest), medum and low vegetaton and smooth surfaces usng a supervsed fuzzy learnng system. In our smulaton example we appled the fuzzy nearest prototype algorthm [12], whch s mplemented n our fuzzy nteractve analyss system for SAR mages FIAS [4]. To ths end, we chose as feature vectors the ordered ntenstes of a 7 by 7 neghborhood centered at the consdered pxel. We selected 30 test samples for each of the fve classes. After orderng the wndows to 49-dmensonal vectors class a = ( a1,..., a49) wth a1... a, 49 = 1,...,30, we averaged these vectors for each class to produce a typcal class 30 class test sample T = 1/30å a. The values of the = 1 class components of T are consdered to be typcal for the values of the class. For classfcaton the ordered feature vector v = ( v1,..., v49) of a pxel p s compared to the typcal class test samples T and a grade of membershp s computed wth the formula 1 class m ( p, class) d( v, T ), 1 class' d( v, T class ' ) whch s nterpreted as smlarty of the pxel to the class. Ths s the fuzzy output for a pxel. Defuzzyfcaton wth the rule p s of class k f m( p, class k) m( p, class ) for all and m( p, class k) t, where t s a classfcaton threshold, leads to a crsp classfcaton. For more detals to our fuzzy classfcaton please refer to [4]. Up to now supervsed classfcaton s appled, however, future studes wll consder automatc refnng of the search patterns to compensate varyng data take condtons. The classfcaton map assgns one basc class to each pxel n tme doman. Data compresson tself takes place n transform doman. Therefore, a sgnfcance map has to be evaluated, whch ndcates relevant coeffcents n transform doman and allocates the number of bts for ther quantzaton. Accordng to the flter length L of the wavelet transform more coeffcents have to be quantzed and transmtted than the number of foreground pxels. In the worst case, nstead of one sngle pxel L 2 coeffcents n all four subbands are necessary to reconstruct the pxel wth the desred qualty. The more pxels of one class are n a closed regon and the shorter the flter length the less dsadvantageous s ths effect. In our approach the same sgnfcance map s used for all subbands. If more teratons of wavelet transform or wavelet packets are employed, sgnfcance maps for all subbands have to be evaluated. Advantageously, the effort wll be small, due to the herarchcal structure of the wavelet decomposton and can follow the wellknown strateges for zero-tree assgnment [15] [18]. Probably, optmzaton wll be possble to mnmze the number of sgnfcant coeffcents n the hgher decomposton levels. Josh et al. [10] and Yoo et al. [19] descrbe another approach for classfcaton dependent compresson and the achevable gan. Here, classfcaton does not mean assgnment of physcal object classes, but assgnment of dfferent data classes, accordng to ther statstc. However, to gan the hgh adaptablty to the user requrement, class assgnment to physcal object classes s necessary. Advantageously, data belongng to one object class have smlar statstc and thus necessary parameters for optmal quantzaton are easer to choose. Up to now, we splt these classes also n small data blocks as n FLECS standard mode for two reasons: Smlar desgn for all modes makes decompresson easy, whch wll take place at the clent; data statstcs are too heterogeneous for a sngle quantzer. Optmzaton of the pre-classfcaton wth respect to data compresson can lead to mproved results Server-Clent-Lnk The followng strategy wth seven steps s suggested. 1. At the server, the mage s stored n wavelet doman, already decomposed nto bt planes, whch allows transmsson of ordered bt planes (see step 6), plane after plane, accordng to the requred performance. 2. The clent asks for a data set.

6 3. Frst, he gets the classfcaton map requrng a mnmum number of bts. The classfcaton map can be used by the clent to dentfy whether the correct data set s selected parts of the data set for further transmsson classes of nterest and background requred qualty for regons of nterest and background. 4. Ths nformaton controls further data compresson and s sent to the server. 5. Based on ths nformaton and the classfcaton map sgnfcant coeffcents n wavelet doman are assgned. The approprate number of bts for quantzaton s selected. 6. A bt stream s formed and sent to the clent. The arrangement of the bt stream ensures contnuously mprovement of mage qualty, e.g. f n a second request the clent wants for one class a hgher qualty, only the mssng bts are transmtted. 7. The classfcaton map sent n the begnnng serves as header nformaton for the decompresson step at the clent. Fgure 5 shows a SAR ntensty mage wth 32 bts per element and below the accordng classfcaton map (5 basc classes). Three bts per element are used n our smulaton. Here, entropy codng could be added and wll reduce the data rate sgnfcantly. Server classfcaton map look up table qualty bt allocaton mage (part of) data set; foreground & background clent select sgnfcant coeffcents qualty requrements for foreground & background reconstructed data assgn approprate number of bts WVT -1 form bt stream of quantzed coeffcents Decoder Fgure 4: Server-Clent-Lnk wth strategy for progressve transmsson startng wth a classfcaton map Parts of ths mage are used n the followng examples: In example 1 (Fgure 7a) roads and arfelds (smooth surface) are classes of nterest. The compresson algorthm compresses and transmts only the coeffcents relevant for reconstructon of these classes. These coeffcents are decoded and the nverse wavelet transform s performed. The reconstructed coeffcents replace the classfcaton map for all pxels belongng to smooth surface. Ths means, for ths class any sophstcated further evaluaton can take place, background nformaton

7 here the classfcaton map of the remanng classes serves only for localzaton. Example 2 (Fgure 7b) shows a smlar case but now forest s consdered as foreground. In Example 3 (Fgure 7c) both background and foreground are reconstructed. However, only 1 bt per element s used for background. Foreground s transmtted wthout any measurable loss (no further compresson n the second step). The resultng mage looks much lke a common SAR mage, automatc classfcaton and vsual nterpretaton s even possble on all background regons, detaled analyss of the complex data s addtonally possble on the foreground. Fgure 6 shows the performance of the extended FLECS. Of course, wth an ncreasng rato between the percentage of foreground to background, the overall compresson rato drops down. The performance converges to the compresson rato wthout mage contents adaptaton, however t does not get worse than the results wthout any adaptaton. smooth surface urban low vegetaton medum vegetaton forest Fgure 5: SAR ntensty mage and classfcaton n basc classes SDNR n [db] all classes transfered classes 4+5 only rms phase error n [ ] ,75 3,5 5,25 7 compresson rato compresson rato Fgure 6: Performance FLECS extended by adaptablty to mage contents

8 a) foreground: smooth surface (20bpe) b) foreground: forest (20 bpe) c) foreground (smooth surface and forest): 20bpe, background: 1 bpe Fgure 7: Image content dependent compresson and transmsson, a) and b) only foreground elements are reconstructed, c) both background and foreground are reconstructed but wth dfferent reconstructon qualty and data rate 4 DISCUSSION In ths paper we showed a general approach for adaptve data compresson servng the needs of system desgn and user requrements. The resultng compresson rato and performance are not yet optmzed. Ths s ether subject of an operatonal mplementaton or future studes: Addng entropy codng to compress the classfcaton map and the quantzed coeffcents wll reduce the data rate wthout addtonal loss. The technology s state of the art and can be mplemented n operatonal desgn As Shapro et al [15] show, successve approxmaton quantzaton nstead of smple bt plane transmsson leads to reduced quantzaton dstorton. More teratons of wavelet and decomposton n wavelet packets promse sgnfcant mprovements. A better energy compacton s possble and the energy concentrated n medum frequency bands can be extracted. Due to the rapd development of technology, (e.g. CWIC descrbed by Schaefer et al. [14]) mplementaton even onboard the satellte can be envsaged and can be therefore consdered for STEP 1 compresson. Integraton n our module s n progress and results wll be shown n followng publcatons. Man advantage out of ths fner decomposton wll be acheved, f a vector quantzer or trells-coded vector quantzer [9] exchanges the lnear quantzer. It wll allow fractons of bts per sample, t s more effectve than the scalar quantzer n parttonng the data space and makes a better adaptaton to the statstcs of wavelet coeffcents of hgh resoluton

9 SAR mages possble (compare also studes from Antonn et al [2]). An nterestng research topc n future wll be a class dependent quantzaton. We expect sgnfcant mprovements, because the detected basc classes are characterzed by ther statstc. The better the quantzer s adapted to a statstc, the better the results wll be. For each class there wll be a optmzed quantzer. The selecton of the decoder at the clent can be based on the classfcaton map. No addtonal header wll be necessary. Up to now, problems are stll the large heterogenety wthn one class whch requres further parttonng nto small blocks. Pre-classfcaton has to be optmzed wth respect to data compresson. 5 CONCLUSION Synthetc Aperture Radar provdes nformaton for the remote sensng communty, whch s complementary to optcal sensors. However, data rate and amount of data exceed the capacty of usual data lnks and storage devces by far. SAR data compresson s necessary to ensure effcent use of acqured data and processed mages. Here, we proposed a two-step data compresson: Frst a nearly lossless compresson at the sensor, whch does not nfluence any applcaton but at least trplcates the amount of transmttable data. Second, an mage content adaptve compresson whch accommodates the user requrements. Ether a homogeneous dstorton s realzed or only relevant parttons or classes of the data set are transmtted to reduce the data rate sgnfcantly. The presented results are nether optmzed n terms of mage reconstructon qualty nor n terms of mnmum compresson rato. The am of ths study was to show the ablty and the possble gan by splttng data compresson n mage ndependent and mage dependent compresson. The addtonal computatonal requrements for edge detecton and classfcaton are only moderate and can be easly performed on the ground staton server network. No expensve space qualfed hardware s necessary and no addtonal computatonal power s requred at the clent. The suggested algorthms for edge detecton and classfcaton base on fuzzy systems, whch possess a hgh robustness for slghtly varyng parameters. 6 REFERENCES [1] Ancs, M., Murron, M., Gusto, D., "Regon- Based Remote-Sensng Image Compresson n the Wavelet Doman", Proc. of IGARSS 99, vol. 4, pp [2] Antonn, M., Barlaud, M., Matheu, P., Daubeches, I., "Image Codng Usng Wavelet Transform", IEEE Trans. on Image Processng, vol. 1, no. 2, Aprl 92 [3] Benz, U., Fscher, J., "Adaptve SAR Image Compresson n Wavelet Doman", Proc. of EUSAR 2000, to be prnted [4] Benz, U., Jäger, G.: "Multchannel Classfcaton of SAR-Images Usng Fuzzy Logc", Proc. 4 th. Int. Arborne Remote Sensng Conference, Ottawa, Ontaro, Canada, Vol. II, , 1999 [5] Buccgross, R., Smoncell, P., "Image Compresson va Jont Statstcal Characterzaton n the Wavelet Doman", IEEE Trans. on Image Processng, vol. 8, no. 12, 1999 [6] Dmou, Jäger, G., Benz, U., Makos, V., "A fuzzy edge detector for SAR mages", Proc.3 rd EUSAR, 2000, pp [7] Donoho, D.L,"De-nosng va Soft-Thresholdng", IEEE Trans. Inform. Theory, vol. 41, no. 3, 1995,pp [8] Fscher, J., Benz, U., Morera, A., ScanSAR Image Compresson Usng Wavelets, [9] Fscher, T., Marcelln, M., Wang, M., "Trells- Coded Vector Quantzaton", IEEE Trans. on Informaton Theory, vol. 37, no. 6, 1991., pp [10] Josh, R., Jafarkhan, H., Kasner, J., Fscher, T., Farvardn, N., Marcelln, M., Bamberger, R., "Comparson of Dfferent Methods of Classfcaton n Subband Codng of Images", IEEE Trans. on Image Processng, vol. 6, no. 11, 1997 [11] Karvonen, J. Smlä, M., "Wavelet-Based Vsual codng of Sea Ice SAR Images", Proc. of IGARSS 99, vol. 4, pp [12] Keller, J.M., Gray, M.R., Gvens, J.A.: "A Fuzzy K-Nearest Neghbor Algorthm", IEEE Trans. Syst., Man, Cybern., vol. 15, no. 4, pp , 1985 [13] Odegard, J., Guo, H., Lang, M., Burrus, C.S., Wells, Jr, R.O., Novak, L.M., Hett, M., "Wavelet Based SAR Speckle reducton and Image Compresson", SPIE Proc. Aprl 95, Orlando, Fl. [14] Schaefer, C., Krahn, E., "Constant-Rate Wavelet- Based Image Compressor (CWIC)", Proc. of IGARSS 99, pp. [15] Shapro, J., "Embedded Image Codng Usng Zerotrees of Wavelet Coeffcents", IEEE Trans. on Sgnal Processng, vol. 41, no. 12, 1993 [16] Vllasenor, j., Belzer, B., Lao, J., "Wavelet Flter Evaluaton for Image Compresson", IEEE Trans.

10 on Image Processng, vol. 4, no. 8, 1995, pp [17] Werness, S., We, S., Carpnella, R., "Experments wth Wavelets for Compresson of SAR Data", vol. 32, no. 1, 1994, pp [18] Xong, Z., Ramchandran, K., Orchard, M., "Space-Frequency Quantzaton for Wavelet Image Codng", IEEE Trans. on Image Processng, vol. 6, no. 5, 1997 [19] Yoo, Y., Ortega, A., Yu, B.: "Image Subband Codng Usng Context-Based Classfcaton and Adaptve Quantzaton", IEEE Transactons on Image Processng, vol. 8, no. 12, 1999, pp [20] Zyl, J., Burnette, C., "Data Volume Reducton for Sngle-Look Polarmetrc Imagng Radar Data", IEEE Trans. on Geosc. & Remote Sensng, vol. 29, no. 5, 1991, pp Vew publcaton stats