WIDE-ANGLE ISAR PASSIVE IMAGING USING SMOOTHED PSEUDO WIGNER-VILLE DISTRIBUTION. Yong Wu and David C. Munson, Jr.

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1 IDE-ANGLE ISAR PASSIVE IMAGING USING SMOOTHED PSEUDO IGNER-VILLE DISTRIBUTION Yong u and David C. Munson, J. Coodinated Science Lab and Depatment of Electical and Compute Engineeing, Univesity of Illinois at Ubana-Champaign, Ubana, IL, 68 yongwu@uiuc.edu, d-munson@uiuc.edu ABSTRACT e ae investigating passive ada imaging of aicaft using eflected TV signals. UHF-band ISAR imaging equies wide-angle data to poduce good coss-ange esolution. e show that diect Fouie econstuction (DFR causes degadation of the econstucted image due to aspect-dependent scatteing. e find that a Smoothed Pseudo igne-ville distibution (SPVD applied in the coss-ange diection in place of the Fouie tansfom can geneate a sequence of images, which shows the taget eflectivity as a function of aspect angle. Compaed to DFR esults, these images have highe coss-ange esolution. A final image can be synthesied fom these images and used fo taget ecognition. XPATCH is used to simulate monostatic data fom an aicaft. The poposed SPVD-based imaging method poduces a useful image of the aicaft fom this data.. INTRODUCTION e ae investigating passive ada imaging of aicaft using eflected TV signals. In elated wok, Lockheed Matin has developed the system which can detect and tack tagets using eflected adio o TV signals [. e ae inteested in foming images of aicaft fom passive data, fo the pupose of classification. Conventional X-band ISAR imaging systems opeate aound GH and use a small synthetic apetue (e.g. 3 degees to collect data. e conside a passive ada system that opeates aound 6 MH, which is a fa lowe fequency than X-band. Theefoe, a much wide apetue is needed to povide simila coss-ange esolution. In a wide apetue scenaio, the taget s scatteing is aspect-dependent (micowave specula eflection and cone/edge diffaction ae all aspect-dependent [2, 3, which will cause poblems in diect Fouie econstuction (DFR. This wok is suppoted by DARPA unde the contact numbe F e show that, fo two point tagets, the econstucted image using DFR will be blued if the scatteing changes with aspect. A possible solution is the sub-apetue appoach: divide the wide apetue into seveal smalle sub-apetues and fom a sub-image using each sub-apetue. A final image can be synthesied fom these sub-images. Obviously, the image esolution will suffe. Time-Fequency (T-F tansfoms have been used in moving taget ISAR imaging [4. Hee, we apply a T-F tansfom in the coss-ange diection to eplace the Fouie tansfom, since the scatteing changes with aspect angle. In fact, the sub-apetue appoach is simila to pocessing the wide-angle data using the Shot Time Fouie Tansfom (STFT in the coss-ange diection and the Fouie tansfom in the ange diection. e find that, if the Smoothed Pseudo igne-ville distibution (SPVD is used in the coss-ange diection to eplace the Fouie tansfom, a sequence of images can be obtained that show the eflectivity as a function of aspect angle and have highe coss-ange esolution than sub-apetue o STFT appoaches. These images can be combined to synthesie one final image, which is close to the optical appeaance of the aicaft and easily ecogniable. XPATCH is used to geneate monostatic data which is used to test ou algoithm. It is demonstated that the SPVD-based image fomation method is supeio to sub-apetue and STFT-based appoaches. 2. DFR ITH ASPECT-DEPENDENT SCATTERING e fist conside DFR fo the econstuction of an image fom Fouie data collected on pola gid [, 6. The Fouie data equie intepolation to a ectangula gid followed by a 2D FFT to poduce the image. Conside two point tagets at and, with

2 eflectivity $# & # '(*+ The Fouie tansfom is 234(# 768:9<;=>@?BACD>E &,'(-. 76F8:9G;=HI?BAC:HIE / ( / (2 If the two points scatteing data vaies with aspect, then the collected data is this Fouie tansfom, weighted in the 2 diection accoding to aspect dependence. Hee, we assume that 2 is the Fouie coodinate coesponding to coss-ange. Futhemoe, assume that the aspect-dependent weighting has the fom JK2L# 69<;M6NEO, whee 2P#RQTS, Q is a constant, S is the aspect angle and U(VMQ is the aspect angle having maximum eflection. The weighting function is bell-shaped and is chosen fo mathematical tactability. The collected data becomes 6F8:9G;= >?BAC > E 6&9G;76LN > EO 68:9G;= H?BAC H E 69G;76LN H EO 234(# / (3 If the bandwidth available is wide and Fouie invesion is used, we get & YX & # '( '( Z =\[ 6=O 8@N > =^ 769G=M6= > EÖ 8@N > 9<=6L= > E 769G=M6= H EÖ 8@N H 9<=6L= H E Z =\[ 6=O 8@N H =^ / (4 In the diection, the ' functions ae spead out and the complex multiplie may cause cancelation of the two signals. To see this, suppose _#`. Then, if the two points ae vey 6&9G= > 6= H EO close, Xba, thus Xc'( [ ad 8@N HD9<= >:6=^H E Now, if 8@N H 9G= > 6= H E #b\a (which is possible, Moe geneally, / ( 7 X_e. $X '( 6&9G=M6=>IEO 8@N> 9G=M6=>E [ ad 8:f 9<N H6LN>gE=?N>=>6N H =^Hih / (6 The function & might become vey noisy, since the tem [ aj 8:f 9kN HD6N>E=?N:>=>6LN H =^Hih might vay fom e to l apidly. Hence, it may be impossible to even detect the two point-tagets, and the esulting image quality may be seveely degaded. This analysis can be extended to moe point tagets fo an aicaft scatteing-cente model, suggesting that DFR applied to wide-angle data may degade image quality. 3. SUB-APERTURE APPROACH A wide-angle apetue can be divided into seveal smalle sub-apetues with the eflectivity assumed constant acoss each sub-apetue. DFR applied to individual sub-apetues yields a set of images. Since the micowave scatteing is highly aspect-dependent, only a subset of scattees of the taget actually appea in each obseving sub-apetue. This is diffeent fom optical imaging of aicaft [7. Reconstucted images fom seveal sub-apetues can be combined togethe to yield one final image which may show moe scattees of the taget and may be close to the optical image. A suggested algoithm fo image synthesis fom subapetues is: Fist nomalie each sub-apetue image so that the maximum is and minimum is ; then otate these subapetue images so that the taget has the same oientation in each image; assign to each pixel in the synthesied image the maximum of the coesponding pixel values in the subapetue images. Symmety enhancement has been suggested by Steinbeg [7 to impove the quality of ada images of aicaft, since aicafts ae symmetic. In ou algoithm, the maximum magnitude of the two symmetic pixels of the image is taken as the value fo both pixels. This will give a moe ecogniable image fo a human obseve. The disadvantage of the sub-apetue appoach is that it is difficult to choose a suitable sub-apetue width: to get good aimuth esolution, the subapetue should be lage, but then the eflectivity may change significantly acoss the subapetue and the image will be smeaed; if the subapetue is too small, the aimuth esolution will be poo and the image quality will be degaded. 4. IMAGE FORMATION BASED ON STFT AND VD As the eflectivity pofile of the taget changes with aspect angle, the Fouie data collected ove a lage aimuth inteval will be time-vaying (hee time efes to the aspect. e can apply a Time-Fequency (T-F tansfom in the aimuth diection to eplace the Fouie tansfom to poduce a sequence of instantaneous images [8. T-F tansfoms have been applied to moving taget imaging using the angedopple appoach[4. The Shot Time Fouie Tansfom (STFT is a simple T- F tansfom that can be used. In ou poblem, the STFT is defined as m m 2&g # a ln oqp 6 ps tf uvtw.2 8g= xmy t (7 whee 2L is the Fouie data in the coss-ange diection and uj2l is a shot-time window function. The STFT has

3 } a a t l } y y poo coss-ange esolution fo a naow window and is simila to sub-apetue pocessing with the same window width. The igne-ville Distibution(VD has highe time and fequency esolution than the STFT. e define the VD in ou poblem as 23# o p 6 p 2{ t l 8g=x y l^n ^ 2- t/ (8 The VD of the sum of two signals M is 2LL } 2Lg# g 23& }g} 23L,lM~ 2&gD / The coss-tem 23 can be suppessed by using the Smoothed Pseudo igne-ville distibution (SPVD, which is defined as bƒ\ o p o p 2&g$# l^n 6 p 6 p 2-.2 kˆ&w. < bƒj 2L g Š 2L i/ (9 and ˆ& ae the smoothing window functions (e.g. whee Hamming windows. The SPVD allows the smoothing spead in 2 and to be adjusted independently of each othe. Thus it can have bette time-fequency esolution than the STFT, which equies a tadeoff between the spead in 2 and [9. Fo the two point-taget model, we assume aspect weighting functions J\2L # 6 Œ Ž 7 >@ O > 6 Œ Ž 7 Hg O and JjM2 # H, whee : indicates the pulse width of each weighting function in the Fouie data. Then the collected data becomes 2&g4T# 68:9G;=>g?BACD>gE J 2L( 6F8:9G;=HI?BAC:H E JjM2/ ( Applying the VD to the weighted data in the 2 diection, we get the econstucted image i B & 2#R wš l^n&v [ * bœlk 2+ [ K. : Ÿœl ^2+ Z = 6 > = O 6 O O }@ > 9G;76N>EO *š l^n&vm [ w l{ 2. [ K.L : Ÿœl ^2+ Z = 6 HI= O 6 O O }@ H 9G;76N H EO ^ I / ( whee Z = indicates convolution in, B2 ª Vl, is the bandwidth in the coss-ange diection. The coss-tems can be suppessed by the SPVD, which convolves Eq. ( with the window functions in the 2 and diections. Thus a sequence of images is poduced fo diffeent values of 2 : g2l# [ g2lbz ; 2 Z = ˆ&L/ (2 e can model a set of scattees with aspect-dependent eflectivity as gs7#$«g i'(*+ 6 Œ 7 O ± / (3 is the numbe of scattees, indicates the pulse width of the scatteing pofile in S and SM is the oientation having maximum eflection. The sequence of images poduced by the SPVD (assuming coss-tems have been suppessed is: whee ² i 2# [ d«i w³ l^n [ < w Ÿ lk 2. [ K+ bœlk 2+ Z = 6 }D = O 6 O O 9G;76N E O BZ ; 2L Z = ˆ&L (4 Hee is the econstucted eflectivity as a function of aspect angle (2µ#`QTSgU #`QTS, Q is a constant. Since the SPVD is eal and positive, the aspect-dependence does not poduce a complex multiplication tem in the esult, thus avoiding the cancelation of neighboing points. This also ensues that only the subset of scattees visible at a cetain aspect ae shown in the coesponding instantaneous 6 Oi image O (popely weighted by the weighting functions 9<;M6N EO. Intefeence between adjacent scattees is avoided. The SPVD suppesses coss-tems in VD, but the esolution is also educed. Most of the images fom the SPVD have highe esolution than those poduced by the STFT using the same data. (Fo some images with 2 close to {Vl, esolution in becomes poo and these images ae not used to synthesie the final image. The final synthesied image can show moe clealy the shape and eflectivity of the taget. Hence it might be vey useful fo taget ecognition puposes. The SPVD-based image fomation algoithm is descibed by the flow chat in Figue. Fo a vey-wideangle data, this algoithm can be used to pocess data in seveal Me -wide subapetues (with et¹ ovelap and poduce seveal synthesied images, which can be combined into one final image using the image synthesis algoithm.. SIMULATIONS USING XPATCH DATA Testing of ou image fomation algoithm is simplified by using synthetically geneated aicaft signatues. Among the pime tools fo doing this, XPATCH loses accuacy below about GH and the Fast Illinois Solve Code (FISC is vey demanding in tems of both computation and memoy. Thus, to assist in ou peliminay investigations, we have used XPATCH to geneate L-band data at fequencies -. GH. e expect that ou study based on this data will help in undestanding wide-angle ISAR imaging at UHF fequencies (4 MH - 8 MH. e simulated monostatic ada echoes fom an X29 ai-

4 Intepolate data on pola gid to ectangula gid Apply FFT in ange diection Apply SPVD in coss-ange diection to geneate a sequence of images Combine images into a final image Apply symmety enhancement fo viewing Fig.. Flow chat of the SPVD-based image fomation algoithm caft. The data was simulated fom et to aºme (e7 at nose,» e at boadside, and ä º7e at tail, e elevation. The fequency step was 6 MH and the aimuth step was.3 degees. HH polaiation was used. Figue 2 shows an optical image of an X29 aiplane. Figue 3 shows the log of magnitude of the Fouie data. Figues 4 and show the image fomed using all of the data via DFR and the esult afte symmety enhancement, which shows only the fuselage (wings ae missing. Figues 6, 7 and 8 show the image poduced by combining seveal sub-apetue images fom DFR, whee each sub-apetue is 6, and 7. degees wide, espectively, with ovelap. The shape of the plane is oughly visible. Figue 9 shows the esult given by STFT pocessing, which shows moe scattees on the body of the plane, but with even lowe esolution. A wide hamming window was used in the STFT pocessing. Figue shows the esult given by the SPVD, with bette esolution than the pevious images. Note that the font pat of the aicaft is cleae and the two inlets and the fuselage ae shown moe clealy in Fig. ( they ae smeaed all togethe in Figs. 7, 8 and 9. Fig. 6 doesn t show the wings and the font pats of the plane as clealy. All scatteing centes ae spead out moe by the naow sub-apetue and STFT methods, with the imagey degaded compaed to the SPVD. This suggests that SPVD-based image fomation is supeio to the DFR subapetue method fo aspect-dependent imaging using wideangle L-band data. e believe that this same obsevation will hold in the UHF band. 6. CONCLUSION e studied the wide-angle ISAR passive imaging poblem. The DFR method was shown to cause degadation in the econstucted image fo two point tagets when the scatteing vaied with aspect. The sub-apetue appoach is less than ideal, since it cannot guaantee good coss-ange esolution and small degadation caused by aspect-dependent scatteing simultaneously. e showed that, if the SPVD is used in the coss-ange diection to eplace the Fouie tansfom, a sequence of images can be poduced which show the eflectivity as a function of aspect. These images have highe quality and bette coss-ange esolution than those poduced by the DFR and sub-apetue methods. They can be combined togethe to yield one final image, which is close to the optical image. Simulation esults using XPATCH data was given to validate ou appoach. e expect that the SPVD-based image fomation method might be useful in the UHF-band fo ISAR imaging and taget classification. The XPATCH data set we used, howeve, is at a highe fequency and is moe complete than could be obtained in a ealistic passive scenaio. Thus consideable futhe study is needed. 7. REFERENCES [ Lockheed Matin web page,. [2 M. J. Gey and L. C. Potte, A paametic model fo synthetic apetue ada measuements, IEEE Tans. Antennas Popagat., vol. 47, no. 7, pp , July 999. [3 C. C. Chen and H. C. Andews, Multifequency imaging of ada tuntable data, IEEE Tans. Aeosp. Electon. Syst., vol. AES-6, no., pp. 22, Jan 98. [4 V. C. Chen and S. Qian, Joint time-fequency tansfom fo ada ange-dopple imaging, IEEE Tans. Aeosp. Electon. Syst., vol. 34, no. 2, pp , Ap 998. [ J. L. alke, Range-dopple imaging of otating objects, IEEE Tans. Aeosp. Electon. Syst., vol. AES-6, no., pp. 23 2, Jan 98. [6 D. C. Munson J., J. D. O Bien, and. K. Jenkins, A tomogaphic fomulation of spotlight mode synthetic apetue ada, Poc. IEEE, vol. 7, no. 8, pp , Aug 983. [7 B. D. Steinbeg, Micowave imaging of aicaft, Poc. IEEE, vol. 76, no. 2, pp , Dec 988.

5 [8 L. Cohen, Time-fequency distibutions - a eview, Poc. IEEE, vol. 77, no. 7, pp , Jul 989. [9 F. Hlawatsch and G. F. Boudeaux-batels, Linea and quadatic time-fequency signal epesentations, IEEE SP Magaine, pp. 2 67, Ap 992. Fig. 2. An optical image of an X29 aicaft ange (m coss ange (m Fig.. Image poduced by DFR using full-apetue data afte symmety enhancement. Fig. 3. Log of magnitude of the Fouie data simulated by XPATCH ange (m ange (m coss ange (m coss ange (m Fig. 4. Image poduced by DFR using full-apetue data. Fig. 6. Synthesied image by DFR fom sub-apetue images, each sub-apetue width is 6 degees.

6 ange (m. ange (m coss ange (m coss ange (m Fig. 7. Synthesied image by DFR fom sub-apetue images, each sub-apetue width is degees. Fig. 9. Synthesied image by STFT fom instantaneous images, wide hamming window used ange (m coss ange (m Fig. 8. Synthesied image by DFR fom sub-apetue images, each sub-apetue width is 7 degees. Fig.. Synthesied image by SPVD fom instantaneous images.