THE quality of high-resolution synthetic aperture radar

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1 06 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO., FEBRUARY 05 A Resample-Based SVA Algorithm for Sidelobe Reduction of SAR/ISAR Imagery With Noninteger Nyquist Sampling Rate Tao Xiong, Associate Member, IEEE, Shuang Wang, Biao Hou, Member, IEEE, Yong Wang, and Hongying Liu Abstract A resample-based spatial variant apodization (SVA) algorithm for sidelobe reduction was studied for synthetic aperture radar (SAR) and inverse SAR (ISAR) imagery with a noninteger Nyquist sampling rate. The weighting function of every sample in the image domain was calculated with the sample and two adjacent noninteger samples. The noninteger samples were obtained by interpolation in the image domain using sinc function. With the proper selection of two noninteger samples, the monotonic property of the weighting function on each side of the sampling point was preserved. The unequivocal determination of sidelobe suppression was achieved for noninteger Nyquist sampled (NINS) SAR and ISAR imagery. In addition, the lower and upper boundaries of the weighting function under the cosine-on-pedestal condition were extended for further sidelobe suppression and main lobe sharpening. The algorithm was implemented and applied to NINS imagery that is simulated. The algorithm was then assessed for acquired SAR and ISAR images. Improved results have been qualitatively and quantitatively achieved in sidelobe suppression and main lobe sharping in comparison with an existing algorithm. Index Terms Inverse synthetic aperture radar (ISAR), noninteger Nyquist sampled (NINS) imagery, SAR, sidelobe reduction algorithm. I. INTRODUCTION THE quality of high-resolution synthetic aperture radar (SAR) and inverse SAR (ISAR) [] [7] images may be negatively affected when radar signals are collected from an area where numerous targets of strong radar return exist. The targets, for example, can be corner reflectors formed by buildings and streets, as well as metallic objects such as air conditioning units on rooftops and vehicles on surface roads in urban area. The targets are not only of strong main lobes but also of high sidelobes in radar returns. Visually, they are no longer any points on an image. Instead, they are brightand starlike Manuscript received August 30, 03; revised March 8, 04; accepted May 7, 04. This work was supported in part by Xidian University under Grant JB4030 and Grant K and in part by the Program for Cheung Kong Scholars and Innovative Research Team in University under Grant IRT70. T. Xiong, S. Wang, and B. Hou are with the Key Laboratory of Intelligent Perception and Image Understanding of the Ministry of Education, International Research Center for Intelligent Perception and Computation, Xidian University, Xi an 7007, China ( xtlmtb006@63.com). Y. Wang is with the Department of Geography, Planning and Environment, East Carolina University, Greenville, NC 7858 USA. H. Liu with the School of Electronic Engineering and the Key Laboratory of Intelligent Perception and Image Understanding of the Ministry of Education, Xidian University, Xi an 7007, China. Digital Object Identifier 0.09/TGRS crosses. In such cases, linear segments off the cross centers could overlap or shadow other targets, particularly weak targets spatially. Therefore, the entire imagery might be degraded because of the negative influence of the sidelobes of the strong targets. Sidelobe at low levels or sidelobe reduction is explicitly required in the application of SAR and ISAR imagery. There are two types of widely used methods to reduce sidelobes. One is the linear technique and is applied in the frequency domain before a final formation of a SAR or an ISAR image [], []. With weights in the frequency domain such as Hanning and Hamming weights, the sidelobes can be suppressed to a very low level. Unfortunately, due to a constant weight used, the main lobe is usually widened. The image resolution becomes coarse []. Thus, the linear technique may not applicable for high-resolution imaging. The other is the nonlinear technique that is typically called as the spatial variant apodization (SVA) [8] [6]. Of the SVA technique, different weighting functions for individual samples of the SAR or ISAR image are generated in the image domain. For each sample, the weight is calculated from the values of the sample itself and of two adjacent sample points. Under the cosine-on-pedestal condition, the lower and upper limits of the weighting function are typically from 0 to / [8]. The output is obtained from the combination of weight and three samples. The SVA of [8] is developed for integer Nyquist sampled (INS) SAR or ISAR data. Satisfactory results in sidelobe suppression are obtained in image processing of INS data. The algorithm [8] becomes a benchmark in sidelobe suppression (for INS radar imagery) because numerous derivative algorithms are studied [0] [] and all are assessed by the algorithm [8]. To increase the applicability of the INS SVA algorithm, Smith [3] successfully extends the algorithm to process noninteger Nyquist sampled (NINS) SAR or ISAR image. Promising results in sidelobe suppression have been achieved for most of the NINS images. Since then, Smith s algorithm [3] becomes a representative for the NINS SVA algorithm, and is widely used in the processing of NINS images. Several derivatives from Smith s algorithm are developed [4] [6]. However, as one closely examines imagery output from Smith s algorithm, some sidelobe effects could not be minimized. Analytically, the success of sidelobe suppression in INS SAR and ISAR data using the INS SVA algorithms [8] [] is attributed to the weighting function that is monotonic on either side of a sample point. In other words, the monotonic attribute of the two-side function helps unequivocally determine whether IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

2 XIONG et al.: SVA FOR SIDELOBE REDUCTION OF SAR/ISAR IMAGERY WITH NYQUIST SAMPLING RATE 07 Fig.. (a) Impulse response of. (b) Weighting function for one target. sidelobe suppression is needed or not. Unfortunately, after the extension of the INS SVA algorithms [8] [] to the NINS SVA ones [3] [6], the monotonic feature is not preserved. Thus, the unequivocal determination of sidelobe suppression cannot be accomplished for NINS SAR or ISAR data. Sidelobes at unacceptably high level could remain. The quality of SAR and ISAR data can be adversely affected. Therefore, the impetus is to develop a NINS SVA algorithm in which the monotonic property of weighting function should not be altered. Indeed, the property is kept in the proposed resample-based NINS SVA algorithm that consists of the following major steps. First, two values of adjacent noninteger samples of each related sample are selected and calculated using sinc interpolation. Then, the weight function for the sample is derived through minimization. Next, ranges of lower and upper limits of the weighting function are studied and expanded with the understanding of their roles played in suppressing sidelobes and sharpening main lobes. Then, the algorithm is implemented and applied in analyses of simulated and acquired SAR and ISAR data. Finally, in the performance assessment of the algorithm, benchmark algorithms of the INS SVA [8] and the NINS SVA [3] are implemented as well. Results from three algorithms are evaluated. II. SVA ALGORITHM A. Algorithm for INS SAR and ISAR Images For simplicity, the SVA [8] is discussed along -D data of one Nyquist sampled SAR/ISAR image. Let g SVA (n) be the nth sample of complex value of one row data after the processing of SVA with N elements or pixels and g SVA (n) I SVA (n)+ jq SVA (n). I SVA (n) and Q SVA (n) are the real and imaginary components of g SVA (n), respectively. One way to reduce sidelobes is to minimize I SVA (n) and Q SVA (n) separately [8]. As an example, the output of the real part can be written as I SVA (n) +w(n)[i(n ) + I(n +)] () where is the input of the real part. Therefore, the aim is to find w(n) such that I SVA (n) is minimized. Mathematically, with d I SVA (n) /dw(n) 0, w(n) is solved as w(n) I(n ) + I(n +). () Then, the output of the real part is [8], w(n) < 0 I SVA (n) 0, 0 w(n) + [I(n )+I(n +)], w(n) >. (3) (It should be noted that Q SVA (n) output of the imaginary part can be similarly obtained.) In the image domain, the discussed SVA can be understood using an INS sinc function. Under the INS case or one Nyquist sampled case as the simplest example, a single sinc function is initially considered. If there is only one target in the scene, can be expressed as sinc(n n 0 ) sin π(n n 0). (4) π(n n 0 ) In addition sin π(n n 0 ± ) sin π(n n 0 ). (5) Substituting (4) into (), one obtains w(n) I(n ) + I(n +) sinc(n n 0 ) sinc(n n 0 )+sinc(n+ n 0 ) (n n 0) (n n 0 ). (6) Graphically, the impulse response and the weighting function under the INS from one target are illustrated (see Fig. ). Clearly, on either side of n n 0, and w(n) are monotonic. When n n 0, the sample is within the interval of the main lobe [see Fig. (a)] [8] and w(n) 0 [see Fig. (b)]. Hence, with I SVA (n) in (3), the main lobe is not widened. When n n 0 >, 0 w(n) / [see Fig. (b)]. Thus, the sample falls inside sidelobes [see Fig. (a)]. Let I SVA (n) 0; therefore, the sidelobes are removed. From (6), one also has { lim w(n) n n 0 + (7) w(n) n n0 ± 0. Thus, w(n) cannot be greater than / when there is a single target. In the case of multiple targets, w(n) may be greater than /. The SVA still works, and the sidelobes are reduced to a very low level [8].

3 08 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO., FEBRUARY 05 Fig.. (a) Impulse response of. Weighting function for one target under a NINS case. W s B. Algorithm for NINS SAR and ISAR Images The SVA can suppress sidelobes well for the INS case [8], [9]. However, the algorithm might not be able to suppress the sidelobes completely under the NINS case although there is only one single sinc function. Under such case, the real part of the signal is sinc [W s (n n 0 )] sin πw s(n n 0 ) (8) πw s (n n 0 ) with 0 <W s <. In (8), /W s is the noninteger Nyquist sampling rate and is also called as the oversampling ratio [0]. Therefore sin πw s (n n 0 ± ) sin [πw s (n n 0 ) ± πw s ] sin [πw s (n n 0 )]. (9) Similar to (), the weighting function can be computed as w(n) I(n )+I(n+) sinc [W s (n n 0 )] sinc [W s (n n [ 0 )]+sinc [W s (n n 0 +)] (n n0 ) ] tan π[w s (n n 0 )] (n n 0 ). tan π[w s (n n 0 )]cos πw s (n n 0 )sin πw s (0) Equivalently to Fig., (8) and w(n) (0) are illustrated in Fig.. Different from the INS case, and w(n) are not monotonic on either side of n n 0 [see Fig. (a) cf., Fig. (a); and Fig. (b) cf., Fig. (b)]. In the example, the main lobe can be preserved without widening using () (3). However, the sidelobes may not be suppressed because some samples such as P at (n x n 0 )can be located inside the sidelobes [see Fig. (a)] and their related w(n) is less than zero. Therefore, when w(n) < 0 [see the first condition in (3)], I SVA (n). Values related to the sidelobes are unchanged, or the reduction of sidelobes is not done. III. RESAMPLE-BASED SVA ALGORITHM UNDER NINS CONDITION The monotonic property of w(n) is not held for a NINS SAR image as discussed above. Therefore, a new algorithm is proposed in which the weighting function is monotonic at either side of the sample point, and the algorithm should be applicable to the NINS case. A. Derivation for the Resample-Based SVA Algorithm Let n be the sample of interest. (n /W s ) and (n +/W s ) are two adjacent noninteger sample locations of n. Mathematically, the values of noninteger samples at (n /W s ) and (n +/W s ) for the single sinc function are { I(n /Ws ) sin[πw s(n n 0 /W s )] πw s (n n 0 /W s ) I(n +/W s ) sin[πw s(n n 0 +/W s )] () πw s (n n 0 +/W s ). To be concise, we only present one sinc function in the derivation. The developed algorithm works for multiple sinc functions, as shown in the analyses of simulated and acquired SAR and ISAR data. Numerators on the right side of () can be simplified as sin [πw s (n n 0 ± /W s )] sin [πw s (n n 0 ) ± π] sin [πw s (n n 0 )]. () At sample locations (n /W s ) and (n +/W s ), clearly, () is equivalent to (5). Similar to the SVA, w(n) in the proposed SVA algorithm is w(n) I(n /W s )+I(n +/W s ) sin πw s (n n 0 ) πw s (n n 0 ) sin πw s (n n 0 ) π[w s (n n 0 ) ] + sin πw s(n n 0 ) π[w s (n n 0 )+] W s (n n 0 ) Ws (n n 0 ). (3) As shown in Fig. 3, w(n) is monotonic in either left or right side of n n 0. In short, (3) is very similar to the weight function in the INS case (6). The monotonic feature of the weighting function is preserved. B. Resampling Operation for the Proposed SVA Algorithm Since values of I(n /W s ) and I(n +/W s ) cannot be obtained directly from radar signal parameters of SAR or ISAR,

4 XIONG et al.: SVA FOR SIDELOBE REDUCTION OF SAR/ISAR IMAGERY WITH NYQUIST SAMPLING RATE 09 Fig. 3. Weight function for the proposed resample-based SVA algorithm. a resampling or an interpolation operation is alternatively used. Interpolation can be implemented using convolution [] I(n /W s ) + [I(n p)δ( /W s p)] p I(n +/W s ) + (4) [I(n p)δ(/w s p)] p where δ( ) is an interpolation function []. Although many interpolation (e.g., polynomial and cubic spline) functions exist [7], [8], a special and widely used interpolation function for a radar signal [] is used. The function is based on a sinc function. In particular, if a radar signal is sampled at discrete and evenly spaced intervals, the signal can be reconstructed without loss or error if the following conditions of Nyquist s sampling theorem are met []. The signal is band limited. The sampling satisfies Nyquist s sampling rule. A sinc function δ(n) sinc(n) sin(πn) (5) πn for the SAR or ISAR system always meets above two conditions. In addition, as a tradeoff between accuracy and computational efficiency, (4) is often approximated as [], [] I(n /W s ) I(n +/W s ) P p P P p P [I(n p)sinc( /W s p)] [I(n p)sinc(/w s p)] (6) and only (P +)samples are used to calculate I(n /W s ) and I(n +/W s ), respectively. Then, w(n) is derived as w(n) I(n /W s )+I(n /W s ). (7) Furthermore, two parameters, i.e., γ min and γ max (see Fig. 3), are introduced to help expand the range of cosine-on-pedestal condition. The output of the real part I RSVA (n) is exampled as I RSVA (n), w(n)<γ min 0, γ min w(n) γ max +γ max [I(n /W s ) + I(n+/W s )], w(n)>γ max. (8) The imaginary part Q RSVA (n) can be obtained in the same way. Therefore, the output using the resample-based SVA algorithm under the NINS condition is obtained. When γ min 0and γ max /, the range for the weighting function is the same as that of the weight function in [8]. As shown in Fig. 3, γ min is set to be less than zero. A negative γ min helps sharpen the main lobe because at the edge of the main lobe and with (3), one has w(n) W s (n n 0 ) Ws (n n 0 ) γ min. (9) Solving (n n 0 ), one obtains n n 0 ±. (0) W s γmin The width of the main lobe after the proposed algorithm is ( ) L. W s γmin W s γmin W s γmin () L decreases as γ min varies from 0 to a negative value. Thus, the main lobe is narrowed, or the resolution of the image is improved. Theoretically, the smaller the value of γ min is, the higher the resolution of the image could be. However, when γ min becomes too small, some energy within the main lobe from a target can be lost. As a result, the signal from the main lobe can be low. The signal-to-noise ratio is adversely impacted. If w(n) >γ max, γ max is used to replace w(n) in (8). As observed in the analysis of simulated and acquired images, w(n) >γ max occurs when multiple targets in the same scene exist. In such cases, a target or targets with the weak radar returns are covered by echoes of the sidelobes from one or multiple strong radar targets. The real part of the sample is δ r sinc [W s (n n r )] + N(n) r r δ r sin πw s (n n r ) πw s (n n r ) + N(n) () where there are R targets in the scene. δ r and n r are the magnitude and location for each target; N(n) is the possible unsystemic error. The output becomes I RSVA (n) +γ max [I(n /W s )+I(n +/W s )] δ r sinc [W s (n n r )] + N(n) r [ R + γ max δ r sinc [W s (n n r /W s )] r + δ r sinc [W s (n n r +/W s )] ] r + N(n /W s )+N(n +/W s ) δ r sinc [W s (n n r )] r + {sinc [W s(n n r /W s )] +sinc [W s (n n r +/W s )]} +ΔE(n) (3)

5 00 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO., FEBRUARY 05 with ( ΔE(n) γ max ) { R δ r sinc [W s (n n r )] r } + δ r sinc [W s (n n r +)] In addition r ( + γ max ) [N(n )+N(n+)]+N(n). (4) sinc [W s (n n r )] + {sinc [W s(n n r /W s )] sin πw s(n n r ) πw s (n n r ) sin πw s(n n r ) πw s (n n r ) [ + sinc [W s (n n r +/W s )]} + [ sin πws (n n r /W s ) πw s (n n r /W s ) + sin πw ] s(n n r +/W s ) πw s (n n r +/W s ) sin πw s (n n r ) πw s (n n r /W s ) + (n n r +/W s ) sin πw s(n n r ) /Ws πw s (n n r ) (n n r ) /Ws. (5) With substitution of (5) into (3), the output of the real part is I RSVA (n) r sinc [W s (n n r )] δ r Ws [(n n r ) /Ws +ΔE(n). (6) ] From (6), one also has (7), shown at the bottom of the page. Therefore, the output of (6) consists of two parts. In the first part, the impulse response becomes sinc[w s (n n r )]/ [(n n r ) /W s ]. The magnitude is nearly unchanged when n n r 0. Most of the main lobes are preserved. When n n r is far away from zero, the related magnitude is rapidly decreasing by dividing (n n r ) /W s. Thus, the sidelobes are suppressed. The second term in (6) is related to the noise of I(n /W s ),, and I(n +/W s ). With appropriate selection of γ max, the term can be minimized or the noise decreases to some extent. Unfortunately, the optimal parameter cannot be analytically obtained. Furthermore, energy from scatterers within the scene could be severely suppressed or become undetectable when γ max is too large. ] C. Implementation and Assessment of an Image Before and After Processing The resample-based SVA algorithm is implemented along the range direction first and then the azimuth direction. In addition, in the assessment of image quality after this algorithm, an image contrast is used. It is defined as C α max σ α (8) α max μ α α with μ α g normalized (α, β) σ α β max β max β β max [ β max ] (9) (g normalized (α, β) μ α ) β where g(α, β) is the image of the number of rows α max and the number of columns β max. α α max and β β max. g normalized (α, β) is g(α, β) after normalization. Normalization is needed in order to intercompare among the input image and output images from this algorithm and others used in comparison. Finally, the higher the contrast value is, the better the image quality is quantitatively. IV. RESULTS A. Analysis of Simulated Data The proposed algorithm was first assessed using simulated -D SAR data [real part, Fig. 4(a)]. The expression of the data was I (n)+i (n) I (n) sinc [W s (n n )] (30) I (n) a sinc [W s (n n )] where 8 n 8, W s 0.67, n.35, n 4.85, and a.56. There were two targets of strong radar return or two NINS sinc functions I (n) and I (n). They were located at n.35 and n 4.85, individually. The width of each main lobe was.5 sample widths. Due to the sidelobe interference among targets, the main lobe of the first strong target was now centered at n.00, and the main lobe of the second strong target at n Thus, two centers were 3.00 samples apart. Peaks of sinc functions, as circled in Fig. 4(a), represented intensities of two main lobes, respectively. The main lobes might overlap that could lead to the ambiguity of two targets. sinc [W s (n n r )] lim n n r /W s (n n r ) /Ws sinc [W s (n n r )] lim n n r 0 Ws [(n n r ) /Ws ] sin [πw s (n n r /W s )] lim n n r /W s [πw s (n n r )] [(n n r ) /W s ][(n n r )+/W s ] lim n n r /W s (n n r )[(n n r )+/W s ] W s (7)

6 XIONG et al.: SVA FOR SIDELOBE REDUCTION OF SAR/ISAR IMAGERY WITH NYQUIST SAMPLING RATE 0 Fig. 4. (a) Simulated input data. Results after (b) the SVA and (c) this algorithm. Outside of the overlapped area, local maxima were sidelobes, as exampled by arrows [see Fig. 4(a)]. Thus, sidelobes were obvious. The first sidelobe (on the right side of the main lobe on the left) was about.63 db less than the value of the main lobe (on the left) and 3.5 db less than the value of the main lobe on the right. However, a commonly acceptable level of the first sidelobe should be approximately 0 db below the main lobe []. Thus, sidelobe reduction was needed. As suggested in [8], the INS SVA was applicable to NINS imagery with an increase in the upper limit. Here, the upper limit of w(n) was 0.75, and the lower limit was 0.0. Clearly, sidelobes greatly decreased, and the power of the first sidelobe was 5 db below the main lobe on the left [see Fig. 4(b)]. However, the overlapped area was nearly unchanged. Therefore, the SVA was unable to reduce the level of overlap. The cause for the inability was attributed to that the SVA was intended for an INS image but not for the NINS image. The data after the proposed algorithm were illustrated [see Fig. 4(c)]. With γ max 0.89, sidelobes were greatly reduced and the first sidelobes were about 35 db less than the main lobe. The overlapped area was removed. At γ min.3, the width of each main lobe became.6 sample widths. As compared with the width of 3.0 samples for each main lobe in the input, the main lobe was sharpened. (Width of each main lobe in Fig. 4(c) was much narrower than.6 sample widths, and the narrowness was caused by discrete sampling.) B. Analysis of Acquired SAR The SAR image was collected by an X-band system [see Fig. 5(a)]. The image was 048 (slant range) 4096 (azimuth) with the spatial resolution of m. Nyquist sampling rate was.5 times, and W s The image was an urban Fig. 5. (a) Input SAR image. Images after (b) the SVA and (c) this algorithm. area of Xi an, Shaanxi Province, China. Buildings and roads of different densities and sizes and with distinct row and column features were noticeable. Open space or fields were patched here and there. However, some parts of the image could be affected due to presence of point targets that are strong in backscatter. For instance, three bright starlike crosses were pointed by arrows [see Fig. 5(a)]. The crosses could be caused by corner reflectors of buildings and streets, metallic objects such as air conditioning units and vents on rooftops, or building edges that acted as strong point targets. Thus, other targets in the surrounding areas and of weak radar return could be covered by sidelobes of the strong ones. The contrast value of the image was.36. After being processed by the SVA [see Fig. 5(b)], the crosses became thinner and smaller. Thus, sidelobes were suppressed and their effect decreased. The quality of the processed image was quantitatively improved with the contrast value of However, there were numerous bright crosses in Fig. 5(b), particularly around areas indicated by two arrows. Incidentally, the lower and upper limits used for w(n) were 0 and 0.75, respectively. After being processed by the proposed algorithm, there were no obvious bright crosses in the SAR image [see Fig. 5(c)]. The reduction or disappearance of the crosses was due to the suppression of sidelobes of strong point targets to a very

7 0 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO., FEBRUARY 05 Fig. 6. Close-view images of three regions (by row). By column, SAR images as input, images after the SVA, and images after the proposed algorithm. low level. Furthermore, metallic edges of buildings became narrower (as exampled by three arrows) in Fig. 5(c) than those in Fig. 5(a) or (b). The contrast value was It should be noted that γ min.3 and γ max 0.89 were used. As previously discussed, the lower limit less than 0 and the upper limit greater than 0.75 for w(n) could not only further suppress sidelobes but could also sharpen main lobes. Because of the sharping in main lobes and sidelobe suppression, the equivalent signal strength in Fig. 5(c) decreased. Thus, Fig. 5(c) looked visually darker than Fig. 5(a) or (b). In short, there should be a tradeoff of image quality measured by the signal-to-noise ratio, as well as the sharping of main lobes and suppression of sidelobes. Therefore, γ min should not be too small, and γ max should not be too big. The determinations of both parameters were further studied later. To further discuss the performance of the proposed algorithm, three small areas were identified as regions I, II, and III [see Fig. 5(a)]. Each region is 5 (slant range) 5 (azimuth). In Region I, there was nearly lack of targets (or scatterers) that are of strong radar returns. Thus, effects from sidelobes of the strong targets could be minimal. No bright crosses were obviously noted in Fig. 6(a) (c). Their contrast values were given in Table I. Thus, the quality of images after the SVA and proposed algorithm was improved due to the increase in contrast values. In Region II, there was an increase in the number of strong targets shown as bright crosses [see Fig. 6(d)]. Most strong targets were far apart spatially except for two clusters (of strong ones). Although some crosses were converted as bright spots using the SVA, there were several crosses remained [see Fig. 6(e)]. Thus, the effectiveness of the SVA in TABLE I CONTRAST VALUES OF IMAGES IN THREE REGIONS sidelobe suppression decreased. After being processed by the proposed algorithm, all the crosses were nearly converted as bright spots [see Fig. 6(f)]. As quantified by contrast values (see Table I), the proposed algorithm performed the best in sidelobe suppression in Region II. Finally, there were significantly more strong scatterers or targets in Region III [see Fig. 6(g)], as compared with those in Region I [see Fig. 6(a)] and Region II [see Fig. 6(d)]. In addition, the targets were clustered and overlapped by each other [see Fig. 6(g)]. Areas of targets that are of low radar returns were severely contaminated by sidelobes of strong targets. The contrast value was.005 (see Table I). Fig. 6(h) was processed with the SVA. A majority of all crosses existed and were scattered around the image although the contrast value increased (see Table I). Thus, one could argue that the SVA did not suppress sidelobes well. Finally, using the proposed algorithm, there was significant reduction in the number of crosses [see Fig. 6(i)]. The contrast value became.908 (see Table I). In summary, the proposed algorithm and SVA were able to suppress sidelobes of strong targets and to increase contrast values. The proposed algorithm outperformed the SVA.

8 XIONG et al.: SVA FOR SIDELOBE REDUCTION OF SAR/ISAR IMAGERY WITH NYQUIST SAMPLING RATE 03 Fig. 7. (a) ISAR image. (b) Image after the SVA. (c) Image after this algorithm. C. Analysis of Acquired ISAR Data An ISAR image showing a Yak-4 airplane was recorded by a C-band ISAR experimental system [see Fig. 7(a)]. The image was 56 (slant range) 8 (azimuth) with the Nyquist sampling rate of.5 and W s The resolution was m. The image consisted of many individual strong scatterers. Effect of sidelobes was visible such as the formation of two horizontal and linear features. Additionally, there were noiselike spots scattered around. Due to these sidelobes and unexpected noise, the quality of whole imagery could degrade. The contrast value was After the SVA, the effect of sidelobes decreased to some extent [see Fig. 7(b)]. The nose and fuselage of the airplane became slightly thinner than those of Fig. 7(a). The noiselike spots around the fuselage disappeared mostly. The contrast value increased to Visually, it is still possible to improve the quality further [see Fig. 7(b)]. Finally, applying the proposed algorithm with γ min 0.56 and γ max 0.75, we observed substantial reduction in black spots and disappearance of two linear features [see Fig. 7(c)]. The image quality was improved because the contrast value was Again, one could conclude that the SVA and proposed algorithm suppressed sidelobes, whereas the performance of the proposed algorithm was better than that of the SVA by visual assessment and contrast values. D. Influence of γ min and γ max on an Output Image γ min and γ max play critical roles in the proposed algorithm. γ min helps reduce the width of a main lobe, and γ max is useful to suppress radar returns from sidelobes of strong targets. As illustrated in (8), both influence the output image. In addition, a contrast value has been used to assess the quality of an output image. An improvement in the quality is judged by an increase in the value. Thus, the contrast value varies as γ min and γ max change. When there are many strong targets, the image could be more or less homogeneous at a high level of intensity of radar returns. Thus, μ α is large but σ α could be small, as calculated row by row in (9). Thus, C (8) is small. As sidelobes of strong targets are suppressed and main lobes of the targets sharpened, the overall level of radar backscatter in the image decreases and so does μ α. Because the reduction of sidelobes and sharping of main lobes are local operations, the resulting image could be less homogeneous [e.g., Fig. 5(c) cf., Fig. 5(a); Fig. 6(i) cf., Fig. 6(g)]. Thus, an increase in σ α occurs very likely. C increases [as observed in Figs. 5(c), 6(c), 6(f), 6(i), and 7(c)]. However, as the suppression and sharpening continue, one should not only observe the further reduction of overall level of radar backscatter or μ α but also note that the image becomes more or less homogeneous again at a moderate or low level of intensity in radar returns. Therefore, C becomes small again. To support these arguments, or more importantly to evaluate the influence of γ min and γ max on resulting images, we will analyze the following. For the sake of simplicity in presentation, the ISAR image in Fig. 7(a) was studied. Output images with three sets of γ min and γ max were given (see Fig. 8). The range of γ min and γ max increased from Fig. 8(a) (c). The contrast value varied from.7965 [see Fig. 8(a)],.8000 [see Fig. 8(b)], to.5643 [see Fig. 8(c)]. The result was not only in agreement with above arguments but also indicated that a maximum or maxima existed for C as a function of (γ min,γ max ) or C f(γ min, γ max ). Therefore, one should use a pair or pairs of (γ min,γ max ) that maximize f(γ min,γ max ). Unfortunately, the search of analytical solutions of the pair or pairs was beyond the scope of this paper because f(γ min,γ max ) was too complicated. Alternatively, (γ min,γ max ) pair or pairs were empirically determined through trial and error. In other words, for the input ISAR image in Figs. 7(a), 8(b) or even 8(a) was equally acceptable as Fig. 7(c) because contrast values of the images were very close to each other. Finally, as demonstrated in Fig. 8(c), γ min could not be too small and γ max could not be too large. Otherwise, the image was degraded too much, and the airplane became unrecognizable. V. D ISCUSSION A. Comparison With Smith s Algorithm Smith s algorithm [3] is another popular NINS SVA method in sidelobe suppression. Since its inception, the algorithm has been considered as a benchmark in sidelobe suppression using

9 04 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO., FEBRUARY 05 Fig. 8. ISAR images after this algorithm. (a) γ min 0, γ max 0.75, andc (b)γ min., γ max.50, andc (c)γ min 4.48, γ max 6.0, andc Fig. 0. Regions (a) I, (b) II, and (c) III after Smith s algorithm. Fig. 9. Result from Smith s algorithm. noninteger Nyquist samples [4] [6]. In this paper, Smith s algorithm was implemented. With the simulated data [real part, Fig. 4(a)] as input to the algorithm, the output was shown in Fig. 9. Clearly, the sidelobes from sample 8 to sample and samples 6 8 were well suppressed. However, overlap between two main lobes existed. Thus, when targets were of strong radar return and close to each other, they could not be spatially separated due to the adverse interference of each other. Furthermore, if there were weak targets within the overlapped area, they could not be delineated either. Regions I, II, and III [see Fig. 5(a)] were also analyzed using Smith s algorithm. Visually, no bright crosses in Region I were observed after the algorithm [see Fig. 0(a)]. In Region II, crosses were mostly converted as bright spots but some remained [see Fig. 0(b)]. There were still scattered crosses although majority of them was changed into bright spots in Region III [see Fig. 0(c)]. Contrast values of three regions were.58 in Fig. 0(a),.065 in Fig. 0(b), and.95 in Fig. 0(c). In the reference of Table I, each contrast value, region by region, was greater than that of the input image or after the SVA but smaller than that after the proposed algorithm. In summary, although Smith s algorithm suppressed sidelobes of strong targets, the proposed algorithm outperformed Smith s algorithm. As the final comparison, the ISAR image [see Fig. 7(a)] was processed using Smith s algorithm [see Fig. ]. Due to the suppression of sidelobes, scattered spots such as noise decreased [see Fig. 7(a) cf., Fig. ]. Although some spots Fig.. ISAR image after Smith s algorithm. beyond the tail of the plane horizontally and below the fuselage existed, the airplane was clearly identifiable. The contrast value of Fig. was.759 that is smaller than.8004 of Fig. 7(c) after the proposed algorithm. B. Understanding of Smith s Algorithm Mathematically With the discussion above, the performance of Smith s algorithm is not at the same level as that of the proposed algorithm. Possible explanation is mathematically argued next. At samples

10 XIONG et al.: SVA FOR SIDELOBE REDUCTION OF SAR/ISAR IMAGERY WITH NYQUIST SAMPLING RATE 05 g(n), g(n W s ), and g(n + W s ), the output of one sample is obtained, where 0 <W s <. To calculate w(n) using g(n), g(n W s ), and g(n + W s ), one could, similar to the derivation of w(n) in (5), minimize g output (n) or I output (n) and Q output (n).(i output (n) is the real part of g output (n), and Q output (n) is the imaginary part.) Let I output (n) w(n)[i(n W s )+I(n + W s )]. (3) Then, after the minimization of I out (n), w(n) can be written as w(n) I(n W s )+I(n + W s ). (3) Equivalent to the proposed algorithm [from () (3)], one can calculate I(n W s ) and I(n + W s ) using sinc interpolation and has I(n W s ) + [I(n p)sinc( W s p)] p I(n + W s ) + (33) [I(n p)sinc(w s p)]. p The sum of I(n W s ) and I(n + W s ) is I(n W s )+I(n + W s ) + p [I(n p)sinc( W s p)+i(n p)sinc(w s p)]. (34) Since sinc( ) is an even function, sinc( W s p)sinc(w s +p). Thus I(n W s )+I(n + W s ) + p {I(n p)[sinc(w s + p)+sinc(w s p)]}. (35) With new index k ( k<+ ) I(n W s )+I(n + W s )sinc(w s ) + + k [I(n k)+i(n + k)] [sinc(w s k)+sinc(w s + k)]. (36) Hence, after the insertion of (36) into (3), w(n) is expressed in (37), shown in (38), at the bottom of the page. Similar to the INS SVA, the upper limit of w(n) is confirmed by lim w(n) and (38), shown at the bottom of the page. It should be noted that lim I(n k)+i(n + k)/ is expressed in (39), shown at the bottom of the next page. Therefore, (40) is expressed, shown at the bottom of the next page, with ζ πw s [sinc(w s )+sinc(w s +)] χ + (4) {[sinc(w s k)+sinc(w s +k)] cos πkw s }. k If ζ and χ 0, (40) becomes lim w(n) πw s. (4) sin(πw s ) πw s cos πw s Let γ min 0be the lower limit of w(n) and γ max πw s / [ sin(πw s ) πw s cos πw s ] be the upper limit, or 0 w(n) πw s sin(πw s ) πw s cos πw s. (43) This is the weighting function of Smith s algorithm [3]. In addition, the output of the real part is I output (n) w(n)[i(n W s )+I(n + W s )] [ w(n) sin πw ] s πw s w(n) I(n W s )+I(n + W s ) sinc(w s )+ + [I(n k)+i(n + k)] [sinc(w s k)+sinc(w s + k)] sinc(w s )+ + k k {[ I(n k)+i(n+k) ] [sinc(w s k)+sinc(w s + k)] } (37) lim w(n) lim sinc(w s )+ + sinc(w s )+ + k k {[ I(n k)+i(n+k) ] [sinc(w s k)+sinc(w s + k)] { [sinc(w s k)+sinc(w s + k)] lim } [ ] } (38) I(n k)+i(n+k)

11 06 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO., FEBRUARY 05 with + w(n) [I(n k)+i(n + k)] k [sinc(w s k)+sinc(w s + k)] [ w(n) sin πw ] s πw s κw(n)[i(n ) + I(n +)]+Δε (44) { κ sinc(ws ) + sinc(w s +) Δε χw(n)/. (45) C. Comparison With Two Other Approaches In addition to Smith s method, Castillo-Rubio et al. [9] and Yocky et al. [0] proposed two modified NINS SVAs to suppress sidelobes. The output of the real part of the method of Castillo-Rubio et al. was I C (m,n)aw sm W sn I(m, n) + w m W sm W sn [I(m,n)+I(m +,n)] + w mm W sm W sn [I(m,n)+I(m +,n)] + w n W sm W sn [I(m, n ) + I(m, n +)] + w nn W sm W sn [I(m, n ) + I(m, n +)] + w mn W sm W sn [I(m+p,n)+I(m,n+q)] p{,} q{,} (47) If κ and Δε 0, (44) is simplified as [ I output (n) w(n) sin πw ] s πw s + w(n)[i(n ) + I(n +)]. (46) This is Smith s algorithm [3]. Thus, extending the derivation scheme in the development of the proposed algorithm for sidelobe suppression, we have shown that Smith s algorithm can be derived as a special case here. Because ζ, χ 0, κ, and Δε 0cannot be always valid at locations where multiple strong targets are highly and locally concentrated [e.g., Fig. 7(g)], some sidelobes that are at unacceptably high level of intensity could still exist after Smith s algorithm. The invalidation was attributed as one of possible causes of the deficiency in Smith s algorithm. with a w m sinc(w sm ) w mm sinc(w sm ) w n sinc(w sn ) w nn sinc(w sn ) 4w mn sinc(w sm )sinc(w sn ) (48) where m and p are indices in the m-direction, and n and q areinthen-direction of an image. W sm and W sn are known constants. w m, w n, w mn, w nn, and w mm are weights unknown. Five weights are solved using a linear function in a 5-D space such that I C (m, n) is minimized [9]. This method could be generally interpreted as an extension of Smith s method from -D into -D. In [0], the output of the real part as an example was I Y (m, n) I(m, n)+w m Q m + w n Q n + w m w n P (49) with (50), shown at the bottom of the page. Q m, Q n, and P are obtained by interpolation. w m is within interval [0, /], and so is w n. Together, the intervals form a square with four corners sin πw s (n n 0 k) I(n k)+i(n + k) πw lim lim s (n n 0 k) + sin πw s(n n 0 +k) πw s (n n 0 +k) sin πw s (n n 0 ) πw s (n n 0 ) (n n 0 ) sin πw s (n n 0 )cos πkw s (n n 0 )cos πw s (n n 0 )sin πkw s lim [(n n 0 ) ] sin πw s (n n 0 ) cos πkw s (39) lim w(n) sinc(w s )+ + {[sinc(w s k)+sinc(w s + k)] cos πkw s } k πw s sin(πw s )+ζπw s cos(πw s )+χ (40) Q m I(m /W sm,n)+i(m +/W sm,n) Q n I(m, n /W sn )+I(m, n +/W sn ) P I(m /W sm,n /W sn )+I(m +/W sm,n /W sn ) +I(m /W sm,n+/w sn )+I(m +/W sm,n+/w sn ) (50)

12 XIONG et al.: SVA FOR SIDELOBE REDUCTION OF SAR/ISAR IMAGERY WITH NYQUIST SAMPLING RATE 07 of (0,0), (/,0), (/,/), and (0,/). To minimize I Y (m, n), Yocky et al. calculate I Y (m, n) at four corners. If one of the four I Y (m, n) s has the opposite sign with that of I(m, n), I Y (m, n) is set to zero. For all I Y (m, n) s of the same sign (positive or negative), the one of the smallest absolute value is chosen as the output. Thus, the sidelobe is suppressed. Different from Smith s algorithm and ours, two -D filters are used [9], [0]. As Stankwitz et al. [8] previously stated, the -D approach was fast in sidelobe suppression (in comparison with a -D approach in general). VI. CONCLUSION A novel SVA algorithm to handle INS SAR and ISAR images has been studied. With the appropriate selection of two adjacent noninteger samples, the weighting function became monotonic in both sides of the sample point or away from peak again. Whether sidelobe suppression was needed or not, it has been unequivocally determined for NINS SAR and ISAR imagery. In addition, the range of lower and upper limits of the weighting function was expanded to suppress sidelobes and to sharpen main lobes further. The algorithm was implemented in analyses of simulated and acquired data sets. In simulation studies, sidelobes were well suppressed, and widths of two main lobes narrowed after applying the proposed method. In addition, the overlapped area between two main lobes was removed. Thus, the two-side monotonic feature of the weighting function was invaluable in sidelobe reduction for NINS imagery through resampling operation. Then, acquired SAR and ISAR images were then processed using this algorithm. Overall, there was a significant reduction in sidelobes of strong targets because various bright starlike crosses were converted as points. The contrast value increased. To further assess the performance of the algorithm, we evaluated outputs from three closed-view areas where strong radar targets changed from a minimum number to a high number, and from spatially apart to highly concentrate. Since sidelobes were greatly suppressed, one actually could identify and count the number of bright crosses that are converted as bright points. In addition, metallic edges of buildings became narrower in comparison with those of the input image. Thus, the results were very promising quantitatively and quantitatively. Similar performance in sidelobe suppression and main lobe sharpening was achieved in the analysis of an ISAR image showing an airplane. The nose, wings, fuselage, and tail were clearly identified. As case-by-case comparisons, the proposed algorithm outperformed the INS SVA visually and quantitatively as measured by contrast values of imagery. As discussed, values of the lower limit γ min and upper limit γ max of the weighting function played critical role in the studied algorithm. The main lobe width has been analytically derived as a function of γ min.asγ min decreases, the width decreases. Thus, γ min was invaluable in narrowing main lobe. γ max was useful in sidelobe reduction. Due to the complicity, the derivation of the analytic relationship of the sidelobe suppression and γ max was believed to be beyond the scope of this paper. Alternatively, pairs of (γ min,γ max ) that can maximize contrast values were determined as empirically solutions, alternatively. Smith s algorithm has been popular in processing NINS imagery. The algorithm has been implemented. Outputs from this algorithm and Smith s one were assessed. Again, case by case, this algorithm outperformed Smith s algorithm. Finally, having developed this algorithm, we proved that Smith s algorithm was derivable as a special case using the derivation scheme for this algorithm and analytically explored possible cause or causes for the deficiency of Smith s algorithm in processing some NINS imagery. It was attributed that if ζ, χ 0, κ, and Δε 0were not valid simultaneously, Smith s algorithm could not suppress some sidelobes to a very low level. REFERENCES [] I. G. Cumming and F. H. Wong, Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation. Norwood, MA, USA: Artech House, 005. [] W. G. Carrara, R. S. Goodman, and R. M. Majewski, Spotlight Synthetic Aperture Radar: Signal Processing Algorithm. Boston, MA: Artech House, 995. [3] M. Soumtkh, Reconnaissance with ultra wideband UHF synthetic aperture radar, IEEE Signal Process. Mag., vol., no. 4, pp. 40, Jul [4] G. C. Sun et al., A unified focusing algorithm for several modes of SAR based on FrFT, IEEE Trans. Geosci. Remote Sens., vol. 5, no. 5, pp , May 03. [5] A. Ferro, D. Brunner, and L. Bruzzone, Automatic detection and reconstruction of building radar footprints from single VHR SAR images, IEEE Trans. Geosci. Remote Sens., vol. 5, no., pp , Feb. 03. [6] B. Zhang et al., Ocean vector winds retrieval from C-band fully polarimetric SAR measurements, IEEE Trans. Geosci. Remote Sens., vol. 50, no., pp , Nov. 0. [7] G. O. Glentis, K. X. Zhao, A. Jakobsson, and J. Li, Non-parametric highresolution SAR imaging, IEEE Trans. Signal Process., vol. 6, no. 7, pp , Apr. 03. [8] H. C. Stankwitz, R. J. Dallaire, and J. R. Fienup, Nonlinear apodization for side lobe control in SAR imagery, IEEE Trans. Aerosp. Electron. Syst., vol. 3, no., pp , Jan [9] S. R. DeGraaf, SAR imaging via modern -D spectral estimation methods, IEEE Trans. Image Process., vol. 7, no. 5, pp , May 998. [0] C. H. Seo and J. T. Yen, Side lobe suppression in ultrasound imaging using dual apodization with cross-correlation, IEEE Trans. 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13 08 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO., FEBRUARY 05 Tao Xiong (A 3) was born in Hubei, China, in January 984. He received the Master s degree in control technology and instrument from Xidian University, Xi an, China, in 006. He is currently with the Key Laboratory of Intelligent Perception and Image Understanding of the Ministry of Education of China, Xidian University. His research interests include imaging of several synthetic aperture radar modes and autofocus. Yong Wang received the Ph.D. degree from the University of California, Santa Barbara, CA, USA, in 99, with focus on synthetic aperture radar and its application in forested environments. He is currently a Faculty Member with East Carolina University, Greenville, NC, USA. His general research area is the application of remotely sensed and geospatial data sets to environments, natural hazards, and air pollution and is firmly couched within coastal areas of the USA. Shuang Wang was born in Shaanxi, China, in 978. She received the B.S. and M.S. degrees and the Ph.D. degree in circuits and systems from Xidian University, Xi an, China, in 000, 003, and 007, respectively. Currently, she is a Professor with the Key Laboratory of Intelligent Perception and Image Understanding of the Ministry of Education of China, Xidian University. Her main research interests are sparse representation, image processing, and highresolution synthetic aperture radar image processing. Hongying Liu received the B.E. and M.S. degrees in computer science and technology from Xi An University of Technology, Xi An, China, in 00 and 006, respectively, and the Ph.D. degree in engineering from Waseda University, Tokyo, Japan, in 0. Currently, she is a Faculty Member with the School of Electronic Engineering and the Key Laboratory of Intelligent Perception and Image Understanding of the Ministry of Education, Xidian University, Xi An, China. Her major research interests include intelligent signal processing, machine learning, compressive sampling, etc. Biao Hou (M 07) was born in China in 974. He received the B.S. and M.S. degrees in mathematics from Northwest University, Xi an, China, in 996 and 999, respectively, and the Ph.D. degree in circuits and systems from Xidian University, Xi an, in 003. Since 003, he has been with the Key Laboratory of Intelligent Perception and Image Understanding of the Ministry of Education of China, Xidian University, where he is currently a Professor. His research interests include multiscale geometric analysis and synthetic aperture radar image processing.