An Enhanced Forward-Looking SAR Imaging Algorithm Based on Compressive Sensing

Transcription

1 Progress In Eletromagnetis Researh M, Vol. 78, 69 81, 2019 An Enhaned Forward-Looking SAR Imaging Algorithm Based on Compressive Sensing Bo Pang, Hao Wu *, Shiqi Xing, Dahai Dai, Yongzhen Li, and Xuesong Wang Abstrat Having the imaging ability of the area in front of flight diretion, forward-looking syntheti aperture radar (SAR) has beome a hot topi in areas of SAR researh. Nevertheless, onstrained by limited azimuth aperture length, the imaging of forward-looking SAR suffers from poor azimuth resolution. Aiming at this problem, an enhaned forward-looking SAR imaging algorithm is proposed in this paper. This algorithm takes both super-resolving ability and omputational burden into aount. Firstly, an imaging framework is proposed to derease the omputational burden. Seondly, an iterative regularization implementation of ompressive sensing (CS) is proposed to improve azimuth resolution. Finally, imaging experiments based on simulated data and Ku-band omplex valued image data from the MiniSAR system demonstrate the effetiveness of the proposed algorithm. 1. INTRODUCTION By interrogating a sene with pulses from diverse angles, syntheti aperture radar (SAR) is able to produe its high-resolution images. Having the ability to operate at night and under all-weather irumstanes, SAR has beome one of the most promising researh tool for remote sensing appliations suh as forestry, agriulture, geology, and military reonnaissane in reent years. However, beause of poor doppler resolution and azimuth ambiguities, onventional SAR is not appliable with respet to the forward-looking diretion, whih hinders its appliation. In early 1990s, the onept of forward-looking radar was firstly proposed by Witte [1, 2]. By replaing the virtual antennas in SAR with a set of physially existent antenna elements distributed in spae and swithing the elements sequentially [1], the forward-looking radar ould eliminate the visualization gap with respet to the forward diretion of the flight path by a oherent proessing of the radar ehoes similar to a onventional SAR system [3]. Therefore, in many artiles, this kind of forwardlooking radar is also alled forward-looking SAR [4 10]. With the ability to provide two-dimensional [4 7] and three-dimensional images [8 10] of the earth ground in front of the platform, forward-looking SAR beomes more and more attrative to industrial and aademi ommunities. During the last deades, some progresses about forward-looking SAR have been made. The most representative one is the system named setor imaging radar for enhaned vision (SIREV) whih was developed by German Aerospae Center [11]. For the two-dimensional imaging algorithm of forward-looking SAR, the mathed filter (MF) based algorithms are always utilized. For instane, in [12], the extended hirp saling (ECS) algorithm is adopted. The ECS algorithm enables effetive imaging for forward-looking SAR by ombining the operations of spetral analysis (SPECAN) and azimuth saling. However, its omputational load is very high. Next, by taking the untreated phase in the ECS algorithm into aount and using the Reeived 5 November 2018, Aepted 14 Deember 2018, Sheduled 23 January 2019 * Corresponding author: Hao Wu (jszjtwh@126.om). The authors are with the State Key Laboratory of Complex Eletromagneti Environment Effets on Eletronis and Information System, National University of Defense Tehnology, Changsha , China.

2 70 Pang et al. azimuth proessing tehnique of SanSAR as a referene, a revised hirp saling algorithm for forwardlooking SAR is proposed in [7]. This algorithm is omputationally more effiient than ECS. [13] and [14] propose two algorithms whih are suitable for high veloity platform based on the idea of range Doppler (RD) and Doppler beam sharpening (DBS), respetively. Taking aeleration into aount, [15] proposes a hirp saling algorithm for forward-looking SAR with onstant aeleration. Although they are easy to implement, these MF based algorithms suffer from poor azimuth resolutions due to limited azimuth aperture, whih hinders the appliations of forward-looking SAR. In order to improve azimuth resolutions of forward-looking radar system, some approahes suh as deonvolution algorithms and bistati SAR have been proposed. However, for bistati SAR, it is diffiult to implement in pratie due to synhronization problem, large range ell migration (RCM), and ompliated struture [16 18]. For deonvolution, it is essentially a highly ill-posed problem whih is sensitive to noise and hardly ensures a robust solution [19, 20]. As a burgeoning tehnique, ompressive sensing (CS) has brought about a breakthrough to the reonstrution of sparse signal. Aording to this theory, the exat reonstrution of an unknown sparse signal an be obtained from limited measurements by solving a sparsity-onstrained optimization problem [21]. Furthermore, the super-resolving ability of CS ould ontribute to overome the limitation indued by syntheti aperture and bandwidth [22]. Now CS has been disussed and explored in different areas. In [23], a new radar system whih an eliminate the need for the mathed filter in the radar reeiver and redue the required analog-to-digital (AD) onversion bandwidth is designed based on the CS theory. For wide-angle imaging, where the assumption of isotropi point sattering does not hold up, the CS theory is utilized to enhane the resolution [24, 25]. In [26, 27], the CS theory is applied to ground penetrating radar (GPR) imaging. As a result, sparser and sharper target images are aquired by using only a small subset of the measurements. In tomographi SAR (Tomo-SAR) area, the CS theory provides a reliable solution for the aliasing effet and poor resolution brought by nonuniform inter-trak distane and limited overall baseline. Consequently, the height sattering profile of man-made objets suh as stadiums and buildings are better reonstruted [22, 28]. For SAR imaging, espeially when the imaging of man-made strutures is onsidered, the sattered signal an be well approximated as a sum of responses from a limited number of strong sattering enters. As a result, the sparsity ondition is well satisfied [29], whih provides a foundation for exploring the CS theory in SAR imaging. In this paper, the CS theory is exploited to improve the azimuth resolution of forward-looking SAR. The rest of the paper is organized as follows. In Setion 2, the signal model of forward-looking SAR is established. Based on this signal model, Setion 3 is dediated to presenting the enhaned imaging algorithm for forward-looking SAR. In Setion 4, imaging experiments based on simulated data and Ku-band omplex valued image data from the MiniSAR system demonstrate the effetiveness of the proposed method. The images reonstruted by the proposed method are also ompared with images generated by the RD algorithm [13], as it is lassial and is often used by the radar imaging ommunity for omparison and verifiation of imaging algorithms. Finally, onlusions are presented in Setion SIGNAL MODEL OF FORWARD-LOOKING SAR Figure 1 shows the imaging setors of SAR, Squint SAR and forward-looking SAR. The differenes between them an be easily distinguished. As shown in Figure 1, forward-looking SAR fills the visualization gap of SAR and squint SAR with respet to the diretion in front of radar movement. Figure 2 illustrates the imaging geometry of forward-looking SAR. The plane flies along x axis (i.e., ground range diretion) with veloity v at height h. The diretion along the wing of plane is defined as y axis (i.e., azimuth diretion). The diretion perpendiular to xoy plane is defined as z axis. Forward-looking SAR onsists of a linear array of antennas whih uniformly distribute along y axis. During the flight, these antennas sequentially transmit LFM signal with high pulse repetition frequeny (PRF) and reeive the baksattered signal. The swith frequeny is the same as PRF. Assuming that the distane between adjaent antennas is d, the length of the antenna array is L. Consequently, the position of the urrently working antenna an be derived as (vt, L/2+v a t, h). For a point satterer situated at (x, y, 0), the travel path of radar signal an be expressed as R (t) =2 (vt x) 2 +(( L/2 + v a t) y) 2 + h 2 (1)

3 Progress In Eletromagnetis Researh M, Vol. 78, Squint SAR Setor Forward-looking SAR Setor Squint SAR Setor SAR Setor SAR Setor Figure 1. Imaging setor of forward-looking SAR. Figure 2. Imaging geometry of forwardlooking SAR. where t stands for the slow time; vt is the x position of the urrently working antenna; L/2+v a t is the y position of the urrently working antenna; v a = d PRF is the equivalent veloity in azimuth diretion. Assume that the LFM signal transmitted by radar is s i (τ,t) = ret (τ)exp ( j2πf 0 τ + jπkτ 2) (2) where τ denotes the range time; K stands for the hirp rate; f 0 is the arrier frequeny. The orresponding range and azimuth Fourier resolutions of forward-looking SAR an be expressed as ρ r = 2B ρ a = λl (4) 2R 0 where denotes the speed of light, and B denotes signal bandwidth. When signal shown in Eq. (2) is transmitted, the baseband signal baksattered by the target situated at (x, y) an be written as s 0 (τ,t; x, y) =g (x, y) ret ( τ R (t; x, y) ) ( ( exp jπk τ ) ) R (t; x, y) 2 ( exp j2π (3) ) R (t; x, y) λ (5) where g(x, y) stands for the omplex refletivity of the target situated at (x, y). Nevertheless, for a sene omposed of many targets, the reeived signal should be expressed as the superposition of the sattering omponents from all targets whih are illuminated by the radar s beam. Consequently, the reeived signal has the form s 0 (τ,t)= G s 0 (τ,t; x, y) dxdy (6) By far, the model of the baseband signal reeived by forward-looking SAR has been derived. Then the task of image formation is to deode g(x, y) from the reeived signal s 0 (τ,t). 3. IMAGING ALGORITHM IMPLEMENTATION From the above analysis, it an be observed that the main bottlenek of forward-looking SAR imaging is the poor azimuth resolution whih is limited by the azimuth aperture length. For example, if the

4 72 Pang et al. Table 1. Simulation parameters. Parameters Values Wavelength m Chirp bandwidth 60 MHz Pulse Width 1 µs PRF Hz Platform veloity 300 m/s Antenna array length 2.85 m Numbers of reeive antenna 56 Platform Height 1056 m Looking angle 40 Beamwidth in range 6 Beamwidth in azimuth 6 parameters listed in Table 1 are adopted, the azimuth resolution (7.62 m) is muh worse than the range resolution (2.5 m). Furthermore, while the range resolution an be improved by inreasing signal bandwidth, the azimuth resolution is severely onstrained by the size of the platform itself. Therefore, an enhaned forward-looking SAR imaging algorithm based on CS is proposed in this setion. This algorithm takes both the super-resolving ability and the omputational burden into aount and produes satisfying results. The derivation of this algorithm is summarized as follows Imaging Framework When the enhaned forward-looking SAR imaging algorithm based on CS is used, the reeived baseband signal shown in Eq. (6) should be firstly Fourier transformed in range. Aording to the priniple of stationary phase (POSP), the range frequeny spetrum of the reeived signal an be expressed as [30] ( ) ( ) ( g (x, y) fτ R (t; x, y) S 0 (f τ,t)= ret exp j2π (f 0 + f τ ) exp jπ f 2 ) τ dxdy (7) K KT p K where 1/ K denotes amplitude of the range frequeny spetrum of the LFM signal. Then the range ompression is done in range frequeny domain by multiplying Eq. (7) with exp(jπfτ 2 /K ). After that, the range ompressed signal is transformed to range time domain to get s r (τ,t)= g (x, y) B ( ( )) R (t; x, y) sin πb τ exp K ( j2πf 0 R (t; x, y) ) dxdy (8) Then range ell migration orretion (RCMC) is applied to Eq. (8). The orreted signal an be expressed as s (τ,t)= g (x, y) B ( ( )) ( ) R(0; x, y) R (t; x, y) sin πb τ exp j2πf 0 dxdy (9) K The seond order Taylor s series expansion of R (t; x, y)att =0whihisusedinEq.(9)anbeexpressed as R (t; x, y) R (0; x, y)+r (0; x, y) t + R (0; x, y) t 2 (10) 2 Take s(τ 0,t) as the signal s(τ,t) sampled at range time τ 0. As wide band LFM signal is exploited in forward-looking SAR, the 3 db main-lobe width of sin ( ) is so narrow that s(τ 0,t) an be viewed as being omposed of only baksattering ontributions by satterers situated at r 0 = τ 0. As a result, Eq. (9) an be rewritten as B ( ( s (τ 0,t)= g (r 0,y)sin πb τ 0 r )) ( 0 exp j2π R (t; r ) 0,y) dy (11) K λ

5 Progress In Eletromagnetis Researh M, Vol. 78, Beause all the targets situated at r 0 in the range ell migration orreted image satisfy r 0 = R(0; x, y) = 2 x 2 +(L/2+y) 2 + h 2, we an obtain x = (r 0 /2) 2 (L/2+y) 2 h 2. Under this ondition, R(t; r 0,y) in Eq. (11) has the expression ( ) 2 R (t; r 0,y)=2 vt (r 0 /2) 2 (L/2 + y) 2 h 2 +( L/2 + v a t y) 2 + h 2 (12) In order to apply enhaned forward-looking SAR imaging algorithm based on CS, s(τ 0,t)andg(r 0,y) in Eq. (11) should be sampled in azimuth time and azimuth, respetively. After that, Eq. (11) an be rewritten as s (τ 0 )=Ag (r 0 ) (13) where s (τ 0 )=[s(τ 0,t 1 ),s(τ 0,t 2 ),...,s(τ 0,t M )] T (14) g (r 0 )=[g(r 0,y 1 ),g(r 0,y 2 ),...,g(r 0,y N )] T (15) The elements of ditionary matrix A has the form A mn = B ( sin πb K ( τ 0 2r 0 )) ( exp j2π R (t ) m; r 0,y n ) λ In the presene of noise, the signal model of Eq. (13) beomes s (τ 0 )=Ag (r 0 )+w (17) where w stands for the additive measurement noise. Next, Equation (17) will be solved to obtain super-resolving azimuth profile by utilizing the CS theory Iterative Regularization Implementation of CS The super-resolving ability of CS has been demonstrated in [31 33]. However, the resolving abilities vary with different implementations of CS. For example, although orthogonal mathing pursuit (OMP) and its variations are effiient implementations for CS, their super-resolving ability is poor [34]. In this paper, an iterative regularization implementation of CS is proposed. By taking both data fidelity and features of interest into aount, the proposed method is effetive in generating images with enhaned resolution and suppressed artifats. The derivation of this method an be summarized as follows. First, the imaging problem shown in Eq. (17) is formulated as following regularization problem ) ĝ =argmin g ( s Ag μ g k k (18) where s Ag 2 2 is used to preserve the data fidelity of the solution; μ is the salar parameter to balane the emphasis between signal energy and data fidelity; k denotes the l k -norm. In the following experiments, k 1 will be restrited sine smaller k implies fewer penalties on large pixel values and results in better preservation of the satter magnitudes omparing with larger k [31]. Next, we denote J (g) = s Ag μ g k k (19) as the objetive funtion. In order to minimize J(g), the differential of J(g) with respet to g should firstly be alulated. However, in order to eliminate the non-differentiability of the l k -norm around the origin, J(g) should be modified as N J (g) = s Ag μ ( k/2 g i 2 + ξ) (20) where ξ is so small a onstant that N ( g i 2 + ξ) k/2 is equivalent to g k k. In following experiments, i=1 ξ =10 5 is hosen. Then the differential of J(g) an be expressed as J (g) =H (g) g 2A H s (21) i=1 (16)

6 74 Pang et al. where H (g) = ( 2A H A + μkλ (g) ) (22) { ( ) 1 Λ (g) =diag 1/ g i 2 k } 2 + ξ (23) The supersript H denotes the omplex onjugate. Our objetive is to find a g satisfying J(g) = 0. However, onsidering that H(g) is the funtion of unknown targets sattering refletivity g, itis impossible to obtain the estimation of g by simply letting g =2H 1 (g)a H s. Instead, an iterative method will be exploited to solve this problem. By examining the expression of Eq. (21), it is appealing to notie that H(g) an be seen as a oeffiient matrix of g. As a result, H(g) is taken as the Hessian matrix [35]. By doing so, the iterative proess an be expressed as where g n+1 = g n H 1 (g n ) J (g n ) (24) H 1 (g n )=( ( J (g n ))) 1 = ( 2A H A + μkλ (g n ) ) 1 The iteration shown in Eq. (24) will arry on until g n+1 g n 2 2 / g n 2 2 <δwith δ asmallpositive threshold. In following experiments, δ is set as By solving Equation (17) aording to the aforementioned iterative regularization method, the super-resolved azimuth profile orresponding to range sample at r 0 an be obtained. After azimuth profiles at all the range samples are proessed, the image reonstrution is ompleted. There are two parameters k and μ that should be seleted in the proposed super-resolving imaging algorithm. However, they are not seleted by trial-and-error proedure. In the following experiments, the parameter seletion method that we proposed in [36] is adopted. As shown in [36], while ensuring performane, the parameter seletion method that we proposed has higher effiieny than that proposed in [37] and [38] Computational Burden Analysis Another ontribution of this paper is the development of a omputationally effiient implementation. For onventional SAR imaging algorithms based on the CS theory, an inherent requirement of two dimensional sampling for both the signal and the sene is required [39, 40]. Although super-resolving ability an be ahieved in both range and azimuth diretions in this way, extensive omputational effort is also involved, whih hinders its pratial usefulness. For example, for an M N dimensional signal and a P Q dimensional sene, the orresponding size of ditionary matrix A is MN PQ. Generally, in order to ahieve high resolution, the sene should be finely sampled. The sampling interval is usually 1/10 of the Fourier resolution ell or even finer, thus making P and Q large numbers. Consequently, the algorithm will beome omputationally intratable for large senes imaging. Considering that the range resolution an be improved by inreasing signal bandwidth, the algorithm proposed in this paper puts emphasis on the improvement of azimuth resolution. Namely the CS theory is applied to enhane azimuth resolution but not range resolution. In this way, the size of ditionary matrix A is redued to N Q, and the omputational burden is greatly redued, making the proposed algorithm appliable to larger senes. 4. EXPERIMENT RESULTS Laking forward-looking SAR system, the field experiment data are not available at this moment. Therefore, in this setion, in order to validate the effetiveness of the proposed algorithm, forwardlooking SAR imaging simulation experiments are arried out. The simulation parameters are listed in Table 1. They are the same as the parameters of SIREV system exept that the veloity is muh higher, as we want to test the performane of the proposed algorithm for platform with higher veloity. Aording to Table 1, the orresponding Fourier resolution ells of this system are 2.5 m/3.89 m in (25)

7 Progress In Eletromagnetis Researh M, Vol. 78, range/ground range and 7.62 m in azimuth, respetively. One an image how bad imaging performane will be if the MF based imaging algorithms are used. Firstly, imaging of some point satterers is simulated. Figure 3(a) illustrates the real positions of 9 point satterers whih form a trapezia. The distanes between adjaent satterers are one resolution ell in ground range diretion and 2/5, 3/10, 1/5 resolution ell in azimuth diretion, respetively. Figure 3(b) shows the imaging results generated by the proposed algorithm. It an be seen that 9 point satterers are all well foused at right positions. As a result, an exat trapezia is formed in the imaging result, whih demonstrates that the proposed algorithm has no less than 5 times superresolving ability in azimuth diretion. Figure 3() shows the superposition of the ground truth and the reonstruted results. The good agreement further validates the imaging and super-resolving apability of the proposed algorithm. (a) (b) () Figure 3. Forward-looking SAR imaging simulation of 9 point satterers whih form a trapezia. (a) Real positions of 9 point satterers. (b) Image generated by the proposed algorithm. () Comparison between imaging result and ground truth. In the following part, in order to demonstrate the effetiveness of the proposed algorithm for the real sene, forward-looking SAR imaging simulation experiments are arried out based on Kuband omplex valued image data from the MiniSAR system of Sandia National Laboratory. The MiniSAR system is an unmanned aerial vehile (UAV)-borne SAR system whih operates at spotlight mode. During its fight experiments, some omplex valued image data are aquired and then provided online publily. Figure 4(a), Figure 5(a) and Figure 6(a) show three omplex valued images of the MiniSAR system. Aording to the referenes provided by Sandia National Laboratory, they are a building, a C130 plane and an Osprey plane, respetively. In eah omplex valued image, (ground range azimuth) sattering points uniformly distribute in the sene. Assuming that the size of

8 76 Pang et al. (a) (b) () Figure 4. Forward-looking SAR imaging simulation of a building. (a) Ku-band omplex valued image of MiniSAR whih is used as omplex refletive template in forward-looking SAR eho generation. (b) Image generated by the RD algorithm. () Image generated by the proposed algorithm. eah sene is 120 m 120 m (ground range azimuth), then the distanes between adjaent sattering points are about 1/10 resolution ell of the forward-looking SAR in both ground range and azimuth diretions. In order to make our validation more reliable, we plae every sattering point in the omplex valued images from the MiniSAR system using a oordinate in ground range-azimuth plane (i.e., xoy plane in Figure 2). In this way, the omplex valued images of the MiniSAR system are taken as the omplex refletive templates of the senes (namely g(x, y) in Equation (5)). During simulation, the forward-looking SAR system transmits signal to the sene in front of it, and omplex sattering points in the sene baksatter signal to it. By reeiving baksattered signal, the eho data of forward-looking SAR are generated, and then the effetiveness of the proposed CS-based algorithm is demonstrated. The simulation parameters are also the parameters listed in Table 1. The orresponding imaging results are shown in Figure 4 Figure 6. Figure 4(a) shows a omplex valued image of the MiniSAR system. In this image, there is a building surrounded by the lawn, and the vertial and horizontal axes orrespond to x and y axes in Figure 2, namely the ground range and the azimuth, respetively. Figure 4(b) shows the image generated by the RD algorithm. Due to the poor azimuth resolution onstrained by limited azimuth aperture length and the mutual interferene of adjaent sattering points whose separation distanes are about 1/10 resolution ell in both ground range and azimuth, the outline and detail of the building are not well preserved. Meanwhile, the image suffers from ontaminations with ground lutter and noise, whih make it harder for us to reognize the building. In ontrast, the image reonstruted by the proposed algorithm is preferable. Firstly, the geometry features of the building are well preserved. Consequently, the T - shape struture of the building an be easily observed, and shape-based target reognition algorithm an be effetively utilized to reognize it. Seondly, although quantitative super-resolving evaluation is

9 Progress In Eletromagnetis Researh M, Vol. 78, (a) (b) () Figure 5. Forward-looking SAR imaging simulation of a C130 plane. (a) Ku-band omplex valued image of MiniSAR whih is used as omplex refletive template in forward-looking SAR eho generation. (b) Image generated by the RD algorithm. () Image generated by the proposed algorithm. not so easy for this omplex target, it seems that more details about the building are reonstruted by the proposed algorithm. Thirdly, the sparse image reonstruted by the CS-based algorithm enable the effetive use of the automati target reognition system for detetion and reognition [41]. Fourthly, the dense and lean look of Figure 4() demonstrates the robustness of the proposed algorithm in the presene of noise and lutter, espeially when only strong sattering points over a noisy bakground are of interest. Fifthly, beause 5 times oversampling is adopted in range ompressing, and azimuth super-resolving proessing is arried out along eah range sample, the harateristi of the target is also better depited in range diretion by the proposed algorithm, although no designed super-resolving proessing is inluded in range diretion. Comparing Figure 4(a) and Figure 4(), one may doubt that exept for leaner bakground, it is hard to onlude that the imaging quality is greatly improved by the proposed algorithm. However, it should be notied that Figure 4(a) is generated by the MiniSAR system whih operates at Ku-band spotlight mode and is utilized as omplex refletive template in imaging simulation. However, Figure 4() orresponds to an image generated by a forward-looking SAR whih operates at forward-looking mode and X-band. For spotlight-mode, the antenna is steered to map a sene at multiple viewing angles during a single pass, so it an provide higher resolution than strip-map and san mode SAR. However, for forward-looking SAR, as its azimuth resolution is severely limited by azimuth aperture length, how to ahieve high resolution image is a problem that should be dealt with. Therefore, it is more reasonable to ompare imaging quality at same imaging mode and frequeny band, suh as Figure 4(b) and Figure 4(), whih orrespond to images reonstruted by RD and the proposed algorithm at the same imaging mode and frequeny band, respetively. Another aspet worth to mention is the omputational burden redution and the omputational

10 78 Pang et al. (a) (b) () Figure 6. Forward-looking SAR imaging simulation of an Osprey plane. (a) Ku-band omplex valued image of MiniSAR whih is used as omplex refletive template in forward-looking SAR eho generation. (b) Image generated by the RD algorithm. () Image generated by the proposed algorithm. apability enhanement introdued by the proposed algorithm. In this experiment, the size of the two-dimensional radar eho is , and the size of the sene is If the onventional CSbased imaging algorithm is used [39, 40], namely CS is used to improve range and azimuth resolutions simultaneously, the orresponding size of ditionary matrix A will be It means that variables should be solved from equations, whih is obviously an extensive omputation burden. However, when the proposed algorithm is used, the size of A will redue to , whih means that 158 variables should be solved from 56 equations. Consequently, the omputation effiieny is greatly enhaned. Figure 5(a) shows the omplex valued image of the MiniSAR system. In this image, a C130 plane is parked on the runway. Figure 5(b) shows the image generated by the RD algorithm. Similarly, due to poor resolution, mutual interferene of adjaent sattering points lies in the same resolution ell and ontamination by noise and lutter, only some strong sattering points an be observed. Consequently, it is diffiult for us to find any relationship between them and a plane. In ontrast, Figure 5() whih is reonstruted by the proposed algorithm gives us a muh better impression. Firstly, the shape of the C130 plane is well reonstruted, espeially the array of sattering points orresponding to the wing and tail of the plane. Seondly, ontamination of noise and lutter is eliminated by using the proposed algorithm. Thirdly, in the image reonstruted by the proposed algorithm, the strong sattering point whih is highlighted by the red irle in Figure 5(a) is imaged at the right position with strong appearane. Considering that it is an isolated sattering point, this ould be deemed as another demonstration for the effetiveness of the proposed algorithm. Figure 6(a) shows the omplex valued image of the MiniSAR system. In this image, an Osprey plane is parked on the runway. Figure 6(b) and Figure 6() show the images reonstruted by RD and

11 Progress In Eletromagnetis Researh M, Vol. 78, the proposed algorithm, respetively. From the image reonstruted by the proposed algorithm, it an be seen that the Osprey plane is well reonstruted that we an reognize it as a plane from its shape. Besides that, the thread-like objets in the lower part of the image are also aurately reonstruted. At the same time, the less spurious bakground is preferable. The experimental results demonstrate the superiority of the proposed algorithm. 5. CONCLUSION In this paper, an enhaned forward-looking SAR imaging algorithm based on the CS theory is proposed. Firstly, by separating the imaging proess into range ompression based on mathed filter and azimuth super-resolving reonstrution based on CS, the omputational burden is greatly dereased. Seondly, by proposing an iterative regularization implementation of CS, the super-resolving ability is greatly improved. The desirable harateristis of the proposed algorithm are verified using simulated data and Ku-band omplex valued image data from the MiniSAR system. In the images reonstruted by the proposed algorithm, the ontours and details of the point satterers, plane and building are well preserved. In this paper, uniform sampling is used in the proposed forward-looking SAR imaging algorithm based on CS. However, it has been delared in some literatures that sparse sampling onfiguration has better performane and less omputational burden [42, 43]. How to hoose sparse samples and its impat on forward-looking imaging performane is our ongoing area of researh. ACKNOWLEDGMENT This work is partly supported by the National Natural Siene Foundation of China (No , ) and Exellent Youth Foundation of Hu nan Sientifi Committee (No. 2017JJ1006). The authors would like to thank the Sandia National Laboratories for providing omplex valued image data of the MiniSAR system. REFERENCES 1. Witte, F., Forward looking radar, US Patent , Sutor, T., F. Witte, and A. Moreira, A new setor imaging radar for enhaned vision-sirev, Proeedings of SPIE, 39 47, July Curlander, J. C. and R. N. MDonough, Syntheti Aperture Radar: Systems and Signal Proessing, John Wiley & Sons, Wang, J. and Z. L. Zong, Forward-looking SAR imaging algorithm via ompressive sensing, Radar Siene and Tehnology, Vol. 10, No. 1, 27 31, Xu, G., Q. Q. Chen, Y. X. Hou, Y. C. Li, and M. D. Xing, Super-resolution imaging of forwardlooking san SAR, Journal of Xidian University, Vol. 39, No. 5, , Soldovieri, F., G. Gennarelli, I. Catapano, D. Liao, and D. Dogaru, Forward-looking radar imaging: A omparison of two data proessing strategies, IEEE Journal of Seleted Topis in Applied Earth Observations & Remote Sensing, Vol. 10, No. 2, , Chen, Q. and R. L. Yang, Researh of hirp saling imaging algorithm for air-borne forwardlooking SAR, Journal of Eletronis & Information Tehnology, Vol. 30, No. 1, , Ren, X. Z. and R. L. Yang, Study on three-dimensional imaging algorithm for airborne forwardlooking SAR, Journal of Eletronis & Information Tehnology, Vol. 32, No. 6, , Ren, X. Z., J. T. Sun, and R. L. Yang, A new three-dimensional imaging algorithm for airborne forward-looking SAR, IEEE Geosiene and Remote Sensing Letters, Vol. 8, No. 1, , Ren, X. Z., L. L. Tan, and R. L. Yang, Researh of three-dimensional imaging proessing for airborne forward-looking SAR, Proeedings of IET International Radar Conferene, 1 4, April 2009.

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