# A Sparse Bayesian Approach for Forward-Looking Superresolution Radar Imaging
## 1 Introduction  
Forward-looking radar imaging with high cross-range resolution is of great significance for many civil and military applications [1; 2]. Regrettably, the principle of a classic monostatic synthetic aperture radar (SAR) or Doppler beam sharpening (DBS) prevents high-resolution imaging in the forward-looking direction. The reason for this resolution problem is that terrain points situated symmetrically about the flight path have the same Doppler history, and the gradient of the Doppler frequency is small in the flight direction. Many approaches are proposed for solving this low resolution problem. Monopulse and clean techniques are the beam sharpening techniques that could realize high target measurement accuracy [3; 4; 5]. However, this kind of method has serious location error when more than one target is distributed in one beam. Bistatic SAR is proposed to overcome the forward-looking imaging problem with a specific geometric structure. However, the complicated structure and synchronization problem are hardly solved [6; 7; 8; 9]. Bececcause the cross-range echo can be expressed by a linear equation system in the time domain, one may reconstruct the ground truth by solving the equation system. Inverse filter approaches have been presented, and achieve the improvements of cross-range resolution on a high signal-to-noise ratio (SNR) [10; 11]. However, the linear equation system is typically ill-conditioned because of the low-pass property of the antenna pattern, and the solution of the associated system can cause noise amplification and blurring effects. In [12; 13; 14], a scheme of the truncated singular value decomposition (TSVD) method was proposed by rejecting the small singular values. The method was demonstratedto significantly suppress the noise. However, this advantage is at the cost of limited resolution improvement. In addition, the number of reserved truncated values--which plays the role of the regularization parameter--is difficult to determine. Recently, the Bayesian deconvolution approach has been developed for high-resolution radar imaging [15; 16; 17; 18]. It can also be employed to deal with the forward-looking imaging problem model because the received signal of the forward-looking scanning radar in the cross-range dimension can be regarded as the convolution of the antenna pattern and the ground truth [19; 20; 21]. As will be demonstrated in this paper, the Bayesian deconvolution approach can provide much higher resolution than the real beam image. However, the target location error appears, and the noise is amplified severely. This is because, firstly, in most of the traditional Bayesian deconvolution approaches, they compute the maximum a posteriori estimation based only on the amplitude statistics property of received echo for calculation convenience. Therefore, the added phase caused by the platform movement will certainly lead to the error of recovery result. Secondly, without reasonable prior information about the practical applications of forward-looking imaging, the false targets that result from the noise amplification seriously influence the imaging performance. In this paper, the received echo of forward-looking scanning radar in the cross-range dimension is deduced first. We derive a novel signal model for forward-looking radar imaging. Different from the conventional convolution model in the cross-range dimension, the proposed model will consider the effect of Doppler history, and will be more accurate. Then, the Gaussian-based modeling of the noise is considered in the proposed method, which has been investigated and successfully applied to synthetic aperture radar imaging and multiple-input multiple-output (MIMO) radar imaging [22; 23; 24; 25]. Compared to the traditional statistical hypothesis, the Gaussian distribution is often more accurate for modeling the characteristics of noise in radar imaging.