# A Sparse Bayesian Approach for Forward-Looking Superresolution Radar Imaging
## 3 Sparse Bayesian Algorithm for High Cross-Range Resolution
### Scene Simulation  
This section shows the simulation results of a 2D scene containing ships. Figure 5a-d are the original scene, the real beam received signal after pulse compression and motion compensation, the superresolution results processed by the Poisson-based MAP algorithm, and the proposed sparse Bayesian algorithm, respectively. Because forward-looking imaging mainly concentrates on the applications of target searching and resolving, the original scene we consider is an area of strong scattering targets in part of an SAR image. In this simulation, the forward-looking imaging region is from \(-5^{\circ}\) to \(5^{\circ}\), and the working distance is 5 km. The platform velocity is 200 m/s, and the SNR is 20 dB. Because this simulation is for sea surface targets, sea clutter that obeys the \(K\) distribution is added in the image, and the signal-to-clutter ratio (SCR) is 15 dB. Figure 5b shows that the ships have very low cross-range resolution, and the adjacent ships cannot be distinguished in the real beam image.  
In the simulation results of the two algorithms, although the performance of the proposed sparse Bayesian algorithm is influenced by the sea clutter, we can clearly find that it has better superresolution performance than the Poisson-based MAP algorithm. When some ships are in one beamwidth, the performance of the Poisson-based MAP algorithm has serious degradation. Not only are the targets hardly resolved, but severe location error exists in the processed result. The proposed algorithm avoids these phenomena, whether or not the isolated ships or the adjacent ships all have high cross-range resolution and location accuracy. We can easily obtain accurate information of the ship number and position. The scene simulation also verified that the proposed sparse Bayesian algorithm is an effective superresolution algorithm for forward-looking imaging under a cluttered background.  
Figure 6 shows the profile of the range bin of 5.16 km of the scene simulation. The pink, green, red, and blue lines are the profiles of the original targets distribution, the real beam echo after motion compensation, the simulation results processed by the Poisson-based MAP algorithm, and the proposed sparse Bayesian algorithm, respectively. At this range, there are two targets in one beamwidth, at about \(-2.2^{\circ}\) and \(-0.2^{\circ}\). The proposed algorithm successfully distinguishes the two targets and causes very small location error, and the recovered cross-range width of the target almost equals the real target, which reaches a resolution improvement of 1.5-times. However, the Poisson-based algorithm has poor superresolution performance. The adjacent targets are hardly distinguished, and the target at \(-2.2^{\circ}\) has very serious location error of 0.31\({}^{\circ}\), whereas the proposed sparse Bayesian algorithm enjoys a lower location error of 0.08\({}^{\circ}\).  
Figure 4: Root mean squared error (RMSE) curves of the Poisson-based MAP algorithm and the proposed sparse Bayesian algorithm.  
Figure 5: Simulation results of scene when the SNR and signal to clutter ratio (SCR) are 20 dB and 15 dB, respectively. (**a**) Original scene. (**b**) Real beam image after pulse compression and motion compensation. (**c**) Superresolution result processed by the Poisson-based MAP algorithm. (**d**) Superresolution result processed by the proposed sparse Bayesian algorithm.  
Figure 6: Profiles of the single range bin.