$L_{1}$ -Regularization-Based SAR Imaging and CFAR Detection via Complex Approximated Message Passing

Abstract

Synthetic aperture radar (SAR) is a widely used active high-resolution microwave imaging technique that has all-time and all-weather reconnaissance ability. Compared with traditionally matched filtering (MF)-based methods, ${L_{q}}({0 \le q \le 1})$ regularization technique can efficiently improve SAR imaging performance e.g., suppressing sidelobes and clutter. However, conventional $L_{q}$ -regularization-based SAR imaging approach requires transferring the 2-D echo data into a vector and reconstructing the scene via 2-D matrix operations. This leads to significantly more computational complexity compared with MF, and makes it very difficult to apply in high-resolution and wide-swath imaging. Typical $L_{q}$ regularization recovery algorithms, e.g., iterative thresholding algorithm, can improve imaging performance of bright targets, but not preserve the image background distribution well. Thus, image background statistical-property-based applications, such as constant false alarm rate (CFAR) detection, cannot be applied to regularization recovered SAR images. On the other hand, complex approximated message passing (CAMP), an iterative recovery algorithm for $L_{1}$ regularization reconstruction, can achieve not only the sparse estimation of the original signal as typical regularization recovery algorithms but also a nonsparse solution simultaneously. In this paper, two novel CAMP-based SAR imaging algorithms are proposed for raw data and complex radar image data, respectively, along with CFAR detection via the CAMP recovered nonsparse result. The proposed method for raw data can not only improve SAR image performance as conventional $L_{1}$ regularization technique but also reduce the computational cost efficiently. While only when we have MF recovered SAR complex image rather than raw data, the proposed method for complex image data can achieve a similar reconstructed image quality as the regularization-based SAR imaging approach using the full raw data. The most important contribution of this paper is that the proposed CAMP-based methods make CFAR detection based on the regularization reconstruction SAR image possible using their nonsparse scene estimations, which has a similar background statistical distribution as the MF recovered images. The experimental results validated the effectiveness of the proposed methods and the feasibility of the recovered nonsparse images being used for CFAR detection.