A Robust Maximum a Posteriori Algorithm for 1-Bit Synthetic Aperture Radar Imaging

Over the past decade, extensive research has been conducted on 1-bit synthetic aperture radar (SAR) imaging algorithms. These algorithms aim to replace high-speed and high-precision analog-to-digital converters (ADCs) with comparators for low cost, noise robustness, and lightened transmission and storage burdens. The conventional maximum a posteriori (MAP) approach is commonly employed for reconstructing sparse scenes in SAR imaging. It can effectively reconstruct scenes containing discrete targets with relatively high quality under sufficiently low signal-to-noise ratio (SNR) conditions. However, when SNR increases, this algorithm has limitations as it cannot significantly improve imaging results. Furthermore, when it comes to reconstructing continuous targets, the imaging quality is notably poor. To address these challenges, this article proposes a robust maximum a posteriori (RMAP) algorithm. It reconstructs sparse scenes by optimizing a convex function derived from the bound optimization approach and employing the adaptive gradient descent (AGD) method. A vital approximation is utilized to prominently improve the stability of the algorithm, and it can be generally extended to other related imaging methods as long as the ratio of the cumulative distribution function (cdf) and the probability density distribution (pdf) of the standard normal distribution is involved. The results of both simulation and real data experiments validate the effectiveness of the RMAP algorithm. It accurately reconstructs sparse scenes in low SNR conditions and exhibits superior robustness compared to alternative methods such as the MAP, binary iterative hard threshold (BIHT), and adaptive outlier pursuit (AOP) algorithms.