RFI Suppression for SAR via a Dictionary-Based Nonconvex Low-Rank Minimization Framework and Its Adaptive Implementation

Synthetic aperture radar (SAR) frequently suffers from radio frequency interference (RFI) due to the simultaneous presence of numerous wireless communication signals. Recently, the narrowband RFI is found to possess the low-rank property benefiting from stable frequency occupancy, hence the reconsideration of RFI suppression as a joint sparse and low-rank optimization problem. The existing methods either use the non-sparse useful signal itself as the sparse regularizer, or employ the nuclear norm to approximate the rank function, which punishes all singular values with the same penalty via singular value thresholding (SVT), resulting in the improper punishment problem. Hence, both are consequentially subject to performance limitation. In this paper, a novel dictionary-based nonconvex low-rank minimization (DNLRM) optimization framework is proposed for RFI suppression, which concurrently considers the improvements for both the sparse regularizer and the low-rank regularizer. For the former, an over-completed dictionary is constructed, for which the sparse coefficient acts as the sparse regularizer. For the latter, the rank function is more accurately approximated by innovatively introducing the nonconvex function, for which the supergradient is synchronously used to generate the weighted penalty, thus solving the improper punishment problem. The derivation of the closed-form solution and the convergence analysis are described in detail. Additionally, the adaptive selection scheme for the model parameter is uniquely proposed for further ensuring the practicality of the DNLRM framework. The superiority of the proposed method is demonstrated via not only the RFI-free real SAR data combined with the measured RFI, but the RFI-contaminated real SAR data.