Reweighted Nuclear Norm and Reweighted Frobenius Norm Minimizations for Narrowband RFI Suppression on SAR System

Synthetic aperture radar (SAR), as a wideband radar system, is subject to interference by radio frequency systems, such as radio, TV, and cellular networks. Since the narrowband radio frequency interference (RFI) has a stable frequency in a snapshot sequence, it has a low-rank property that can be used to substract RFI from the received signal. The nuclear norm is a common convex relaxation to constrain the rank, but it is optimized by the singular value thresholding (SVT) algorithm, which uses a single threshold to treat all singular values and greatly over-punishes large singular values. Hence, in this paper, we propose two methods, the reweighted nuclear norm (RNN) algorithm and the reweighted Frobenius norm (RFN) algorithm, to separate the RFI and the useful signal. The RNN and RFN minimization problems are the approximations of the real rank function, which can protect large singular values and restrict the rank. As a result, the RFI is accurately extracted and the useful signal is successfully protected. Also, we strictly derive the closed-form solutions of the RNN and RFN minimization problems for complex radar signals, and we also employ downsampling to extract the mainband of the signal spectrum to speed up the convergence. Real SAR data is applied to demonstrate the effectiveness of the proposed methods for RFI suppression.