LAUSR

Dear editor, Sparse signal processing offers a framework for synthetic aperture radar (SAR) imaging [1, 2]. As an efficient tool in sparse signal processing, L1 minimization is often used in the reconstruction of SAR images. When implemented in SAR imaging [3–5], L1 minimization offers significant improvement in the properties by suppressing the sidelobes and clutter. However, L1 minimization is known to be a biased estimator. The L1 minimization based algorithms such as the iterative soft thresholding algorithm (IST) and complex approximate message passing (CAMP) often underestimate the amplitude of the signal [6,7]. In SAR imaging, the estimated radar cross section (RCS) is related to the image pixel intensity. The estimated RCS is essential for the quantitative use of the SAR data. It can be used as input data in numerous inverse problems to derive physical quantities such as soil moisture level, biomass and salinity. The underestimation of the L1 minimization can cause radiometric errors and negatively affects the quantitative use of the SAR data. In [7], a generalized minimax-concave (GMC) penalty is proposed. As a generalization of the L1 norm, the GMC is a non-convex penalty that does not underestimate the intensity of a sparse solution to the extent that L1 penalty does. Concurrently, the cost function with GMC is convex, and its solution has no suboptimal local minima. In this study, we present a GMC based SAR imaging method to avoid the underestimation of L1 regularization. The GMC problem can be reconstructed via a forward-backward (FB) algorithm. The proposed method can avoid the underestimation of L1 regularization in the noisy case as well. The simulation and real data results demonstrate the validity of the proposed method. L1 regularization based SAR imaging. The SAR system model is expressed as