Speckle Noise Reduction in SAR Images Using Rank Residual Constraint Regularization

The operational utility of Synthetic Aperture Radar (SAR) in remote sensing is frequently hampered by coherent speckle, an intrinsic form of multiplicative noise that compromises image analysis. In this paper, we propose a novel method for SAR image despeckling, named SAR-RRC. This approach is built upon two key components: a data fidelity term based on the Fisher-Tippett (FT) distribution, which accurately captures the statistics of log-transformed speckle in SAR images, and a Rank Residual Constraint (RRC) model for regularization. The proposed approach leverages the low-rank property of matrices constructed from non-local, structurally similar image patches. Unlike standard methods such as Nuclear Norm Minimization (NNM), the RRC model reframes the problem by progressively approximating the clean image. It aims to minimize the "rank residual"—the difference between the singular values of the current estimate and an iteratively updated reference matrix—thereby achieving more precise despeckling. To solve the resulting optimization problem, an efficient and stable algorithm is developed within the Alternating Direction Method of Multipliers (ADMM) framework. The effectiveness of the SAR-RRC algorithm is validated through extensive experiments on both simulated and real-world SAR images, where it is benchmarked against several leading despeckling algorithms. The results affirm that the proposed SAR-RRC method constitutes a competitive new alternative to established SAR image despeckling methods in the literature.