SAR Image Speckle Reduction Based on Nuclear Norm Minus Frobenius Norm Regularization

Synthetic aperture radar (SAR) is a powerful imaging system with all-day and all-weather capabilities, making it suitable for a wide range of applications. However, SAR images often suffer from coherent speckle noise, which degrades image quality and hampers subsequent analysis and interpretation. Recently, methods based on the Fisher-Tippett (FT) distribution and nonlocal low-rank (NLR) techniques have shown great potential in SAR despeckling. Building upon these methods, this article proposes a novel SAR image despeckling method named SAR nuclear norm minus Frobenius norm (SAR-NNFN). This method effectively restores clean images using singular value shrinkage and allows for adaptive shrinkage without the need for additional weighting parameters. SAR-NNFN utilizes NNFN to achieve rank relaxation, resulting in a more robust low-rank solution for speckle reduction. The proposed model comprises two components: a data fidelity term that captures the statistical characteristics of SAR images using the FT distribution in the logarithmic domain, and an NNFN regularization term that enhances low-rank approximations. The optimization problem associated with SAR-NNFN is solved using the alternating direction method of multipliers (ADMM) algorithm. Extensive experiments conducted on both simulated and real SAR images demonstrate that SAR-NNFN can not only adequately suppress speckle noise but also preserve fine textures.