Mixed noise removal in hyperspectral images using low-rank tensor decomposition with spatial-spectral weighted sparsity regularization

This paper addresses the problem of hyperspectral image (HSI) restoration under mixed noise, specifically Gaussian and impulse noise, by proposing a novel method based on low-rank tensor decomposition. While existing low-rank approaches often adopt fixed regularization schemes, they may fail to capture spatial-spectral correlations in HSIs. To overcome this limitation, we introduce a spatial-spectral adaptive model that integrates regularizers with pixel-wise weighting, enabling local structural preservation and improved denoising performance. An efficient optimization algorithm based on the Augmented Lagrangian Method (ALM) is developed, with closed-form solutions derived for subproblems to ensure both accuracy and convergence. Experimental results on both simulated and real HSI datasets demonstrate the superiority of the proposed method over several state-of-the-art approaches, which are based on low-rank tensor decomposition. Our method achieves higher PSNR, SSIM, and FSIM scores, and provides visually cleaner results with better preservation of image details.