Nonlocal Gaussian scale mixture modeling for hyperspectral image denoising

Recent nonlocal sparsity methods have gained significant attention in hyperspectral image (HSI) denoising. These methods leverage the nonlocal self-similarity (NSS) prior to group similar full-band patches into nonlocal full-band groups, followed by enforcing a sparsity constraint, usually through soft-thresholding or hard-thresholding operators, on each nonlocal full-band group. However, in these methods, given that real HSI data are non-stationary and affected by noise, the variances of the sparse coefficients are unknown and challenging to accurately estimate from the degraded HSI, leading to suboptimal denoising performance. In this paper, we propose a novel nonlocal Gaussian scale mixture (NGSM) approach for HSI denoising, which significantly enhances the estimation accuracy of both the variances of the sparse coefficients and the unknown sparse coefficients. To reduce spectral redundancy, a global spectral low-rank (LR) prior is integrated with the NGSM model and consolidated into a variational framework for optimization. Extensive experimental results demonstrate that the proposed NGSM algorithm achieves convincing improvements over many state-of-the-art HSI denoising methods, both in quantitative and visual evaluations, while offering exceptional computational efficiency.