Hyperspectral images (HSIs) denoising aims at recovering noise-free images from noisy counterparts to improve image visualization. Recently, various prior knowledge has attracted much attention in HSI denoising, e.g., total variation (TV), low-rank, sparse representation, and so on. However, the computational cost of most existing algorithms increases exponentially with increasing spectral bands. In this paper, we fully take advantage of the global spectral correlation of HSI and design a unified framework named subspace-based Moreau-enhanced total variation and sparse factorization (SMTVSF) for multispectral image denoising. Specifically, SMTVSF decomposes an HSI image into the product of a projection matrix and abundance maps, followed by a ‘Moreau-enhanced’ TV (MTV) denoising step, i.e., a nonconvex regularizer involving the Moreau envelope mechnisam, to reconstruct all the abundance maps. Furthermore, the schemes of subspace representation penalizing the low-rank characteristic and
-norm modelling the structured sparse noise are embedded into our denoising framework to refine the abundance maps and projection matrix. We use the augmented Lagrange multiplier (ALM) algorithm to solve the resulting optimization problem. Extensive results under various noise levels of simulated and real hypspectral images demonstrate our superiority against other competing HSI recovery approaches in terms of quality metrics and visual effects. In addition, our method has a huge advantage in computational efficiency over many competitors, benefiting from its removal of most spectral dimensions during iterations.
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