Abstract
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 ℓ 2 , 1 -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.
Highlights
With the wealth of spatial and spectral information, hyperspectral image (HSI) delivers a more accurate description ability of real scenes to distinguish precise details than color images and provides potential advantages of application in vegetation monitoring, medical diagnosis, mineral exploration, among numerous others [1,2]
The following representative HSI denoising methods are selected as competitors, i.e., low-rank matrix recovery (LRMR) [18], TV-regularized low-rank matrix factorization (LRTV) [31], fast hyperspectral image denoising based on low-rank and sparse representations (FastHyDe) [46], global matrix factorization and to local tensor factorizations method (GLF) [41], spatial-spectral total variation regularized local low-rank matrix recovery (LLRGTV) [37], Moreau-enhanced total variation regularized local low-rank matrix recovery (LLRMTV) [43], and non-local meets global (NM-meet) denoising paradigm [42]
LLRGTV unites the spatio-spectral TV (SSTV)-regularized method to update all patches simultaneously, while LLRMTV reconstructs the whole HSI by a Moreau-enhanced total variation denoising method
Summary
With the wealth of spatial and spectral information, hyperspectral image (HSI) delivers a more accurate description ability of real scenes to distinguish precise details than color images and provides potential advantages of application in vegetation monitoring, medical diagnosis, mineral exploration, among numerous others [1,2]. There is ever-growing attention in HSI denoising and numerous approaches have been developed in recent decade. Let Y ∈ Rp×h×w represent an observed HSI data with p spectral bands of spatial size h × w. The 3D HSI image is rearranged as a 2D matrix Y ∈ Rp×l(l = h × w) for the purpose of easier analysis, where each row contains a vectorized spectral channel band. Following the studies of [31,37], HSIs are assumed to be contaminated by mixed noise, and its noisy observation can be described in a matrix form as Y = X + S + N, (1). The goal of HSI denoising is to separate the noise from observed image with proper constraints
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