Mixed noise (such as Gaussian, impulse, stripe, and deadline noises) contamination is a common phenomenon in hyperspectral imagery (HSI), greatly degrading visual quality and affecting subsequent processing accuracy. By encoding sparse prior to the spatial or spectral difference images, total variation (TV) regularization is an efficient tool for removing the noises. However, the previous TV term cannot maintain the shared group sparsity pattern of the spatial difference images of different spectral bands. To address this issue, this article proposes a group sparsity regularization of the spatial difference images for HSI restoration. Instead of using ℓ₁- or ℓ₂-norm (sparsity) on the difference image itself, we introduce a weighted ℓ2,1-norm to constrain the spatial difference image cube, efficiently exploring the shared group sparse pattern. Moreover, we employ the well-known low-rank Tucker decomposition to capture the global spatial-spectral correlation from three HSI dimensions. To summarize, a weighted group sparsity-regularized low-rank tensor decomposition (LRTDGS) method is presented for HSI restoration. An efficient augmented Lagrange multiplier algorithm is employed to solve the LRTDGS model. The superiority of this method for HSI restoration is demonstrated by a series of experimental results from both simulated and real data, as compared with the other state-of-the-art TV-regularized low-rank matrix/tensor decomposition methods.

As a preprocessing step, hyperspectral image (HSI) restoration plays a critical role in many subsequent applications. Recently, based on the framework of subspace representation and low-rank matrix/tensor factorization (LRMF/LRTF), many single-factor-regularized methods add various regularizations on the spatial factor to characterize its spatial prior knowledge. However, these methods neglect the common characteristics among different bands and the spectral continuity of HSIs. To tackle this issue, this article establishes a bridge between the factor-based regularization and the HSI priors and proposes a double-factor-regularized LRTF model for HSI mixed noise removal. The proposed model employs LRTF to characterize the spectral global low rankness, introduces a weighted group sparsity constraint on the spatial difference images (SpatDIs) of the spatial factor to promote the group sparsity in the SpatDIs of HSIs, and suggests a continuity constraint on the spectral factor to promote the spectral continuity of HSIs. Moreover, we develop a proximal alternating minimization-based algorithm to solve the proposed model. Extensive experiments conducted on the simulated and real HSIs demonstrate that the proposed method has superior performance on mixed noise removal compared with the state-of-the-art methods based on subspace representation, noise modeling, and LRMF/LRTF.

Coded aperture snapshot spectral imaging (CASSI) is an important technique for capturing three-dimensional (3D) hyperspectral images (HSIs), and involves an inverse problem of reconstructing the 3D HSI from its corresponding coded 2D measurements. Existing model-based and learning-based methods either could not explore the implicit feature of different HSIs or require a large amount of paired data for training, resulting in low reconstruction accuracy or poor generalization performance as well as interpretability. To remedy these deficiencies, this paper proposes a novel HSI reconstruction method, which exploits the global spectral correlation from the HSI itself through a formulation of model-driven low-rank subspace representation and learns the deep prior by a data-driven self-supervised deep learning scheme. Specifically, we firstly develop a model-driven low-rank subspace representation to decompose the HSI as the product of an orthogonal basis and a spatial representation coefficient, then propose a data-driven deep guided spatial-attention network (called DGSAN) to adaptively reconstruct the implicit spatial feature of HSI by learning the deep coefficient prior (DCP), and finally embed these implicit priors into an iterative optimization framework through a self-supervised training way without requiring any training data. Thus, the proposed method shall enhance the reconstruction accuracy, generalization ability, and interpretability. Extensive experiments on several datasets and imaging systems validate the superiority of our method. The source code and data of this article will be made publicly available at https://github.com/ChenYong1993/LRSDN .

Hyperspectral image (HSI) mixed noise removal is a fundamental problem and an important preprocessing step in remote sensing fields. The low-rank approximation-based methods have been verified effective to encode the global spectral correlation for HSI denoising. However, due to the large scale and complexity of real HSI, previous low-rank HSI denoising techniques encounter several problems, including coarse rank approximation (such as nuclear norm), the high computational cost of singular value decomposition (SVD) (such as Schatten $p$ -norm), and adaptive rank selection (such as low-rank factorization). In this article, two novel factor group sparsity-regularized nonconvex low-rank approximation (FGSLR) methods are introduced for HSI denoising, which can simultaneously overcome the mentioned issues of previous works. The FGSLR methods capture the spectral correlation via low-rank factorization, meanwhile utilizing factor group sparsity regularization to further enhance the low-rank property. It is SVD-free and robust to rank selection. Moreover, FGSLR is equivalent to Schatten $p$ -norm approximation ( Theorem 1 ), and thus FGSLR is tighter than the nuclear norm in terms of rank approximation. To preserve the spatial information of HSI in the denoising process, the total variation regularization is also incorporated into the proposed FGSLR models. Specifically, the proximal alternating minimization is designed to solve the proposed FGSLR models. Experimental results have demonstrated that the proposed FGSLR methods significantly outperform existing low-rank approximation-based HSI denoising methods.