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Deep learning (DL) based hyperspectral images (HSIs) denoising approaches directly learn the nonlinear mapping between noisy and clean HSI pairs. They usually do not consider the physical characteristics of HSIs. This drawback makes the models lack interpretability that is key to understanding their denoising mechanism and limits their denoising ability. In this paper, we introduce a novel model-guided interpretable network for HSI denoising to tackle this problem. Fully considering the spatial redundancy, spectral low-rankness, and spectral-spatial correlations of HSIs, we first establish a subspace-based multidimensional sparse (SMDS) model under the umbrella of tensor notation. After that, the model is unfolded into an end-to-end network named SMDS-Net, whose fundamental modules are seamlessly connected with the denoising procedure and optimization of the SMDS model. This makes SMDS-Net convey clear physical meanings, i.e., learning the low-rankness and sparsity of HSIs. Finally, all key variables are obtained by discriminative training. Extensive experiments and comprehensive analysis on synthetic and real-world HSIs confirm the strong denoising ability, strong learning capability, promising generalization ability, and high interpretability of SMDS-Net against the state-of-the-art HSI denoising methods. The source code and data of this article will be made publicly available at https://github.com/bearshng/smds-net for reproducible research. [ABSTRACT FROM AUTHOR]

Hyperspectral image (HSI) denoising is an ill-posed inverse problem. The underlying physical model is always important to tackle this problem, which is unfortunately ignored by most of the current deep learning (DL)-based methods, producing poor denoising performance. To address this issue, this article introduces an end-to-end model-aided nonlocal neural network (MAC-Net) which simultaneously takes the spectral low-rank model and spatial deep prior into account for HSI noise reduction. Specifically, motivated by the success of the spectral low-rank model in depicting the strong spectral correlations and the nonlocal similarity prior in capturing spatial long-range dependencies, we first build a spectral low-rank model and then integrate a nonlocal U-Net into the model. In this way, we obtain a hybrid model-based and DL-based HSI denoising method where the spatial local and nonlocal multi-scale and spectral low-rank structures are effectively exploited. After that, we cast the optimization and denoising procedure of the hybrid method as a forward process of a neural network and introduce a set of learnable modules to yield our MAC-Net. Compared with traditional model-based methods, our MAC-Net overcomes the difficulties of accurate modeling, thanks to the strong learning and representation ability of DL. Unlike most “black-box” DL-based methods, the spectral low-rank model is beneficial to increase the generalization ability of the network and decrease the requirement of training samples. Experimental results on the natural and remote-sensing HSIs show that MAC-Net achieves state-of-the-art performance over both model-based and DL-based methods. The source code and data of this article will be made publicly available at https://github.com/bearshng/mac-net for reproducible research. [ABSTRACT FROM AUTHOR]

Due to the mechanism of the data acquisition process, hyperspectral imagery (HSI) are usually contaminated by various noises, e.g., Gaussian noise, impulse noise, strips, and dead lines. In this article, a spectral–spatial $L_{0}$ gradient regularized low-rank tensor factorization (LRTF $L_{0}$) method is proposed for hyperspectral denoising, in which the restored HSI is approximated by low-rank block term decomposition (BTD). BTD factorizes a tensor into the sum of a series of component tensors, each of which is represented by the outer product of a matrix and a vector. From subspace learning point of view, the vector and matrix can be considered as a spectral atom and its corresponding coding coefficients. In the proposed method, the correlations in both spectral and spatial domains are taken into account via the small size of atom set and low-rankness of coding matrices. In addition, HSIs also have the local structure of piecewise smoothness in both spectral and spatial domains. Motivated by the supreme virtues of $L_{0}$ gradient regularization in image structure exploitation, we develop a spectral–spatial $L_{0}$ gradient regularization and embed it into BTD to explore the spectral–spatial texture information. The proposed method can simultaneously remove various types of noises, and the experimental results on both synthetic data and real-world data show its superiority when compared with several state-of-the-art approaches. [ABSTRACT FROM AUTHOR]