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Recently, due to the ability to exploit perceptual information, superpixel-based methods have received attention for hyperspectral image (HSI) denoising. However, existing superpixel-based denoising methods unfold the irregular 3-D superpixels into the matrices along the spectral mode, which inevitably destroys the intrinsic structure of the irregular 3-D superpixels. To tackle the irregular 3-D superpixels, we introduce the irregular tensor representation for superpixel-guided HSI denoising. More concretely, by introducing the weighted tensor, we suggest a tensor representation of each irregular 3-D superpixel, which can preserve the intrinsic structure of the irregular 3-D superpixel. Equipped with the irregular tensor representation, we establish a superpixel-guided tensor optimization model for HSI denoising, which simultaneously exploits the perceptual information and low-rank structure within 3-D superpixels. To solve the resulting tensor optimization problem, we develop an inexact augmented Lagrange multiplier (IALM) algorithm. Experimental results show that the proposed method outperforms other state-of-the-art HSI denoising methods, particularly matrix-based methods, on both simulated and real data. [ABSTRACT FROM AUTHOR]

Recently, block-term decomposition with rank- $(L_{r}, L_{r}, 1)$ (termed LL1 decomposition), which is physically inspired by linear spectral unmixing, has received increasing attention in hyperspectral images (HSIs) denoising. However, due to the intrinsic nonlinear structure of real-world HSIs, the low-rankness of HSIs is usually implicit. Moreover, the essential uniqueness guarantee is usually violated with the low-rank assumption of the abundance maps unsupported in real scenarios, which hampers the successful deployment of LL1 decomposition. Inspired by the nonlinear spectral unmixing, we propose a nonlinear learnable transform-based LL1 decomposition (NT-LL1) for characterizing the implicit low-rank structure of real-world HSIs. More concretely, the nonlinear learnable transform in NT-LL1 decomposition is a composed transform consisting of a linear semi-orthogonal transform and a componentwise nonlinear transform, which collaboratively enhances the low-rankness of the abundance maps. Empowering with the NT-LL1 decomposition, we propose an NT-LL1 decomposition-based model for HSIs denoising. To tackle the resulting model, we develop an efficient proximal alternating minimization (PAM)-based algorithm with a convergence guarantee. Extensive experimental results, including simulated and real data, collectively verify the superiority of the proposed method as compared with the competing methods. [ABSTRACT FROM AUTHOR]

The general tensor-based methods can recover missing values of multidimensional images by exploiting the low-rankness on the pixel level. However, especially when considerable pixels of an image are missing, the low-rankness is not reliable on the pixel level, resulting in some details losing in their results, which hinders the performance of subsequent image applications (e.g., image recognition and segmentation). In this article, we suggest a novel multiscale feature (MSF) tensorization by exploiting the MSFs of multidimensional images, which not only helps to recover the missing values on a higher level, that is, the feature level but also benefits subsequent image applications. By exploiting the low-rankness of the resulting MSF tensor constructed by the new tensorization, we propose the convex and nonconvex MSF tensor train rank minimization (MSF-TT) to conjointly recover the MSF tensor and the corresponding original tensor in a unified framework. We develop the alternating directional method of multipliers (ADMMs) to solve the convex MSF-TT and the proximal alternating minimization (PAM) to solve the nonconvex MSF-TT. Moreover, we establish the theoretical guarantee of convergence for the PAM algorithm. Numerical examples of real-world multidimensional images show that the proposed MSF-TT outperforms other compared approaches in image recovery and the recovered MSF tensor can benefit the subsequent image recognition. [ABSTRACT FROM AUTHOR]

Recently, transform-based tensor nuclear norm (TNN) minimization methods have received increasing attention for recovering third-order tensors in multi-dimensional imaging problems. The main idea of these methods is to perform the linear transform along the third mode of third-order tensors and then minimize the nuclear norm of frontal slices of the transformed tensor. The main aim of this paper is to propose a nonlinear multilayer neural network to learn a nonlinear transform by solely using the observed tensor in a self-supervised manner. The proposed network makes use of the low-rank representation of the transformed tensor and data-fitting between the observed tensor and the reconstructed tensor to learn the nonlinear transform. Extensive experimental results on different data and different tasks including tensor completion, background subtraction, robust tensor completion, and snapshot compressive imaging demonstrate the superior performance of the proposed method over state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The image nonlocal self-similarity (NSS) prior refers to the fact that a local patch often has many nonlocal similar patches to it across the image and has been widely applied in many recently proposed machining learning algorithms for image processing. However, there is no theoretical analysis on its working principle in the literature. In this paper, we discover a potential causality between NSS and low-rank property of color images, which is also available to grey images. A new patch group based NSS prior scheme is proposed to learn explicit NSS models of natural color images. The numerical low-rank property of patched matrices is also rigorously proved. The NSS-based QMC algorithm computes an optimal low-rank approximation to the high-rank color image, resulting in high PSNR and SSIM measures and particularly the better visual quality. A new tensor NSS-based QMC method is also presented to solve the color video inpainting problem based on quaternion tensor representation. The numerical experiments on color images and videos indicate the advantages of NSS-based QMC over the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The existing low-rank tensor completion methods develop many tensor decompositions and corresponding tensor ranks in order to reconstruct the missing information by exploiting the inherent low-rank structure under the assumption that the data is low-rank under one of the kinds of decompositions. However, the assumption is easily violated for real-world data, e.g., color images and multispectral images, as the low-rank structure of these data is not significant. To better take advantage of the global correlation relationship, we propose a kernel low-rank tensor completion model, where original data is mapped into the feature space using a kernel mapping. Although the original data is high-rank, it is low-rank in the feature space owing to the kernel mapping. Therefore, the proposed model could take advantage of the implicitly low-rank structure in the feature space and estimate the missing entries well. Considering it is not easy to explicitly kernelize the tensor, we reformulate the model as the inner product form and introduce the kernel trick for efficiently solving the resulting model. Extensive experiments on color images and multispectral images show that the proposed method outperforms the state-of-the-art low-rank tensor completion methods. [ABSTRACT FROM AUTHOR]

The existing nonblind cloud and cloud shadow (cloud/shadow) removal methods for remote sensing (RS) images are based on the assumption that cloud/shadow masks are accurately given. Since the masks are usually manually labeled or detected by cloud detection methods, whose accuracy cannot be well guaranteed, the cloud/shadow removal effect may be affected. In this article, we suggest a robust thick cloud/shadow removal (RTCR) method that meets the problem with an inaccurate mask. To faithfully reconstruct the multitemporal information, a coupled tensor factorization is used to explore the relationship between the abundances of the multitemporal images in the same scene. Moreover, an efficient algorithm is developed to solve the proposed model based on the augmented Lagrange multiplier method. The experimental results under accurate masks and inaccurate masks demonstrate its robustness and superiority for thick cloud/shadow removal. [ABSTRACT FROM AUTHOR]

This article proposes a new denoising method for hyperspectral images (HSIs) corrupted by mixtures (in a statistical sense) of stripe noise, Gaussian noise, and impulsive noise. The proposed method has three distinctive features: 1) it exploits the intrinsic characteristics of HSIs, namely, low-rank and self-similarity; 2) the observation noise is assumed to be additive and modeled by a mixture of Gaussian (MoG) densities; 3) the inference is performed with an expectation maximization (EM) algorithm, which, in addition to the clean HSI, also estimates the mixture parameters (posterior probability of each mode and variances). Comparisons of the proposed method with state-of-the-art algorithms provide experimental evidence of the effectiveness of the proposed denoising algorithm. A MATLAB demo of this work will be available at https://github.com/TaiXiangJiang for the sake of reproducibility. [ABSTRACT FROM AUTHOR]

Removing rain streaks in videos has recently received much attention. Existing hand-crafted priors-based methods suffer from limited representation abilities, and supervised deep learning methods need high-quality training data. This paper proposes a novel video rain streaks removal method by reconciling hand-crafted and self-supervised deep priors. The hand-crafted priors include the learned gradient prior, the sparse prior, and the temporal local smooth prior. Meanwhile, a deep convolutional neural network is employed to self-supervisedly capture the deep prior of the clean video without any training data. Our method organically integrates hand-crated priors and self-supervised deep priors to achieve both high generalization abilities and representation abilities. Thus, our method can faithfully remove directional rain streaks in real world videos. To address the resulting model, we introduce an alternating direction multiplier method algorithm. Extensive experiments validate the superiority of our method over state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Sparse unmixing is an important technique for analyzing and processing hyperspectral images (HSIs). Simultaneously exploiting spatial correlation and sparsity improves substantially abundance estimation accuracy. In this article, we propose to exploit nonlocal spatial information in the HSI for the sparse unmixing problem. Specifically, we first group similar patches in the HSI, and then unmix each group by imposing simultaneous a low-rank constraint and joint sparsity in the corresponding third-order abundance tensor. To this end, we build an unmixing model with a mixed regularization term consisting of the sum of the weighted tensor trace norm and the weighted tensor $\ell _{2,1}$ -norm of the abundance tensor. The proposed model is solved under the alternating direction method of multipliers framework. We term the developed algorithm as the nonlocal tensor-based sparse unmixing algorithm. The effectiveness of the proposed algorithm is illustrated in experiments with both simulated and real hyperspectral data sets. [ABSTRACT FROM AUTHOR]

This paper addresses the tensor completion problem, which aims to recover missing information of multi-dimensional images. How to represent a low-rank structure embedded in the underlying data is the key issue in tensor completion. In this work, we suggest a novel low-rank tensor representation based on coupled transform, which fully exploits the spatial multi-scale nature and redundancy in spatial and spectral/temporal dimensions, leading to a better low tensor multi-rank approximation. More precisely, this representation is achieved by using two-dimensional framelet transform for the two spatial dimensions, one/two-dimensional Fourier transform for the temporal/spectral dimension, and then Karhunen–Loéve transform (via singular value decomposition) for the transformed tensor. Based on this low-rank tensor representation, we formulate a novel low-rank tensor completion model for recovering missing information in multi-dimensional visual data, which leads to a convex optimization problem. To tackle the proposed model, we develop the alternating directional method of multipliers (ADMM) algorithm tailored for the structured optimization problem. Numerical examples on color images, multispectral images, and videos illustrate that the proposed method outperforms many state-of-the-art methods in qualitative and quantitative aspects. [ABSTRACT FROM AUTHOR]

Hyperspectral super-resolution (HSR) aims at fusing a pair of hyperspectral and multispectral images to recover a super-resolution image (SRI). This work revisits coupled tensor decomposition (CTD)-based HSR. The vast majority of the HSR approaches take a low-rank matrix recovery perspective. The challenge is that theoretical guarantees for recovering the SRI using low-rank matrix models are either elusive or derived under stringent conditions. A couple of recent CTD-based methods ensure recoverability for the SRI under relatively mild conditions, leveraging algebraic properties of the canonical polyadic decomposition (CPD) and the Tucker decomposition models, respectively. However, the latent factors of both the CPD and Tucker models have no physical interpretations in the context of spectral image analysis, which makes incorporating prior information challenging—but using priors is often essential for enhancing performance in noisy environments. This work employs an idea that models spectral images as tensors following the block-term decomposition model with multilinear rank-(Lr,Lr,1) terms (i.e., the LL1 model) and formulates the HSR problem as a coupled LL1 tensor decomposition problem. Similar to the existing CTD approaches, recoverability of the SRI is shown under mild conditions. More importantly, the latent factors of the LL1 model can be interpreted as the key constituents of spectral images, i.e., the endmembers’ spectral signatures and abundance maps. This connection allows us to incorporate prior information for performance enhancement. A flexible algorithmic framework that can work with a series of structural information is proposed to take advantages of the model interpretability. The effectiveness is showcased using simulated and real data. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Hyperspectral (HS) imaging has shown its superiority in many real applications. However, it is usually difficult to obtain high-resolution (HR) HS images through existing imaging techniques due to the hardware limitations. To improve the spatial resolution of HS images, this article proposes an effective HS-multispectral (HS-MS) image fusion method by combining the ideas of nonlocal low-rank tensor modeling and spectral unmixing. To be more precise, instead of unfolding the HS image into a matrix as done in the literature, we directly represent it as a tensor, then a designed nonlocal Tucker decomposition is used to model its underlying spatial–spectral correlation and the spatial self-similarity. The MS image serves mainly as a data constraint to maintain spatial consistency. To further reduce the spectral distortions in spatial enhancement, endmembers, and abundances from the spectral are used for spectral regularization. An efficient algorithm based on the alternating direction method of multipliers (ADMM) is developed to solve the resulting model. Extensive experiments on four HS image data sets demonstrate the superiority of the proposed method over several state-of-the-art HS-MS image fusion methods. [ABSTRACT FROM AUTHOR]

Hyperspectral imaging, providing abundant spatial and spectral information simultaneously, has attracted a lot of interest in recent years. Unfortunately, due to the hardware limitations, the hyperspectral image (HSI) is vulnerable to various degradations, such as noises (random noise), blurs (Gaussian and uniform blur), and downsampled (both spectral and spatial downsample), each corresponding to the HSI denoising, deblurring, and super-resolution tasks, respectively. Previous HSI restoration methods are designed for one specific task only. Besides, most of them start from the 1-D vector or 2-D matrix models and cannot fully exploit the structurally spectral–spatial correlation in 3-D HSI. To overcome these limitations, in this article, we propose a unified low-rank tensor recovery model for comprehensive HSI restoration tasks, in which nonlocal similarity within spectral–spatial cubic and spectral correlation are simultaneously captured by third-order tensors. Furthermore, to improve the capability and flexibility, we formulate it as a weighted low-rank tensor recovery (WLRTR) model by treating the singular values differently. We demonstrate the reweighed strategy, which has been extensively studied in the matrix, also greatly benefits the tensor modeling. We also consider the stripe noise in HSI as the sparse error by extending WLRTR to robust principal component analysis (WLRTR-RPCA). Extensive experiments demonstrate the proposed WLRTR models consistently outperform state-of-the-art methods in typical HSI low-level vision tasks, including denoising, destriping, deblurring, and super-resolution. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to develop a framelet representation of the tensor nuclear norm for third-order tensor recovery. In the literature, the tensor nuclear norm can be computed by using tensor singular value decomposition based on the discrete Fourier transform matrix, and tensor completion can be performed by the minimization of the tensor nuclear norm which is the relaxation of the sum of matrix ranks from all Fourier transformed matrix frontal slices. These Fourier transformed matrix frontal slices are obtained by applying the discrete Fourier transform on the tubes of the original tensor. In this paper, we propose to employ the framelet representation of each tube so that a framelet transformed tensor can be constructed. Because of framelet basis redundancy, the representation of each tube is sparsely represented. When the matrix slices of the original tensor are highly correlated, we expect the corresponding sum of matrix ranks from all framelet transformed matrix frontal slices would be small, and the resulting tensor completion can be performed much better. The proposed minimization model is convex and global minimizers can be obtained. Numerical results on several types of multi-dimensional data (videos, multispectral images, and magnetic resonance imaging data) have tested and shown that the proposed method outperformed the other testing methods. [ABSTRACT FROM AUTHOR]

Hyperspectral image compressive sensing reconstruction (HSI-CSR) can largely reduce the high expense and low efficiency of transmitting HSI to ground stations by storing a few compressive measurements, but how to precisely reconstruct the HSI from a few compressive measurements is a challenging issue. It has been proven that considering the global spectral correlation, spatial structure, and nonlocal self-similarity priors of HSI can achieve satisfactory reconstruction performances. However, most of the existing methods cannot simultaneously capture the mentioned priors and directly design the regularization term to the HSI. In this article, we propose a novel subspace-based nonlocal tensor ring decomposition method (SNLTR) for HSI-CSR. Instead of designing the regularization of the low-rank approximation to the HSI, we assume that the HSI lies in a low-dimensional subspace. Moreover, to explore the nonlocal self-similarity and preserve the spatial structure of HSI, we introduce a nonlocal tensor ring decomposition strategy to constrain the related coefficient image, which can decrease the computational cost compared to the methods that directly employ the nonlocal regularization to HSI. Finally, a well-known alternating minimization method is designed to efficiently solve the proposed SNLTR. Extensive experimental results demonstrate that our SNLTR method can significantly outperform existing approaches for HSI-CSR. [ABSTRACT FROM AUTHOR]

Stripe noise from different remote sensing imaging systems varies considerably in terms of response, length, angle, and periodicity. Due to the complex distributions of different stripes, the destriping results of previous methods may be oversmoothed or contain residual stripe. To overcome this key problem, we provide a comprehensive analysis of existing destriping methods and propose a deep convolutional neural network (CNN) for handling various kinds of stripes. Moreover, previous methods individually model the stripe or the image priors, which may lose the relationship between them. In this article, a two-stream CNN is designed to simultaneously model the stripe and image, which better facilitates distinguishing them from each other. Moreover, we incorporate the wavelet into our CNN model for better directional feature representation. Therefore, the CNN learns the discriminative representation from the external data set, while the wavelet models the internal directionality of the stripe, in which both the internal and external priors are beneficial to the destriping task. In addition, the wavelet extracts the multiscale information with a larger receptive field for global contextual information modeling; thus, we can better distinguish the stripe from the similar image line pattern structures. The proposed method has been extensively evaluated on a number of data sets and outperforms the state-of-the-art methods by substantially a large margin in terms of quantitative and qualitative assessments, speed, and robustness. [ABSTRACT FROM AUTHOR]

Hyperspectral image (HSI) denoising is a fundamental problem in remote sensing and image processing. Recently, nonlocal low-rank tensor approximation-based denoising methods have attracted much attention due to their advantage of being capable of fully exploiting the nonlocal self-similarity and global spectral correlation. Existing nonlocal low-rank tensor approximation methods were mainly based on two common decomposition [Tucker or CANDECOMP/PARAFAC (CP)] methods and achieved the state-of-the-art results, but they are subject to certain issues and do not produce the best approximation for a tensor. For example, the number of parameters for Tucker decomposition increases exponentially according to its dimensions, and CP decomposition cannot better preserve the intrinsic correlation of the HSI. In this article, a novel nonlocal tensor-ring (TR) approximation is proposed for HSI denoising by using TR decomposition to explore the nonlocal self-similarity and global spectral correlation simultaneously. TR decomposition approximates a high-order tensor as a sequence of cyclically contracted third-order tensors, which has strong ability to explore these two intrinsic priors and to improve the HSI denoising results. Moreover, an efficient proximal alternating minimization algorithm is developed to optimize the proposed TR decomposition model efficiently. Extensive experiments on three simulated data sets under several noise levels and two real data sets verify that the proposed TR model provides better HSI denoising results than several state-of-the-art methods in terms of quantitative and visual performance evaluations. [ABSTRACT FROM AUTHOR]

The tensor tubal rank, defined based on the tensor singular value decomposition (t-SVD), has obtained promising results in hyperspectral image (HSI) denoising. However, the framework of the t-SVD lacks flexibility for handling different correlations along different modes of HSIs, leading to suboptimal denoising performance. This article mainly makes three contributions. First, we introduce a new tensor rank named tensor fibered rank by generalizing the t-SVD to the mode- ${k}$ t-SVD, to achieve a more flexible and accurate HSI characterization. Since directly minimizing the fibered rank is NP-hard, we suggest a three-directional tensor nuclear norm (3DTNN) and a three-directional log-based tensor nuclear norm (3DLogTNN) as its convex and nonconvex relaxation to provide an efficient numerical solution, respectively. Second, we propose a fibered rank minimization model for HSI mixed noise removal, in which the underlying HSI is modeled as a low-fibered-rank component. Third, we develop an efficient alternating direction method of multipliers (ADMMs)-based algorithm to solve the proposed model, especially, each subproblem within ADMM is proven to have a closed-form solution, although 3DLogTNN is nonconvex. Extensive experimental results demonstrate that the proposed method has superior denoising performance, as compared with the state-of-the-art competing methods on low-rank matrix/tensor approximation and noise modeling. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing has attracted much attention in recent years. Single sparse unmixing assumes that a pixel in a hyperspectral image consists of a relatively small number of spectral signatures from large, ever-growing, and available spectral libraries. Joint-sparsity (or row-sparsity) model typically enforces all pixels in a neighborhood to share the same set of spectral signatures. The two sparse models are widely used in the literature. In this paper, we propose a joint-sparsity-blocks model for abundance estimation problem. Namely, the abundance matrix of size $m\times n$ is partitioned to have one row block and $s$ column blocks and each column block itself is joint-sparse. It generalizes both the single (i.e., $s=n$) and the joint (i.e., $s=1$) sparsities. Moreover, concatenating the proposed joint-sparsity-blocks structure and low rankness assumption on the abundance coefficients, we develop a new algorithm called joint-sparse-blocks and low-rank unmixing. In particular, for the joint-sparse-blocks regression problem, we develop a two-level reweighting strategy to enhance the sparsity along the rows within each block. Simulated and real-data experiments demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Multispectral image (MSI) destriping is a challenging topic and has been attracting much research attention in remote sensing area due to its importance in improving the image qualities and subsequent applications. The existing destriping methods mainly focus on matrix-based modeling representation, which fails to fully discover the correlation of the stripe component in both spatial dimensions. In this paper, we propose a novel low-rank tensor decomposition framework based MSI destriping method by decomposing the striped image into the image component and stripe component. Specifically, for the image component, we use the anisotropic spatial unidirectional total variation (TV) and spectral TV regularization to enhance the piecewise smoothness in both spatial and spectral domains. Moreover, for the stripe component, we adopt tensor Tucker decomposition and $\ell _{2,1}$ -norm regularization to model the spatial correlation and group sparsity characteristic among all bands, respectively. An efficient algorithm using the augmented Lagrange multiplier method is designed to solve the proposed optimization model. Experiments under various cases of simulated data and real-world data demonstrate the effectiveness of the proposed model over the existing single-band and MSI destriping methods in terms of the qualitative and quantitative. [ABSTRACT FROM AUTHOR]

Hyperspectral images (HSIs) are often corrupted by a mixture of several types of noise during the acquisition process, e.g., Gaussian noise, impulse noise, dead lines, stripes, etc. Such complex noise could degrade the quality of the acquired HSIs, limiting the precision of the subsequent processing. In this paper, we present a novel tensor-based HSI restoration approach by fully identifying the intrinsic structures of the clean HSI part and the mixed noise part. Specifically, for the clean HSI part, we use tensor Tucker decomposition to describe the global correlation among all bands, and an anisotropic spatial–spectral total variation regularization to characterize the piecewise smooth structure in both spatial and spectral domains. For the mixed noise part, we adopt the $\ell _1$ norm regularization to detect the sparse noise, including stripes, impulse noise, and dead pixels. Despite that TV regularization has the ability of removing Gaussian noise, the Frobenius norm term is further used to model heavy Gaussian noise for some real-world scenarios. Then, we develop an efficient algorithm for solving the resulting optimization problem by using the augmented Lagrange multiplier method. Finally, extensive experiments on simulated and real-world noisy HSIs are carried out to demonstrate the superiority of the proposed method over the existing state-of-the-art ones. [ABSTRACT FROM PUBLISHER]

In this paper, we address the total variation (TV)-based nonlinear image restoration problems. In nonlinear image restoration problems, an original image is corrupted by a spatiallyinvariant blur, the build-in nonlinearity in imaging system, and the additive Gaussian white noise. We study the objective function consisting of the nonlinear least squares data-fitting term and the TV regularization term of the restored image. By making use of the structure of the objective function, an efficient alternating direction method of multipliers can be developed for solving the proposed model. The convergence of the numerical scheme is also studied. Numerical examples, including nonlinear image restoration and high-dynamic range imaging are reported to demonstrate the effectiveness of the proposed model and the efficiency of the proposed numerical scheme. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to study total variation (TV) regularization in deblurring and sparse unmixing of hyperspectral images. In the model, we also incorporate blurring operators for dealing with blurring effects, particularly blurring operators for hyperspectral imaging whose point spread functions are generally system dependent and formed from axial optical aberrations in the acquisition system. An alternating direction method is developed to solve the resulting optimization problem efficiently. According to the structure of the TV regularization and sparse unmixing in the model, the convergence of the alternating direction method can be guaranteed. Experimental results are reported to demonstrate the effectiveness of the TV and sparsity model and the efficiency of the proposed numerical scheme, and the method is compared to the recent Sparse Unmixing via variable Splitting Augmented Lagrangian and TV method by Iordache [ABSTRACT FROM AUTHOR]