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 <inline-formula> <tex-math notation="LaTeX">\ell _{1} </tex-math></inline-formula>- or <inline-formula> <tex-math notation="LaTeX">\ell _{2} </tex-math></inline-formula>-norm (sparsity) on the difference image itself, we introduce a weighted <inline-formula> <tex-math notation="LaTeX">\ell _{2,1} </tex-math></inline-formula>-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.
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 <inline-formula> <tex-math notation="LaTeX">m\times n </tex-math></inline-formula> is partitioned to have one row block and <inline-formula> <tex-math notation="LaTeX">s </tex-math></inline-formula> column blocks and each column block itself is joint-sparse. It generalizes both the single (i.e., <inline-formula> <tex-math notation="LaTeX">s=n </tex-math></inline-formula>) and the joint (i.e., <inline-formula> <tex-math notation="LaTeX">s=1 </tex-math></inline-formula>) 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.
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.
Rain streaks removal is an important issue in outdoor vision systems and has recently been investigated extensively. In this paper, we propose a novel video rain streak removal approach FastDeRain, ...which fully considers the discriminative characteristics of rain streaks and the clean video in the gradient domain. Specifically, on the one hand, rain streaks are sparse and smooth along the direction of the raindrops, whereas on the other hand, clean videos exhibit piecewise smoothness along the rain-perpendicular direction and continuity along the temporal direction. Theses smoothness and continuity result in the sparse distribution in the different directional gradient domain. Thus, we minimize: 1) the 4 norm to enhance the sparsity of the underlying rain streaks; 2) two l1 norm of unidirectional total variation regularizers to guarantee the anisotropic spatial smoothness; and 3) an 4 norm of the time-directional difference operator to characterize the temporal continuity. A split augmented Lagrangian shrinkage algorithm-based algorithm is designed to solve the proposed minimization model. Experiments conducted on synthetic and real data demonstrate the effectiveness and efficiency of the proposed method. According to the comprehensive quantitative performance measures, our approach outperforms other state-of-the-art methods, especially on account of the running time. The code of FastDeRain can be downloaded at https://github.com/TaiXiangJiang/FastDeRain.
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.
Remotely sensed images may contain some missing areas because of poor weather conditions and sensor failure. Information of those areas may play an important role in the interpretation of ...multitemporal remotely sensed data. This paper aims at reconstructing the missing information by a nonlocal low-rank tensor completion method. First, nonlocal correlations in the spatial domain are taken into account by searching and grouping similar image patches in a large search window. Then, low rankness of the identified fourth-order tensor groups is promoted to consider their correlations in spatial, spectral, and temporal domains, while reconstructing the underlying patterns. Experimental results on simulated and real data demonstrate that the proposed method is effective both qualitatively and quantitatively. In addition, the proposed method is computationally efficient compared with other patch-based methods such as the recently proposed patch matching-based multitemporal group sparse representation method.
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 <inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula>-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 <inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula>-norm approximation (<xref ref-type="theorem" rid="theorem1">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.
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.
Inspired by the interesting findings regarding the hierarchy and coordination of pigeons in Nagy et al. Nature, 2010, we revisit the discrete-time leader-follower consensus problem with switching ...topologies. The purpose of this paper is to investigate the impact of hierarchical topologies and followers' self-loops on the convergence performance of leader-follower consensus, including the convergence rate and robustness to switching topologies. We first study the fixed topology case, and show that the followers converge to the leader's state in finite time if and only if each follower has no self-loops and the topology is hierarchical. However, we show via counterexample, that leader-follower consensus may not be achieved when some followers have no self-loops and the topology is switching; even if each interaction graph has a spanning tree rooted at the leader. With the aid of binary relation theory, we further develop a new approach to present a novel sufficient condition for leader-follower consensus with switching topologies and with some followers having no self-loops. We prove that when no followers have self-loops and the same hierarchical organization is kept under the switching topologies, then the fastest rate of convergence in leader-follower consensus can be achieved; even in the presence of complex dynamic topologies. This is consistent with the natural phenomena found in pigeons by Nagy et al.
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.
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