Joint Sparse Regularization for Dictionary Learning

Miao, Jianyu; Cao, Heling; Jin, Xiao-Bo; Ma, Rongrong; Xuan, Fu‐Zhen; Niu, Lingfeng

doi:10.1007/s12559-019-09650-2

Cited by 6 publications

(4 citation statements)

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“…+ γtr (P 2 ⊗ P 1 ) T P D (P 2 ⊗ P 1 ) + λ 3 D y P 2 2,1 (16) where Y (2) and Z (2) are the height-mode (2-mode) unfolding matrix of tensors Y and Z, respectively, A 2 = C × 1 P1 × 3 P 3 (2) , and…”

Section: Optimization Of Pmentioning

confidence: 99%

“…Therefore, all these four subproblems can be effectively solved using fast and accurate ADMM technique. Due to the similarity of the solution process of problems ( 14), (16), and ( 18), we include the solution details of the four subproblems and the optimization updates of each variable as appendices for more conciseness. In Appendix A, Algorithms A1-A4 draw a summary of the solution process of the four subproblems in (12).…”

Section: Optimization Of Cmentioning

confidence: 99%

“…VO-based [12] methods are an important class of pan-sharpening methods. Since the main fusion processes of regularization-based methods [13][14][15][16][17], Bayesian-based methods [18][19][20], model-based optimization (MBO) [21][22][23] methods and sparse reconstruction (SR) [24][25][26] based methods are all based on or transformed into an optimization of a variational model, they can be generalized to variational optimization (VO) based methods. In other words, the main process of such pan-sharpening methods is usually based on or transformed into an optimization of a variational model.…”

Section: Introductionmentioning

confidence: 99%

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Hyperspectral Super-Resolution Via Joint Regularization of Low-Rank Tensor Decomposition

Cao

Bao

2021

Remote Sensing

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The hyperspectral image super-resolution (HSI-SR) problem aims at reconstructing the high resolution spatial–spectral information of the scene by fusing low-resolution hyperspectral images (LR-HSI) and the corresponding high-resolution multispectral image (HR-MSI). In order to effectively preserve the spatial and spectral structure of hyperspectral images, a new joint regularized low-rank tensor decomposition method (JRLTD) is proposed for HSI-SR. This model alleviates the problem that the traditional HSI-SR method, based on tensor decomposition, fails to adequately take into account the manifold structure of high-dimensional HR-HSI and is sensitive to outliers and noise. The model first operates on the hyperspectral data using the classical Tucker decomposition to transform the hyperspectral data into the form of a three-mode dictionary multiplied by the core tensor, after which the graph regularization and unidirectional total variational (TV) regularization are introduced to constrain the three-mode dictionary. In addition, we impose the l1-norm on core tensor to characterize the sparsity. While effectively preserving the spatial and spectral structures in the fused hyperspectral images, the presence of anomalous noise values in the images is reduced. In this paper, the hyperspectral image super-resolution problem is transformed into a joint regularization optimization problem based on tensor decomposition and solved by a hybrid framework between the alternating direction multiplier method (ADMM) and the proximal alternate optimization (PAO) algorithm. Experimental results conducted on two benchmark datasets and one real dataset show that JRLTD shows superior performance over state-of-the-art hyperspectral super-resolution algorithms.

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Section: Optimization Of Pmentioning

confidence: 99%

Section: Optimization Of Cmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hyperspectral Super-Resolution Via Joint Regularization of Low-Rank Tensor Decomposition

Cao

Bao

2021

Remote Sensing

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“…By its definition, the 2,1 -norm encourages row sparsity, i.e., it enforces entire row of the matrix to have zero elements. It has been successfully used in feature selection [47], [48], dictionary learning [49], multi-task learning [50], [51], and multi-class classification [52], [53]. Nie et al [47] developed a feature selection model via the 2,1 norm joint minimization on the loss function and spare regularization.…”

Section: B Group Sparsitymentioning

confidence: 99%

Graph-Based Clustering via Group Sparsity and Manifold Regularization

2019

Self Cite

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Clustering refers to the problem of partitioning data into several groups according to the predefined criterion. Graph-based method is one of main clustering approaches and has been shown impressive performance in many literatures. The core issue of graph-based clustering is how to construct a good adjacency graph. A large number of works employ the sparse representation of data as the similarity measure by 1 regularization. However, due to the flat nature of the 1 norm, such methods solve the sparse representation of each data point individually, which do not take into account the global structure of data. To exploit the global and essential structure in data, in contrast to existing methods, we propose to learn a graph with group sparsity. To incorporate more information into the graph, we also use the manifold regularization with adaptive similarity during the process of group sparse self-representation. The resulting model is handled by Alternating Direction Method of Multipliers (ADMM). Further, we employ Iterative Re-weighted Least Squares (IRLS) algorithm and threshold operator to solve the ADMM subproblems. Experimental results on real-world datasets demonstrate the superiority of our method compared to the competing clustering methods. INDEX TERMS Clustering, graph, group sparsity.

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