TenSR: Multi-dimensional Tensor Sparse Representation

Qi, Na; Shi, Yong; Sun, Xiaoyan; Yin, Baocai

doi:10.1109/cvpr.2016.637

Cited by 41 publications

(51 citation statements)

References 31 publications

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“…In addition, as shown in Figure 2e, we give a detailed analysis for another notable representation form for the sparsity prior based on tensor sparse decomposition, which suggests that we can depict the structured sparsity of an HSI from the perspective of core tensor. Some pioneering works are presented in [42,43,[52][53][54]. Here, we draw attention to the structured sparsity formulation of an HSI under tensor sparse representation framework, thus each third-order tensor X p can be approximated by following problem:…”

Section: Non-local Structure Sparsity Modelingmentioning

confidence: 99%

“…where U1p, U2p, and U3p are factor matrices and S(G p ) is sparse constraint term, and we assume S(G p ) = G p 0 as suggested in [42,43,52]. However, the optimization problem based on l 0 constraint deduced by Equation 8is non-convex, the research in [53,54] further relaxes the l 0 -based core sparsity to l 1 case as S(G p ) = G p 1 . The convex optimization problem corresponding to l 1 case can be represented in Lagrangian form as following:…”

Section: Non-local Structure Sparsity Modelingmentioning

confidence: 99%

“…It can be solved by the Tensor-based Iterative Shrinkage Thresholding Algorithm (TISTA) in [53,54]. (c) M p sub-problem:…”

Section: Optimization Algorithmmentioning

confidence: 99%

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Nonlocal Tensor Sparse Representation and Low-Rank Regularization for Hyperspectral Image Compressive Sensing Reconstruction

et al. 2019

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Hyperspectral image compressive sensing reconstruction (HSI-CSR) is an important issue in remote sensing, and has recently been investigated increasingly by the sparsity prior based approaches. However, most of the available HSI-CSR methods consider the sparsity prior in spatial and spectral vector domains via vectorizing hyperspectral cubes along a certain dimension. Besides, in most previous works, little attention has been paid to exploiting the underlying nonlocal structure in spatial domain of the HSI. In this paper, we propose a nonlocal tensor sparse and low-rank regularization (NTSRLR) approach, which can encode essential structured sparsity of an HSI and explore its advantages for HSI-CSR task. Specifically, we study how to utilize reasonably the l 1 -based sparsity of core tensor and tensor nuclear norm function as tensor sparse and low-rank regularization, respectively, to describe the nonlocal spatial-spectral correlation hidden in an HSI. To study the minimization problem of the proposed algorithm, we design a fast implementation strategy based on the alternative direction multiplier method (ADMM) technique. Experimental results on various HSI datasets verify that the proposed HSI-CSR algorithm can significantly outperform existing state-of-the-art CSR techniques for HSI recovery.

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Section: Non-local Structure Sparsity Modelingmentioning

confidence: 99%

Section: Non-local Structure Sparsity Modelingmentioning

confidence: 99%

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Nonlocal Tensor Sparse Representation and Low-Rank Regularization for Hyperspectral Image Compressive Sensing Reconstruction

et al. 2019

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“…To solve (5), one may use an N -mode iterative soft thresholding approach, such as FISTA [3], or TISTA [16], as outlined in Algorithm 1. Note that the 1 -proximity operator may be computed easily as a soft thresholding operator…”

Section: Sparse Tucker Tensor Reconstructionmentioning

confidence: 99%

Sparse Tensor Recovery via N-Mode Fista With Support Augmentation

Prater-Bennette

Shen

2018

2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP)

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A common approach for performing sparse tensor recovery is to use an N -mode FISTA method. However, this approach may fail in some cases by missing some values in the true support of the tensor and compensating by erroneously assigning nearby values to the support. This work proposes a four-stage method for performing sparse tensor reconstruction that addresses a case where N -mode FISTA may fail by augmenting the support set. Moreover, the proposed method preserves a Tucker-like structure throughout computations for computational efficiency. Numerical results on synthetic data demonstrate that the proposed method produces results with similar or higher accuracy than N -mode FISTA, and is often faster.

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“…Two different kinds of sparse coding models have been proposed to preserve the intrinsic spatial structures of images: tensor sparse coding (TenSR) [5,6] and convolutional sparse coding (CSC) [7,8]. For TenSR models [5,6], tensors are exploited for the image representation and a series of separable dictionaries are used to approximate the structures in each mode of images. Though the spatial structures are pre- served by tensor representations, the relationships between the learned sparse coefficients and dictionaries are more complicated, which will cause the encoding (sparse coefficients) hard to interpret.…”

Section: Introductionmentioning

confidence: 99%

Graph regularized tensor sparse coding for image representation

Jiang

Liu

et al. 2017

2017 IEEE International Conference on Multimedia and Expo (ICME)

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Sparse coding (SC) is an unsupervised learning scheme that has received an increasing amount of interests in recent years. However, conventional SC vectorizes the input images, which destructs the intrinsic spatial structures of the images. In this paper, we propose a novel graph regularized tensor sparse coding (GTSC) for image representation. GTSC preserves the local proximity of elementary structures in the image by adopting the newly proposed tubal-tensor representation. Simultaneously, it considers the intrinsic geometric properties by imposing graph regularization that has been successfully applied to uncover the geometric distribution for the image data. Moreover, the returned sparse representations by GTSC have better physical explanations as the key operation (i.e., circular convolution) in the tubal-tensor model preserves the shifting invariance property. Experimental results on image clustering demonstrate the effectiveness of the proposed scheme.

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TenSR: Multi-dimensional Tensor Sparse Representation

Cited by 41 publications

References 31 publications

Nonlocal Tensor Sparse Representation and Low-Rank Regularization for Hyperspectral Image Compressive Sensing Reconstruction

Nonlocal Tensor Sparse Representation and Low-Rank Regularization for Hyperspectral Image Compressive Sensing Reconstruction

Sparse Tensor Recovery via N-Mode Fista With Support Augmentation

Graph regularized tensor sparse coding for image representation

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