research-article

Tensor completion via convolutional sparse coding with small samples-based training

Authors:

Xiongjun ZhangAuthors Info & Claims

Volume 141, Issue C

https://doi.org/10.1016/j.patcog.2023.109624

Published: 01 September 2023 Publication History

Highlights

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To tackle the missing value problem, we proposed two CSC regularized LRTC models, SNN-based and TNN-based, respectively.

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In both models, an overcomplete dictionary is pre-trained only with a minimal amount of data.

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We came up with effective algorithms to solve the LRTC-CSC models, which are based on the inexact ADMM method and plug-and-play framework.

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Our model outperforms state-of-the-art methods on three datasets of different types.

Abstract

Tensor data often suffer from missing value problems due to the complex high-dimensional structure while acquiring them. To complete the missing information, lots of Low-Rank Tensor Completion (LRTC) methods have been proposed, most of which depend on the low-rank property of tensor data. In this way, the low-rank component of the original data could be recovered roughly. However, the shortcoming is that the detailed information can not be fully restored, no matter the Sum of the Nuclear Norm (SNN) nor the Tensor Nuclear Norm (TNN) based methods. On the contrary, in the field of signal processing, Convolutional Sparse Coding (CSC) can provide a good representation of the high-frequency component of the image, which is generally associated with the detail component of the data. To this end, we propose two novel methods, LRTC-CSC-I and LRTC-CSC-II, which adopt CSC as a supplementary regularization for LRTC to capture the high-frequency components. Therefore, the LRTC-CSC methods can not only solve the missing value problem but also recover the details. Moreover, the regularizer CSC can be trained with small samples due to the sparsity characteristic. Extensive experiments show the effectiveness of LRTC-CSC methods, and quantitative evaluation indicates that the performance of our models are superior to state-of-the-art methods.

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Cited By

Wang JLi PZhang YLi ZXu JWang QLi J(2024)Automatic calculation of step size and inertia parameter for convolutional dictionary learningPattern Recognition10.1016/j.patcog.2024.110443152:COnline publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1016/j.patcog.2024.110443
Zhang HFan HLi Y(2024)Tensor recovery based on Bivariate Equivalent Minimax-Concave PenaltyPattern Recognition10.1016/j.patcog.2024.110253149:COnline publication date: 1-May-2024
https://dl.acm.org/doi/10.1016/j.patcog.2024.110253

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Information & Contributors

Information

Published In

cover image Pattern Recognition

Pattern Recognition Volume 141, Issue C

Sep 2023

638 pages

ISSN:0031-3203

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Elsevier Ltd.

Publisher

Elsevier Science Inc.

United States

Publication History

Published: 01 September 2023

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Cited By

Wang JLi PZhang YLi ZXu JWang QLi J(2024)Automatic calculation of step size and inertia parameter for convolutional dictionary learningPattern Recognition10.1016/j.patcog.2024.110443152:COnline publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1016/j.patcog.2024.110443
Zhang HFan HLi Y(2024)Tensor recovery based on Bivariate Equivalent Minimax-Concave PenaltyPattern Recognition10.1016/j.patcog.2024.110253149:COnline publication date: 1-May-2024
https://dl.acm.org/doi/10.1016/j.patcog.2024.110253

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