Tensor Completion via Convolutional Sparse Coding Regularization

TL;DR

This paper introduces two novel tensor completion methods that incorporate convolutional sparse coding to better recover high-frequency details in missing data scenarios, outperforming existing low-rank based approaches.

Contribution

The paper proposes LRTC-CSC-I and LRTC-CSC-II, integrating convolutional sparse coding as a regularizer to enhance detail recovery in tensor completion tasks.

Findings

LRTC-CSC methods outperform state-of-the-art tensor completion techniques.

The methods effectively recover high-frequency details in missing data.

Experiments demonstrate superior quantitative performance of the proposed models.

Abstract

Tensor data often suffer from missing value problem 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 detail 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. Nevertheless, CSC can not handle the low-frequency component well. 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.