FCTN decomposition for tensor completion with factor double sparsity regularization

Ronghuan Zhang; Yiming Zhang; Hualin Zhang; Yingpin Chen; Ronghuan Zhang; Yiming Zhang; Hualin Zhang; Yingpin Chen

doi:10.3934/era.2026255

Electronic Research Archive

2026, Volume 34, Issue 8: 5723-5757. doi: 10.3934/era.2026255

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Research article

FCTN decomposition for tensor completion with factor double sparsity regularization

1.
School of Physics and Information Engineering, Minnan Normal University, Zhangzhou 363000, China
2.
School of Life Sciences, Xiamen University, Xiamen 361000, China
† The authors contributed equally to this work.

Received: 07 May 2026 Revised: 10 June 2026 Accepted: 23 June 2026 Published: 06 July 2026

To address the performance degradation of fully connected tensor network decomposition under high missing rates, where relying solely on global low-rank priors is insufficient, we proposed a novel FCTN decomposition method based on factor double sparsity regularization, termed FCTN-FDS. The proposed method jointly incorporated gradient factor regularization and structural sparsity regularization into the FCTN framework, constraining the model at the same time from two levels: Factor representation ability and network structure, to enhance the robustness of rank selection and reduce redundant parameters. Furthermore, an efficient algorithm based on proximal alternating minimization was designed to guarantee convergence and computational efficiency. Experimental results on color image, multispectral image, and MRI recovery tasks demonstrated that the proposed method achieves superior performance in recovering fine details and complex textures compared to existing approaches, validating its effectiveness and strong representational capability.
- tensor decomposition,
- low rank constraint,
- sparsity regularization,
- tensor completion,
- Full connected tensor network
Citation: Ronghuan Zhang, Yiming Zhang, Hualin Zhang, Yingpin Chen. FCTN decomposition for tensor completion with factor double sparsity regularization[J]. Electronic Research Archive, 2026, 34(8): 5723-5757. doi: 10.3934/era.2026255

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Abstract

To address the performance degradation of fully connected tensor network decomposition under high missing rates, where relying solely on global low-rank priors is insufficient, we proposed a novel FCTN decomposition method based on factor double sparsity regularization, termed FCTN-FDS. The proposed method jointly incorporated gradient factor regularization and structural sparsity regularization into the FCTN framework, constraining the model at the same time from two levels: Factor representation ability and network structure, to enhance the robustness of rank selection and reduce redundant parameters. Furthermore, an efficient algorithm based on proximal alternating minimization was designed to guarantee convergence and computational efficiency. Experimental results on color image, multispectral image, and MRI recovery tasks demonstrated that the proposed method achieves superior performance in recovering fine details and complex textures compared to existing approaches, validating its effectiveness and strong representational capability.

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