FCTN decomposition for tensor completion with factor double sparsity regularization

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.