• 论文 •

### 基于近似稀疏正则化的低秩张量填充算法

1. 1. 赣南师范大学 数学与计算机科学学院, 赣州 341000;
2. 杭州电子科技大学理学院, 杭州 310018
• 收稿日期:2021-10-05 发布日期:2023-03-16
• 基金资助:
国家自然科学基金（62266002，61863001，82060328，12071104，61962003）；浙江省自然科学基金（LD19A010002）和江西省自然科学基金（20224BAB202004，20192BAB205086，20202BAB202017）资助.

Hu Wenyu, Zheng Weidong, Huang Jinhong, Yu Gaohang. APPROXIMATE SPARSITY REGULARIZED LOW-RANK TENSOR COMPLETION[J]. Journal on Numerica Methods and Computer Applications, 2023, 44(1): 53-67.

### APPROXIMATE SPARSITY REGULARIZED LOW-RANK TENSOR COMPLETION

Hu Wenyu1, Zheng Weidong1, Huang Jinhong1, Yu Gaohang2

1. 1. School of Mathematics and Computer Sciences, Gannan Normal University, GanZhou 341000, China;
2. Department of Mathematics, School of Science, Hangzhou Dianzi University, HangZhou 310018, China
Considering that most of the current Low-Rank Tensor Completion (LRTC) models suffer from the shortage of over-constraints on the sparsity, some subtle features of the recovered data are ignored. Based on low-rank matrix decomposition and framelet transform, in this paper we propose an Approximate Sparsity regularization for Low-Rank Tensor Completion (AS-LRTC) by introducing a $\ell_0$-norm regularized term of the soft-thresholding operator. To solve the resulted model effectively, we rewrite the $\ell_0$ norm as a weighted $\ell_1$ norm with a nonlinear discontinuous weight function which is then approximated by a continuous weight function, and then design a Block Successive Upper bound Minimization (BSUM) solving algorithm. Under certain condition, we can prove the convergence of the proposed algorithm. Extensive experiments are conducted to show that the proposed algorithm is better than the classic algorithms at recovering the local detail features of images.