To alleviate the bias generated by the l1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. However, the thresholding functions of these nonconvex regularizers may not have closed-form expressions and thus iterations are needed, which increases the computational loads. To solve this issue, we devise a framework to generate sparsity-inducing regularizers with closed-form thresholding functions. These regularizers are applied to low-tubal-rank tensor completion, and efficient algorithms based on the alternating direction method of multipliers are developed. Furthermore, convergence of our methods is analyzed and it is proved that the generated sequences are bounded and any limit point is a stationary point. Experimental results using synthetic and real-world datasets show that the proposed algorithms outperform the state-of-the-art methods in terms of restoration performance.

提出了一种通过闭合形式的阈值函数来生成稀疏感应正则化器，并应用于低秩张量补全问题中，基于交替方向乘子法的高效算法被开发，证明生成的序列是有界的并且任何极限点都是一个稳定点。在合成和实际的数据集上的实验结果表明，所提出的算法在恢复性能方面优于现有技术方法。

通过新颖的稀疏感应正则化方法进行低秩张量补全