Inspired by the accuracy and efficiency of the $\gamma$ -norm of a matrix, which is closer to the original rank minimization problem than nuclear norm minimization (NNM), we generalize the $\gamma$ -norm of a matrix to tensors and propose a new tensor completion approach within the tensor singular value decomposition (t-svd) framework. An efficient algorithm, which combines the augmented Lagrange multiplier and closed-resolution of a cubic equation, was developed to solve the associated nonconvex tensor multi-rank minimization problem. Experimental results show that the proposed approach has an advantage over current state of the art algorithms in recovery accuracy.

中文翻译：

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一种新颖的三阶张量补全正则化模型


受到矩阵 $\gamma$ 范数的准确性和效率的启发，它比核范数最小化 (NNM) 更接近原始的秩最小化问题，我们将矩阵的 $\gamma$ 范数推广到张量，并且在张量奇异值分解（t-svd）框架内提出一种新的张量完成方法。开发了一种结合了增广拉格朗日乘子和三次方程闭分辨率的有效算法来解决相关的非凸张量多秩最小化问题。实验结果表明，所提出的方法在恢复精度方面优于当前最先进的算法。