基于lP范数的非凸低秩张量最小化

在低秩矩阵、张量最小化问题中,凸函数容易求得最优解,而非凸函数可以得到更低秩的局部解.文中基于非凸替换函数的低秩张量恢复问题,提出基于l_p范数的非凸张量模型.采用迭代加权核范数算法求解模型,实现低秩张量最小化.在合成数据和真实图像上的大量实验验证文中方法的恢复性能.

Nonconvex Low-Rank Tensor Minimization Based on lP Norm

For the low-rank matrix and tensor minimization problem, the optimal solution of convex function can be obtained easily, and the better low-rank solution can be obtained from the local minimum of the corresponding nonconvex function. The low-rank tensor recovery problem based on the nonconvex function is studied in this paper. A nonconvex low-rank tensor model based on l_p norm is proposed. In addition, tensor based iteratively reweighted nuclear norm algorithm is proposed to solve the nonconvex low-rank tensor minimization problem. The weighted singular value thresholding problem is solved by the tensor based iteratively reweighted nuclear norm algorithm. The objective function value monotonically decreases and its convergence can be theoretically proved. The recovery performance of the proposed method is demonstrated by comprehensive experiments on both synthetic data and real images.