加权核范数的矩阵恢复正则化算法

Regularization algorithm for matrix recovery based on reweighted nuclear norm

在压缩感知、矩阵恢复等研究领域,弹性正则化方法引起了广泛的关注.由于该方法可以避免数据建模时(特别是解决复杂问题时)解出现大的波动,从而被视为解决相关问题的优秀方法之一.针对以上情况,提出基于Schatten p-norm最小化的矩阵恢复的弹性正则化模型,旨在加强解决复杂问题时的解的稳定性并改进矩阵恢复研究领域中基于核范数最小化逼近秩函数这一传统方法的缺陷.同时,为了解决提出的非凸模型,采用交替迭代算法和MM算法求解所提出的模型.实验结果表明,所提出的算法能够有效地恢复测量值较少的矩阵.

Whether in the field of compressive sensing or matrix recovery,the elastic-net regularization has attracted wide attention.It is a successful approach in statistical modeling which can avoid large variations which always occur in estimating complex models.In order to improve the defect of the nuclear norm minimization which requires more measurement for exact recovery of low rank solution and enhance the stability of the solution,we proposed a new matrix elastic-net regularization method based on Schatten p-norm minimization（MEN-Sp）.To minimize this no-convex model,alternating iterative algorithm and MM algorithm were adopted.And the superiority of the MEN-Sp regularization algorithm for recovering the matrix with fewer measurement was also proved by the simulation experiment.