一种自适应的鲁棒性矩阵补全方法

An Adaptive Robust Matrix Completion Method

针对传统矩阵补全无约束优化模型在处理奇异噪声损坏的缺失矩阵时鲁棒性较差的问题,提出一种自适应的鲁棒性矩阵补全方法.该方法在目标函数中使用截断核范数作为秩函数旳低秩逼近,并采用对奇异噪声鲁棒的F范数作为损失项恢复矩阵中的缺失值,以降低异常值对算法的影响,提高恢复精确度.在求解该模型过程中,先采用凸优化技巧引入一个动态权重参数,此参数可在更新恢复值时根据当次恢复误差大小自适应地调节下一次更新,再进一步建立求解优化问题的有效迭代方法.实验结果表明,该算法在处理被奇异噪声损坏的矩阵时有较好的鲁棒性和精确性,从而可得到更好的图像修复效果.

Aiming at the problem that the traditional matrix-completion unconstrained optimization model had poor robustness in dealing with missing matrices damaged by singular noise,we proposed an adaptive robust matrix completion method.In this method,truncated kernel norm was used as the low-rank approximation of the rank function in the objective function,and the F-norm robust to singular noise was used as the loss term to recover the missing values in the matrix,so as to reduce the influence of outliers on the algorithm and improve the recovery accuracy.In the process of solving this model,a dynamic weight parameter was introduced by using convex optimization technique,which could be used to adjust the next update adaptively according to the current recovery error when updating the recovery value,and then an effective iteration method was established to solve the optimization problem.The experimental results show that the algorithm has better robustness and accuracy when dealing with matrices damaged by singular noise,so that better image restoration effects can be obtained.