通过随机排序的交替方向乘子法的矩阵恢复

为了解决交替方向乘子法（ADMM）在求解广义的鲁棒主成分分析（G-RPCA）模型时结果不收敛的问题，提出用随机排序的交替方向乘子法（RP-ADMM）来求解这一模型，并且通过数值模拟和实例验证证明了该算法的有效性。结果表明，该算法求解G-RPCA模型较目前已有的算法速度更快、鲁棒性更高；在处理同时被稀疏大噪声和稠密小噪声污染的图片时，能较理想地分离出图像的低秩部分、大噪声部分和小噪声部分。

Matrix recovery by randomly permuted alternating direction method of multipliers (ADMM)

In order to solve the problem that the alternating direction method of multipliers (ADMM) does not converge when solving the generalized robust principal component analysis (G-RPCA)model,this paper proposes randomly permuted ADMM (RP-ADMM) process to solve this model.The effectiveness of the algorithm was proved by numerical experiments and case verification.Numerical experiments showed that the proposed algorithm is faster and more robust than existing algorithms when solving the G-RPCA model.When dealing with pictures that are simultaneously polluted by sparse large noise and dense small noise,the algorithm can effectively isolate the low rank part of the image,the large noise part and the small noise part.