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Low-rank And Sparse Matrix Recovery From Noisy Observations via 3-block ADMM Algorithm
Peng Wang,Chengde Lin,Xiaobo Yang,Shengwu Xiong
Keywords:low-rank, sparse, nuclear norm minimization, l_1-norm minimization, 3-block alternating direction method
      Recovering low-rank and sparse matrix from a given matrix arises in many applications, such as image processing, video background substraction, and so on. The 3-block alternating direction method of multipliers (ADMM) has been applied successfully to solve convex problems with 3-block variables. However, the existing sufficient conditions to guarantee the convergence of the 3-block ADMM usually require the penalty parameter $\gamma$ to satisfy a certain bound, which may affect the performance of solving the large scale problem in practice. In this paper, we propose the 3-block ADMM to recover low-rank and sparse matrix from noisy observations. In theory, we prove that the 3-block ADMM is convergent when the penalty parameters satisfy a certain condition and the objective function value sequences generated by 3-block ADMM converge to the optimal value. Numerical experiments verify that proposed method can achieve higher performance than existing methods both in terms of efficiency and accuracy.