Recovering low-rank matrices from corrupted observations via the linear conjugate gradient algorithm

The matrix nuclear norm minimization problem has received much attention in recent years, largely because its highly related to the matrix rank minimization problem arising from controller design, signal processing and model reduction. The alternating direction method is a very popular way to solve this problem due to its simplicity, low storage, practical computation efficiency and nice convergence properties. In this paper, we propose an alternating direction method, where one variable is determined explicitly, and the other variable is computed by a linear conjugate gradient algorithm. At each iteration, the method involves a singular value thresholding and its convergence result is guaranteed in this literature. Extensive experiments illustrate that the proposed algorithm compares favorable with the state-of-the-art algorithms FPCA and IADM_BB which were specifically designed in recent years.