Abstract: In engineering applications, including intelligent transportation systems, data mining, distance measurements etc., most of matrix recovery models are proposed based on the convex relaxation of matrix rank function, and have obtained the significant recovery performances. However, the studies of compression sensing show that the convex relaxation function has many disadvantages in the signal recovery task. In this paper, the non-convex relaxation function is thus exploited to solve the matrix recovery problem under Poisson noise. In specific, a Log-sum function regularized recovery model is introduced, and then an efficient algorithm is designed for the proposed model and its convergence result is also provided. Experimental results on the simulated and real data demonstrate that the proposed method can obtain better recovery performance compared with the existing methods.

Key words: matrix recovery, non-convex relaxation, Log-sum function, Poisson noise