Low-rank matrix recovery via smooth rank function and its application in image restoration

Recently, due to smooth rank function generally lie much closer to essential rank function than existing methods, it was used to handle matrix completion problem. In this paper, a new approach for solving low-rank matrix recovery problem based on smooth function is proposed. It not only uses a smooth function to approximate the rank function, but also approximates the l_0 -norm with a continuous and differentiable function. In addition, gradient decreasing approach is used to solve the minimization problem. Finally, experimental results show that our proposed algorithm provides a higher accurate in most cases with reasonable running time. Especially, it has higher approximation performance than other methods for additive Gaussian noise, Rayleigh noise, and mixed noise of Gaussian and salt and pepper noise.