Rank adaptive atomic decomposition for low-rank matrix completion and its application on image recovery

Recently, a greedy algorithm called Atomic Decomposition for Minimum Rank Approximation (ADMiRA) was proposed. It has solved the low-rank matrix approximation problem when the rank of the matrix is known. However, the rank of the matrix is usually unknown in practical application. In this paper, a Rank Adaptive Atomic Decomposition for Low-Rank Matrix Completion (RAADLRMC) algorithm is proposed based on the Atomic Decomposition for Minimum Rank Approximation. The advantage of RAADLRMC is that it works when the parameter rank-r of matrix is not given. Furthermore, the step size of iteration is decreased adaptively in order to improve the efficiency and accuracy. As illustrated by our experiments, our algorithm is robust, and the rank of matrix can be predicted accurately.