A Fast Designed Thresholding Algorithm for Low-Rank Matrix Recovery with Application to Missing English Text Completion

This article is proposing a fast version of adaptive iterative matrix designed thresholding (AIMDT) algorithm which is studied in our previous work. In AIMDT algorithm, a designed thresholding operator is studied to the problem of recovering the low-rank matrices. By adjusting the size of the parameter, this designed operator can apply less bias to the singular values of a matrice. Using this proposed designed operator, the AIMDT algorithm has been generated to solve the matrix rank minimization problem, and the numerical experiments have shown the superiority of AIMDT algorithm. However, the AIMDT algorithm converges slowly in general. In order to recover the low-rank matrices more quickly, we present a fast AIMDT algorithm to recover the low-rank matrices in this paper. The numerical results on some random low-rank matrix completion problems and a missing English text completion problem show that the our proposed fast algorithm has much faster convergence than the previous AIMDT algorithm.