Robust Quaternion Matrix Completion via Fast Randomized Low‐Rank Approximation

ABSTRACT Robust quaternion matrix completion (RQMC), which aims to recover clean data from data that is both incomplete and corrupted by noise, has recently attracted extensive attention in the fields of image and signal processing. This problem can be iteratively solved by applying the close‐form solution of proximal operator, including quaternion singular value thresholding (QSVT) operator. However, the computational complexity of the QSVT operator is extremely high, which seriously affects the solution efficiency of the RQMC model. In this paper, we propose a randomized algorithm for the RQMC model based on the randomized low‐rank approximation technique. Then, through theoretical analysis, we prove that the randomized algorithm offers an ideal approximation of the deterministic algorithm. Finally, through some numerical experiments, we demonstrate the effectiveness and reliability of the proposed algorithm.