This paper introduces a novel algorithm for matrix completion, called singular value thresholding (SVT), which efficiently approximates the matrix with minimum nuclear norm under convex constraints. The algorithm is iterative and applies soft-thresholding to the singular values of a matrix at each step. It is particularly effective for low-rank matrix completion problems due to its low storage requirements and computational efficiency. The algorithm is shown to converge to the optimal solution under certain conditions and is demonstrated to work well on large-scale problems, such as recovering a 1000x1000 matrix from a small subset of its entries. The SVT algorithm is related to linearized Bregman iterations for $\ell_1$ minimization and can be extended to handle various convex constraints. The paper also provides a convergence analysis and numerical examples showing the algorithm's effectiveness in solving matrix completion problems.This paper introduces a novel algorithm for matrix completion, called singular value thresholding (SVT), which efficiently approximates the matrix with minimum nuclear norm under convex constraints. The algorithm is iterative and applies soft-thresholding to the singular values of a matrix at each step. It is particularly effective for low-rank matrix completion problems due to its low storage requirements and computational efficiency. The algorithm is shown to converge to the optimal solution under certain conditions and is demonstrated to work well on large-scale problems, such as recovering a 1000x1000 matrix from a small subset of its entries. The SVT algorithm is related to linearized Bregman iterations for $\ell_1$ minimization and can be extended to handle various convex constraints. The paper also provides a convergence analysis and numerical examples showing the algorithm's effectiveness in solving matrix completion problems.