An iterative algorithm for low‐rank tensor completion problem with sparse noise and missing values

Abstract

Robust low‐rank tensor completion plays an important role in multidimensional data analysis against different degradations, such as sparse noise, and missing entries, and has a variety of applications in image processing and computer vision. In this paper, an optimization model for low‐rank tensor completion problems is proposed and a block coordinate descent algorithm is developed to solve this model. It is shown that for one of the subproblems, the closed‐form solution exists and for the other, a Riemannian conjugate gradient algorithm is used. In particular, when all elements are known, that is, no missing values, the block coordinate descent is simplified in the sense that both subproblems have closed‐form solutions. The convergence analysis is established without requiring the latter subproblem to be solved exactly. Numerical experiments illustrate that the proposed model with the algorithm is feasible and effective.