A symmetric ADMM-type algorithm for robust tensor completion problems using a regularized SCAD-Schatten-p model with application in color image and video recovery

Abstract

In this work, we design an efficient method for tackling the robust tensor completion problem. Tensor nuclear norm (TNN) is a conventional approach to solve the robust tensor completion problem. However, TNN may yield suboptimal solutions because the tensor rank is non-convex. With this purpose, we introduce an innovative tensor rank approximation that combines the Schatten-p norm with the Smoothly Clipped Absolute Deviation function. Additionally, we incorporate the Total Variation technique into the model to preserve the local smoothing properties of the image. To address the resulting model, we formulate a symmetric Alternating Direction Method of Multipliers algorithm (ADMM). Under some mild conditions, we validate that the solution produced by the algorithm converges to the KKT point of the model. Comprehensive experiments indicate the excellent performance of the proposed approach.