Low Tucker rank tensor recovery via ADMM based on exact and inexact iteratively reweighted algorithms

In this paper, we establish a non-convex Lp norm relaxation model for low Tucker rank tensor recovery problem, and equivalently transform it to a non-convex minimization problem with separable structure by introducing series of auxiliary variables. In particular, we propose two alternating direction method of multipliers (ADMM) based on exact and inexact iteratively reweighted algorithms to solve the obtained non-convex relaxation problem respectively, which are proved to be convergent. We implement the proposed algorithms in numerical experiments for solving low Tucker rank tensor recovery problem on simulation data and real data, and compare them with other existing state-of-art algorithms. Numerical results show the effectiveness of the proposed algorithms for solving low rank tensor recovery problem and image recovery.