A Fixed Point Iterative Method for Low n-Rank Tensor Pursuit

The linearly constrained tensorn-rank minimization problem is an extension of matrix rank minimization. It is applicable in many fields which use the multi-way data, such as data mining, machine learning and computer vision. In this paper, we adapt operator splitting technique and convex relaxation technique to transform the original problem into a convex, unconstrained optimization problem and propose a fixed point iterative method to solve it. We also prove the convergence of the method under some assumptions. By using a continuation technique, we propose a fast and robust algorithm for solving the tensor completion problem, which is called FP-LRTC (Fixed Point for Lown-Rank Tensor Completion). Our numerical results on randomly generated and real tensor completion problems demonstrate that this algorithm is effective, especially for “easy” problems.