Tensor Completion via Smooth Rank Function Low-Rank Approximate Regularization

Abstract

In recent years, the tensor completion algorithm has played a vital part in the reconstruction of missing elements within high-dimensional remote sensing image data. Due to the difficulty of tensor rank computation, scholars have proposed many substitutions of tensor rank. By introducing the smooth rank function (SRF), this paper proposes a new tensor rank nonconvex substitution function that performs adaptive weighting on different singular values to avoid the performance deficiency caused by the equal treatment of all singular values. On this basis, a novel tensor completion model that minimizes the SRF as the objective function is proposed. The proposed model is efficiently solved by adding the hot start method to the alternating direction multiplier method (ADMM) framework. Extensive experiments are carried out in this paper to demonstrate the resilience of the proposed model to missing data. The results illustrate that the proposed model is superior to other advanced models in tensor completeness.