A Novel Regularized Model for Third-Order Tensor Completion

Abstract

Inspired by the accuracy and efficiency of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\gamma$</tex-math></inline-formula> -norm of a matrix, which is closer to the original rank minimization problem than nuclear norm minimization (NNM), we generalize the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\gamma$</tex-math></inline-formula> -norm of a matrix to tensors and propose a new tensor completion approach within the tensor singular value decomposition (t-svd) framework. An efficient algorithm, which combines the augmented Lagrange multiplier and closed-resolution of a cubic equation, was developed to solve the associated nonconvex tensor multi-rank minimization problem. Experimental results show that the proposed approach has an advantage over current state of the art algorithms in recovery accuracy.