Efficient tensor completion for color image and video recovery: Low-rank tensor train

TL;DR

This paper introduces a novel tensor completion method using tensor train rank, enabling efficient recovery of missing data in color images and videos with superior performance over existing techniques.

Contribution

It proposes new optimization formulations and algorithms based on TT rank, including tensor augmentation to improve recovery effectiveness.

Findings

Outperforms existing tensor completion methods in image and video recovery

Demonstrates effectiveness of tensor train rank in capturing hidden tensor information

Shows significant improvements in recovery accuracy through tensor augmentation

Abstract

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via tensor train (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via tensor train (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher-orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.