"Sparse + Low-Rank'' Tensor Completion Approach for Recovering Images and Videos

TL;DR

This paper introduces a novel tensor completion method combining sparsity and low-rank structures in the DCT domain, significantly improving image and video recovery from highly undersampled data.

Contribution

It proposes two new tensor completion models and algorithms leveraging DCT-based sparsity and low-rank properties, advancing the state-of-the-art in image and video recovery.

Findings

Outperforms existing tensor completion methods in high missing data scenarios

Effective in color image inpainting and video data recovery

Demonstrates superior performance through numerical experiments

Abstract

Recovering color images and videos from highly undersampled data is a fundamental and challenging task in face recognition and computer vision. By the multi-dimensional nature of color images and videos, in this paper, we propose a novel tensor completion approach, which is able to efficiently explore the sparsity of tensor data under the discrete cosine transform (DCT). Specifically, we introduce two ``sparse + low-rank'' tensor completion models as well as two implementable algorithms for finding their solutions. The first one is a DCT-based sparse plus weighted nuclear norm induced low-rank minimization model. The second one is a DCT-based sparse plus $p$-shrinking mapping induced low-rank optimization model. Moreover, we accordingly propose two implementable augmented Lagrangian-based algorithms for solving the underlying optimization models. A series of numerical experiments including color image inpainting and video data recovery demonstrate that our proposed approach performs better than many existing state-of-the-art tensor completion methods, especially for the case when the ratio of missing data is high.