Quaternion Tensor Completion with Sparseness for Color Video Recovery

TL;DR

This paper introduces a quaternion tensor-based low-rank completion algorithm with sparsity constraints for effective color video recovery, preserving RGB structure and local details.

Contribution

It proposes a novel quaternion tensor completion method using TQt-rank, QTDCT regularization, and sparsity modeling, advancing color video recovery techniques.

Findings

Outperforms existing methods in color video recovery accuracy

Effectively preserves local details and RGB structure

Demonstrates robustness across various video datasets

Abstract

A novel low-rank completion algorithm based on the quaternion tensor is proposed in this paper. This approach uses the TQt-rank of quaternion tensor to maintain the structure of RGB channels throughout the entire process. In more detail, the pixels in each frame are encoded on three imaginary parts of a quaternion as an element in a quaternion matrix. Each quaternion matrix is then stacked into a quaternion tensor. A logarithmic function and truncated nuclear norm are employed to characterize the rank of the quaternion tensor in order to promote the low rankness of the tensor. Moreover, by introducing a newly defined quaternion tensor discrete cosine transform-based (QTDCT) regularization to the low-rank approximation framework, the optimized recovery results can be obtained in the local details of color videos. In particular, the sparsity of the quaternion tensor is reasonably characterized by l1 norm in the QDCT domain. This strategy is optimized via the two-step alternating direction method of multipliers (ADMM) framework. Numerical experimental results for recovering color videos show the obvious advantage of the proposed method over other potential competing approaches.