Tensor Deblurring and Denoising Using Total Variation

TL;DR

This paper extends classical variational denoising and deblurring methods to tensors, enabling effective processing of color images and videos through multi-dimensional total variation regularization and a generalized FISTA algorithm.

Contribution

It introduces a tensor-based extension of the ROF functional and a generalized FISTA method for tensor denoising and deblurring tasks.

Findings

Effective tensor denoising and deblurring demonstrated on color images.

Successful application to video deblurring.

Improved results over traditional matrix-based methods.

Abstract

We consider denoising and deblurring problems for tensors. While images can be discretized as matrices, the analogous procedure for color images or videos leads to a tensor formulation. We extend the classical ROF functional for variational denoising and deblurring to the tensor case by employing multi-dimensional total variation regularization. Furthermore, the resulting minimization problem is calculated by the FISTA method generalized to the tensor case. We provide some numerical experiments by applying the scheme to the denoising, the deblurring, and the recoloring of color images as well as to the deblurring of videos.