A Regularization Term Based on a Discrete Total Variation for Mathematical Image Processing

TL;DR

This paper introduces a novel regularization term based on a discretized total variation model that improves edge and corner preservation in noisy image reconstruction and resolution enhancement tasks.

Contribution

A new discretized total variation model (TVnew) is proposed, enhancing image regularization by incorporating directional difference operators and conjugate vector fields.

Findings

Better edge and corner reconstruction in noisy images

Improved resolution enhancement results

Outperforms existing total variation models in experiments

Abstract

In this paper, a new regularization term is proposed to solve mathematical image problems. By using difference operators in the four directions; horizontal, vertical and two diagonal directions, an estimation of derivative amplitude is found. Based on the new obtained estimation, a new regularization term will be defined, which can be viewed as a new discretized total variation (TVprn) model. By improving TVprn, a more effective regularization term is introduced. By finding conjugate of TVprn and producing vector fields with special constraints, a new discretized TV for two dimensional discrete functions is proposed (TVnew). The capability of the new TV model to solve mathematical image problems is examined in some numerical experiments. It is shown that the new proposed TV model can reconstruct the edges and corners of the noisy images better than other TVs. Moreover, two test experiments of resolution enhancement problem are solved and compared with some other different TVs.