Total Variation, Adaptive Total Variation and Nonconvex Smoothly Clipped Absolute Deviation Penalty for Denoising Blocky Images

TL;DR

This paper introduces a new penalty function for image denoising that addresses bias issues in total variation models, demonstrating improved performance on blocky images through theoretical analysis and experiments.

Contribution

Proposes a novel penalty function inspired by high-dimensional statistics, solved efficiently via majorization-minimization, enhancing total variation denoising for blocky images.

Findings

The new penalty reduces bias in total variation models.

The method outperforms traditional TV-based denoising in experiments.

The approach is computationally efficient and theoretically justified.

Abstract

The total variation-based image denoising model has been generalized and extended in numerous ways, improving its performance in different contexts. We propose a new penalty function motivated by the recent progress in the statistical literature on high-dimensional variable selection. Using a particular instantiation of the majorization-minimization algorithm, the optimization problem can be efficiently solved and the computational procedure realized is similar to the spatially adaptive total variation model. Our two-pixel image model shows theoretically that the new penalty function solves the bias problem inherent in the total variation model. The superior performance of the new penalty is demonstrated through several experiments. Our investigation is limited to "blocky" images which have small total variation.