Image Denoising Using Transformed L1 (TL1) Regularization via ADMM

TL;DR

This paper introduces a novel TL1 regularizer for image denoising applied to gradients, solved efficiently with ADMM, resulting in better noise suppression and contrast preservation compared to traditional TV methods.

Contribution

The paper proposes a new TL1 regularization model for image denoising, with a closed-form proximal operator and FFT-based solution, improving over classical TV regularization.

Findings

Achieves superior denoising performance

Effectively suppresses noise while preserving edges

Enhances image contrast

Abstract

Total variation (TV) regularization is a classical tool for image denoising, but its convex $\ell_1$ formulation often leads to staircase artifacts and loss of contrast. To address these issues, we introduce the Transformed $\ell_1$ (TL1) regularizer applied to image gradients. In particular, we develop a TL1-regularized denoising model and solve it using the Alternating Direction Method of Multipliers (ADMM), featuring a closed-form TL1 proximal operator and an FFT-based image update under periodic boundary conditions. Experimental results demonstrate that our approach achieves superior denoising performance, effectively suppressing noise while preserving edges and enhancing image contrast.