Image Denoising Using Transformed L1 (TL1) Regularization via ADMM

2025-11-19

AI Summary

To address staircase artifacts and contrast loss induced by conventional total variation (TV) regularization in image denoising, this paper proposes a novel denoising model based on transformed ℓ₁ (TL1) regularization. TL1, a nonconvex yet semiconvex regularizer, alleviates excessive edge smoothing caused by the convexity of ℓ₁. The model is efficiently and stably solved via an alternating direction method of multipliers (ADMM) framework incorporating a closed-form TL1 proximal operator, FFT-based acceleration, and periodic boundary handling. Experiments demonstrate that the proposed method achieves significantly higher PSNR and SSIM than TV-based and state-of-the-art sparse regularization methods across diverse degradation scenarios—including Gaussian and Poisson noise—while simultaneously suppressing noise, preserving sharp edge structures, and enhancing local contrast. The approach thus offers both theoretical soundness and computational efficiency.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Non-convex Optimization
• Machine Learning: Learning on the Edge & Model Compression

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Addressing staircase artifacts in TV regularization denoising
• Developing TL1 regularization for improved edge preservation
• Enhancing image contrast while suppressing noise effectively

Innovation

• Transformed L1 regularizer applied to image gradients
• ADMM optimization with closed-form proximal operator
• FFT-based image update under periodic boundaries