Efficient Chambolle-Pock based algorithms for Convoltional sparse representation

2025-08-04

AI Summary

Convolutional sparse representation (CSR) methods based on the alternating direction method of multipliers (ADMM) often suffer from slow or unstable convergence due to sensitivity to manually tuned penalty parameters. To address this, we propose an end-to-end optimization algorithm grounded in the Chambolle–Pock (CP) primal-dual framework, jointly solving convolutional sparse coding and dictionary learning. Our approach eliminates the need for handcrafted parameter selection and incorporates anisotropic total variation regularization to better preserve structural features. Theoretically, the algorithm guarantees convergence under standard convexity assumptions; empirically, it demonstrates superior convergence robustness and accelerated iteration speed. In noise-free image reconstruction, it achieves performance on par with state-of-the-art ADMM-based methods; in Gaussian denoising tasks, it consistently yields higher PSNR and markedly improved visual quality, confirming its robustness and practical efficacy.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

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

Abstract

Recently convolutional sparse representation (CSR), as a sparse representation technique, has attracted increasing attention in the field of image processing, due to its good characteristic of translate-invariance. The content of CSR usually consists of convolutional sparse coding (CSC) and convolutional dictionary learning (CDL), and many studies focus on how to solve the corresponding optimization problems. At present, the most efficient optimization scheme for CSC is based on the alternating direction method of multipliers (ADMM). However, the ADMM-based approach involves a penalty parameter that needs to be carefully selected, and improper parameter selection may result in either no convergence or very slow convergence. In this paper, a novel fast and efficient method using Chambolle-Pock(CP) framework is proposed, which does not require extra manual selection parameters in solving processing, and has faster convergence speed. Furthermore, we propose an anisotropic total variation penalty of the coefficient maps for CSC and apply the CP algorithm to solve it. In addition, we also apply the CP framework to solve the corresponding CDL problem. Experiments show that for noise-free image the proposed CSC algorithms can achieve rival results of the latest ADMM-based approach, while outperforms in removing noise from Gaussian noise pollution image.

Problem

• Develops efficient Chambolle-Pock algorithms for convolutional sparse representation
• Eliminates manual parameter selection in convolutional sparse coding
• Improves convergence speed and noise removal in image processing

Innovation

• Chambolle-Pock framework for efficient optimization
• Anisotropic total variation penalty for CSC
• Parameter-free solution with faster convergence