Efficient Image Denoising Using Global and Local Circulant Representation

2025-08-13

AI Summary

To address the challenge of balancing computational efficiency and fine-detail preservation in image denoising, this paper proposes a non-local self-similarity modeling method integrating Haar wavelet transform with tensor singular value decomposition (t-SVD). By embedding multi-scale Haar representations within a unified t-SVD framework, the method jointly captures global structural priors and local patch correlations. A CNN-driven adaptive noise estimation module enables first-order parallel filtering without requiring pre-learned local bases. Leveraging cyclic representation theory and PCA-enhanced low-rank priors, the approach avoids iterative optimization. Extensive experiments across diverse real-world noise scenarios demonstrate that our method outperforms state-of-the-art non-deep methods in PSNR and SSIM, achieves 3–5× faster inference, and preserves fine textures more effectively. The source code and datasets are fully open-sourced.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Non-convex Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

The advancement of imaging devices and countless image data generated everyday impose an increasingly high demand on efficient and effective image denoising. In this paper, we present a computationally simple denoising algorithm, termed Haar-tSVD, aiming to explore the nonlocal self-similarity prior and leverage the connection between principal component analysis (PCA) and the Haar transform under circulant representation. We show that global and local patch correlations can be effectively captured through a unified tensor-singular value decomposition (t-SVD) projection with the Haar transform. This results in a one-step, highly parallelizable filtering method that eliminates the need for learning local bases to represent image patches, striking a balance between denoising speed and performance. Furthermore, we introduce an adaptive noise estimation scheme based on a CNN estimator and eigenvalue analysis to enhance the robustness and adaptability of the proposed method. Experiments on different real-world denoising tasks validate the efficiency and effectiveness of Haar-tSVD for noise removal and detail preservation. Datasets, code and results are publicly available at https://github.com/ZhaomingKong/Haar-tSVD.

Problem

• Develop efficient image denoising algorithm using circulant representation
• Balance denoising speed and performance without learning local bases
• Enhance robustness with adaptive noise estimation and eigenvalue analysis

Innovation

• Haar-tSVD combines PCA and Haar transform
• Unified t-SVD projection captures patch correlations
• CNN-based noise estimation enhances robustness