Image Denoising Using Global and Local Circulant Representation

2025-12-29

AI Summary

To address insufficient modeling of global and local structures and low computational efficiency in image denoising, this paper proposes Haar-tSVD: a learning-free, first-order parallel, plug-and-play denoiser. We theoretically establish the equivalence between PCA and the Haar transform under cyclic representation—a novel insight. Building upon this, we introduce a joint t-SVD and Haar transform projection framework that simultaneously captures global low-rankness and local sparsity. Furthermore, we design an eigenvalue-analysis-based adaptive noise estimation mechanism, enabling interpretable, synergistic enhancement with deep networks. Extensive experiments on multiple benchmark datasets demonstrate state-of-the-art performance; Haar-tSVD achieves real-time, single-step inference with strong robustness to varying noise levels. The implementation is open-source and supports seamless plug-and-play deployment.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Machine Learning: Representation Learning
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

The proliferation of imaging devices and countless image data generated every day impose an increasingly high demand on efficient and effective image denoising. In this paper, we establish a theoretical connection between principal component analysis (PCA) and the Haar transform under circulant representation, and present a computationally simple denoising algorithm. The proposed method, termed Haar-tSVD, exploits a unified tensor singular value decomposition (t-SVD) projection combined with Haar transform to efficiently capture global and local patch correlations. Haar-tSVD operates as a one-step, parallelizable plug-and-play denoiser that eliminates the need for learning local bases, thereby striking a balance between denoising speed and performance. Besides, an adaptive noise estimation scheme is introduced to improve robustness according to eigenvalue analysis of the circulant structure. To further enhance the performance under severe noise conditions, we integrate deep neural networks with Haar-tSVD based on the established Haar-PCA relationship. Experimental results on various denoising datasets demonstrate the efficiency and effectiveness of proposed method for noise removal. Our code is publicly available at https://github.com/ZhaomingKong/Haar-tSVD.

Problem

• Develops a fast image denoising algorithm using circulant representation
• Combines tensor SVD and Haar transform to capture global and local correlations
• Integrates deep neural networks to enhance performance under severe noise

Innovation

• Unified t-SVD projection with Haar transform
• One-step plug-and-play denoiser without learning
• Integration of deep neural networks with Haar-tSVD