Image Denoising Using Global and Local Circulant Representation

TL;DR

This paper introduces Haar-tSVD, a fast and effective image denoising method that combines circulant representations, tensor SVD, and deep learning to improve noise removal performance without complex training.

Contribution

It establishes a theoretical link between PCA and Haar transform under circulant representation and develops a simple, parallelizable denoising algorithm integrating deep neural networks.

Findings

Haar-tSVD effectively balances denoising speed and quality.

The method outperforms existing techniques on various datasets.

Adaptive noise estimation enhances robustness under severe noise.

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.