Efficient Image Denoising Using Global and Local Circulant Representation

TL;DR

This paper introduces Haar-tSVD, a fast and effective image denoising algorithm that exploits nonlocal self-similarity and circulant representations, balancing speed and denoising quality.

Contribution

The paper proposes a novel Haar-tSVD method that simplifies image denoising by unifying global and local correlations without learning local bases.

Findings

Achieves competitive denoising performance on real-world images.

Significantly reduces computational complexity and processing time.

Demonstrates robustness with adaptive noise estimation.

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.