Image Denoising Using Global and Local Circulant Representation

TL;DR

Haar-tSVD introduces a fast, one-step image denoising framework that couples global and local circulant representations via a unified t-SVD projection and the Haar transform. It establishes a theoretical link between PCA and Haar under circulant structure, enabling a one-shot filtering that avoids learning local bases. Adaptive noise estimation using eigenvalue analysis and a learning-based enhancement strategy (RA-Haar-tSVD) improve robustness under real-world and severe noise. The method achieves competitive performance on color images, real-world videos, and hyperspectral imagery, with efficient parallelizable implementation and publicly available code.

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.

Figures (24)

• Figure 1: Illustration of the patch-based framework for traditional denoisers.
• Figure 2: Flowchart of the proposed Haar-tSVD method. It is a one-step filtering algorithm built upon global and local circulant representation.
• Figure 3: Bases $\mathcal{U}$ and $\mathcal{V}$ learned from noisy and clean patches for varying $K$.
• Figure 4: Different strategies for obtaining t-SVD bases $\mathcal{U}$ and $\mathcal{V}$.
• Figure 5: The CNN-based noise estimation approach.

Theorems & Definitions (2)

• Definition 2.1: T-product
• Definition 2.2: T-SVD