Efficient Image Denoising Using Global and Local Circulant Representation
This addresses the need for efficient denoising in imaging applications, but it appears incremental as it builds on existing concepts like PCA and t-SVD with a novel integration.
The paper tackled image denoising by proposing Haar-tSVD, a computationally simple algorithm that uses global and local circulant representation to capture patch correlations, resulting in a one-step, parallelizable method that balances speed and performance, with experiments validating its efficiency and effectiveness on real-world tasks.
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.