Image Denoising Using Global and Local Circulant Representation
This addresses the need for efficient image denoising in applications with high data volumes, but it is incremental as it builds on existing PCA and transform-based methods.
The paper tackled image denoising by proposing Haar-tSVD, a method combining tensor singular value decomposition with Haar transform to capture global and local correlations efficiently, resulting in a fast, plug-and-play denoiser that balances speed and performance, with experimental validation on various datasets.
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.