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.

翻译：随着成像设备的普及与每日海量图像数据的产生，对高效且有效的图像去噪技术提出了日益增长的需求。本文建立了循环表示下主成分分析（PCA）与哈尔变换之间的理论关联，并提出了一种计算简洁的去噪算法。所提出的方法称为Haar-tSVD，它利用统一的张量奇异值分解（t-SVD）投影结合哈尔变换，以高效捕捉全局与局部图像块相关性。Haar-tSVD作为一种单步、可并行化的即插即用去噪器，无需学习局部基函数，从而在去噪速度与性能之间取得平衡。此外，通过循环结构的特征值分析，引入了一种自适应噪声估计方案以提升算法鲁棒性。为了在强噪声条件下进一步提升性能，我们基于已建立的Haar-PCA关系，将深度神经网络与Haar-tSVD相融合。在不同去噪数据集上的实验结果表明，所提方法在噪声去除方面具有高效性与有效性。代码已公开于https://github.com/ZhaomingKong/Haar-tSVD。