Image denoising with patch based PCA: Local versus global

In recent years, overcomplete dictionaries combined with sparse learning techniques became extremely popular in computer vision. While their usefulness is undeniable, the improvement they provide in specific tasks of computer vision is still poorly understood. The aim of the present work is to demonstrate that for the task of image denoising, nearly state-of-the-art results can be achieved using orthogonal dictionaries only, provided that they are learned directly from the noisy image. To this end, we introduce three patch-based denoising algorithms which perform hard thresholding on the coefficients of the patches in image-specific orthogonal dictionaries. The algorithms differ by the methodology of learning the dictionary: local PCA, hierarchical PCA and global PCA. We carry out a comprehensive empirical evaluation of the performance of these algorithms in terms of accuracy and running times. The results reveal that, despite its simplicity, PCA-based denoising appears to be competitive with the state-of-the-art denoising algorithms, especially for large images and moderate signal-to-noise ratios.