BM3D Image Denoising with Shape-Adaptive Principal Component Analysis

We propose an image denoising method that ex- ploits nonlocal image modeling, principal component analysis (PCA), and local shape-adaptive anisotropic estimation. The nonlocal modeling is exploited by grouping similar image patches in 3-D groups. The denoising is performed by shrinkage of the spectrum of a 3-D transform applied on such groups. The effectiveness of the shrinkage depends on the ability of the transform to sparsely represent the true-image data, thus separating it from the noise. We propose to improve the sparsity in two aspects. First, we employ image patches (neighborhoods) which can have data-adaptive shape. Second, we propose PCA on these adaptive-shape neighborhoods as part of the employed 3-D transform. The PCA bases are obtained by eigenvalue decompo- sition of empirical second-moment matrices that are estimated from groups of similar adaptive-shape neighborhoods. We show that the proposed method is competitive and outperforms some of the current best denoising methods, especially in preserving image details and introducing very few artifacts.