A Nonlocal and Shape-adaptive Transform-domain Collaborative Filtering

We propose an image denoising method that exploits both nonlocal image modeling and locally adaptive anisotropic estimation. The method uses grouping of adaptive-shape neighborhoods whose surrounding square supersets have been found similar by a blockmatching procedure. The data deÞned on these grouped neighborhoods is stacked together, resulting in 3-D data structures which are generalized cylinders with adaptive-shape cross sections. Because of the similarity, which follows from the matching, and because of the adaptive selection of the shape of the neighborhoods, these 3-D groups are characterized by a high correlation along all the three dimensions. We apply a 3-D decorrelating transform, computed as a separable composition of the Shape-Adaptive DCT (SA-DCT) and a 1-D orthonormal transform, and subsequently attenuate the noise by spectrum shrinkage with hard-thresholding or Wiener Þltering. Inversion of the 3-D transform produces individual estimates for all grouped neighborhoods. These estimates are returned to their original locations and aggregated with other estimates coming from different groups. Overall, this method generalizes two existing Þlters: the BM3D Þlter, which uses grouping of Þxed-size square blocks, and the Poinwise SA-DCT Þlter, which exploits shrinkage on adaptive-shape supports. We show that the developed method inherits the strengths of both Þlters, resulting in a very effective and ßexible tool for image denoising.