Spatially adaptive alpha-rooting in BM3D sharpening

The block-matching and 3-D filtering (BM3D) algorithm is currently one of the most powerful and effective image denoising procedures. It exploits a specific nonlocal image modelling through grouping and collaborative filtering. Grouping finds mutually similar 2-D image blocks and stacks them together in 3-D arrays. Collaborative filtering produces individual estimates of all grouped blocks by filtering them jointly, through transform-domain shrinkage of the 3-D arrays (groups). BM3D can be combined with transform-domain alpha-rooting in order to simultaneously sharpen and denoise the image. Specifically, the thresholded 3-D transform-domain coefficients are modified by taking the alpha-root of their magnitude for some alpha > 1, thus amplifying the differences both within and between the grouped blocks. While one can use a constant (global) alpha throughout the entire image, further performance can be achieved by allowing different degrees of sharpening in different parts of the image, based on content-dependent information. We propose to vary the value of alpha used for sharpening a group through weighted estimates of the low-frequency, edge, and high-frequency content of the average block in the group. This is shown to be a viable approach for image sharpening, and in particular it can provide an improvement (both visually and in terms of PSNR) over its global non-adaptive counterpart.