Pointwise Shape-adaptive Dct as an Overcomplete Denoising Tool

A novel approach to image-denoising based on the shapeadaptive DCT (SA-DCT) is presented. The anisotropic LPAICI technique is used in order to deÞne the shape of the transform’s support in a pointwise adaptive manner. It means that for each point in the image an adaptive estimation neighborhood is found. For each one of these neighborhoods a SADCT is performed. The thresholded SA-DCT coefÞcients are used to reconstruct a local estimate of the signal within the adaptive-shape region. Since regions corresponding to different points are in general overlapping (and thus generate an overcomplete representation of the signal), the local estimates are averaged together using adaptive weights that depend on the region’s statistics. A Wiener Þltering procedure in SA-DCT domain is also proposed. Simulation experiments conÞrm the advanced quality of the Þnal estimate. Not only objective criteria scores are high, but also the visual appearence of the estimate is superior: edges are clean, and no unpleasant ringing artifacts are introduced by the Þtted transform.