Image denoising: Pointwise adaptive approach

The paper is concerned with the problem of image denoising. We consider the case of black-white type images consisting of a finite number of regions with smooth boundaries and the image value is assumed to be piecewise constant within each region. New method of image denoising is proposed which is adaptive (assumption free) to the number of regions and smoothness properties of edges. The method is based on a pointwise image recovering and it relies on an adaptive choice of a smoothing window. It is shown that the attainable quality of estimation depends on the distance from the point of estimation to the closest boundary and on the smoothness properties of this boundary. As a consequence, it turns out that the proposed method provides the optimal rate of the edge estimation