Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1998,38
The paper is concerned with the problem of image denoising for the case of grey-scale images. Such images consist of a finite number of regions with smooth boundaries and the image value is assumed 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 smoothness properties and orientation of this boundary. It is also shown that the proposed method provides a near optimal rate of the edge estimation.