This paper describes a Bayesian restoration method applied to two-dimensional measured images, whose detector response function is not completely known. The response function is assumed Gaussian with standard deviation depending on the estimate of the local density of the image. The convex hull of the K-nearest neighbours (KNN) of each 'on' pixel is used to compute the local density. The method has been tested on 'sparse' images, with and without noise background. \ua9 1989