New models of image restoration

Abstract

This paper presents two new models of image restoration under consideration the linear-invariant system of image formation, which is described by the convolution type Fradholm integral equation of the first kind. The models come to the preliminary optimal restoration of the noise imposed on the image when the last is formed. The corresponding approximate solutions of the restored image are described and the comparative estimates are given. Also in the framework of these models the well-known inverse and Wiener filters, as well the new filters are considered. The best approximation of the true image in the sense of the mean-root-square error is obtained and its main properties are considered. It is shown that this approximation is better than the Wiener estimate obtained in the classical model of image restoration.