Research on yhe Approximation Properties of Two-Dimensional Stochastic Bases in Image Reconstruction Problems

Abstract

This paper discusses the problems of constructing a basis for two-dimensional stochastic functions, which are samples of random numbers with a given distribution law. The algorithm for constructing an approximation model with the use of this basis is described. The general algorithm for two-dimensional signal recovery using the stochastic basis by the least squares method with a given weight function is given. The approach to solving the problem of recovery of blurred images with a known point scattering function by constructing an inverse filter model is proposed. The approbation of the algorithms was performed on model examples and in the processing of real images obtained by remote sensing of the Earth. To quantify the quality of the recovery, we used a relative root mean square measurement of the difference between the reference and reconstructed images.