Synthesis of the reverse filter on the criterion of minimum quadratic error of the weight function mismatch of the path «direct - reverse filter»

Abstract

Based on the analysis of known approaches for the synthesis of optimal signal reconstruction algorithms, involving the use of regularizing procedures in solving incorrect inverse problems, and related computational problems, a method for constructing digital filters for solving inverse problems of signal recovery, time series and images using the approximation approach. A method for developing a model of the weight function of the inverse filter, based on the criterion of the minimum quadratic error of the weight function mismatch of the path direct - inverse filter. The problem of restoration of blurred and defocused images in space systems of remote sensing of the Earth is formulat ed, the possibility of reducing the amount of calculations in the processing of two-dimensional data sets by moving to the solution of the one-dimensional problem is shown. Along with a General approach for the synthesis of the inverse filter, a variant of the algorithm with a number of restrictions imposed on the weight function of the inverse filter is presented. On the basis of the considered method, an approach to the problem of restoring blurred images with a known point scattering function is proposed. Approbation of algorithms on model examples and at processing of the real images received at remote sensing of the Earth is carried out. To quantify the quality of recovery, a relative mean square measure of the difference between the reference and recovered signals (images) was used. The results of testing show that the use of this approach allows to reduce the error of recovery, which gives an advantage in solving problems of approximation and data recovery.