The formation of image degradation inverse matrix in the Hadamard transformation field

Abstract

Introduction. The algorithm for symbolic method realization of forming image degradation inverse matrix in the Hadamard transforms field is proposed in this work. The problem statement. The main problem for the image restoration is the image degradation inverse matrix computation with different values of Lagrange variation coefficients. It is necessary to lead to diagonal structure the block-diagonal matrices by multiplying for solving this problem. The image degradation inverse matrix is obtained by multiplying of inverse diagonal matrix and matrix of eigenvectors. The program for forming the image degradation inverse matrix of any order was written in software package Matlab. The calculations were performed for matrices of 16, 32 and 128 orders. Conclusions. The algorithm takes into account block-diagonal structure of degradation matrix, that allows to simplify the matrix computation of any order. This algorithm enables to reduce number of calculation operations and to decrease the accumulation of errors.