Restoration of Deterministic and Interference Distorted Signals and Images with Use of the Generalized Spectra Based on Orthogonal Polynomials and Functions

Abstract

Restoration algorithms of signals and images on the basis of their generalized spectra in bases of orthogonal polynomials and functions at absence and presence of random distortions have been examined. It is shown that in absence of hindrances the number of coefficients of the generalized spectrum of a restored signal (image) is determined by the desired approximation error at use of one or another metrics of functional space. If hindrances take place then there is an optimum number of coefficients of the generalized spectrum for signal (image) restoration. Working data of the proposed algorithms for various types of useful signals have been illustrated.

Keywords

• signal and image restoration
• generalized signal spectrum
• orthogonal polynomials
• gauss quadrature formulas
• approximation mean square error
• maximum likelihood method
• incomplete signal reception