Signal reconstruction from incomplete coefficients of orthogonal transformations
Abstract
The Fourier transform concepts of magnitude and phase used in signal processing are extended to generalized orthogonal and unitary transformations. Definition of magnitude and phase of the transform coefficients are defined here in such a way that they apply to general discrete transformation with the classical discrete Fourier transform as a special case. A nonexpansive, generalized phasesubstitution operator is given which replaces the general phase of an incomplete signal by its original or by a corrected phase. An iterative Generalized Error Reduction Algorithm is developed which reduces the mean quadratic signal error. The problem of reconstructing the magnitude can be solved uniquely only with additional information from the object domain. The convergence of the generalized iteration algorithm is demonstrated using a noniterative magnitude reconstruction procedure that offers a testable criterion of uniqueness.
 Publication:

Archiv Elektronik und Uebertragungstechnik
 Pub Date:
 October 1987
 Bibcode:
 1987ArElU..41..264W
 Keywords:

 Error Analysis;
 Fourier Transformation;
 Image Reconstruction;
 Iterative Solution;
 Orthogonality;
 Signal Processing;
 Algorithms;
 Convergence;
 Linear Equations;
 Matrices (Mathematics);
 Communications and Radar