Differential Inclusions, Control and Optimization 20 (2000) 27-40
doi: 10.7151/dmdico.1002

## SIGNAL RECONSTRUCTION FROM GIVEN PHASE OF THE FOURIER TRANSFORM USING FEJÉR MONOTONE METHODS

Dieter Schott

Hochschule Wismar, Fachbereich Elektrotechnik und Informatik
Philipp-Müller-Straβe, D-23952 Wismar, Germany
e-mail: d.schott@et.hs-wismar.de

## Abstract

The aim is to reconstruct a signal function x ∈ L2 if the phase of the Fourier transform [^x] and some additional a-priori information of convex type are known. The problem can be described as a convex feasibility problem. We solve this problem by different Fejér monotone iterative methods comparing the results and discussing the choice of relaxation parameters. Since the a-priori information is partly related to the spectral space the Fourier transform and its inverse have to be applied in each iterative step numerically realized by FFT techniques. The computation uses MATLAB routines.

Keywords: signal reconstruction, convex feasibility problem, projection onto convex sets, Fejér monotone iterative methods, Fourier transforms.

1991 Mathematics Subject Classification: 65J15, 49D20.

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