Differential
Inclusions, Control and Optimization 20 (2000) 27-40

doi: 10.7151/dmdico.1002

Dieter Schott

*Hochschule Wismar, Fachbereich Elektrotechnik und
Informatik
Philipp-Müller-Straβe, D-23952 Wismar, Germany
*

The aim is to reconstruct a signal function x ∈ L_{2}
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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Received 15 November 1999

Revised 15 February 2000