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Ball intersection model for Fejér zones of convex closed sets

100%

Schott D.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2001

tom 21

nr 1

51-79

Strongly Fejér monotone mappings are widely used to solve convex problems by corresponding iterative methods. Here the maximal of such mappings with respect to set inclusion of the images are investigated. These mappings supply restriction zones for the successors of Fejér monotone iterative methods. The basic tool is the representation of the images by intersection of certain balls.

Signal reconstruction from given phase of the Fourier transform using Fejér monotone methods

100%

Schott D.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2000

tom 20

nr 1

27-40

The aim is to reconstruct a signal function x ∈ L₂ if the phase of the Fourier transform [x̂] 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.

Ograniczanie wyników

2 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2 Schott D.

1 2001

1 2000

Wyniki wyszukiwania

Ball intersection model for Fejér zones of convex closed sets

Signal reconstruction from given phase of the Fourier transform using Fejér monotone methods