Geodesic
Signal reconstruction from given phase of the Fourier transform using Fejér monotone methods
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 20 (2000) no. 1, pp. 27-40

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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.
Keywords: signal reconstruction, convex feasibility problem, projection onto convex sets, Fejér monotone iterative methods, Fourier transforms 
Schott, Dieter. Signal reconstruction from given phase of the Fourier transform using Fejér monotone methods. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 20 (2000) no. 1, pp. 27-40. http://geodesic.mathdoc.fr/item/DMDICO_2000_20_1_a1/
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