Absorption and phase retrieval with Tikhonov and joint sparsity regularizations

Bruno Sixou; Valentina Davidoiu; Max Langer; Francoise Peyrin

doi:10.3934/ipi.2013.7.267

Article Contents

2013, Volume 7, Issue 1: 267-282. Doi: 10.3934/ipi.2013.7.267

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Absorption and phase retrieval with Tikhonov and joint sparsity regularizations

1.
CREATIS, CNRS UMR 5220, Inserm U630, INSA Lyon, Université Lyon 1, F-69621 Villeurbanne Cedex
2.
European Synchrotron Radiation Facility, 6 rue Jules Horowitz, F-38043, Grenoble Cedex

Received: June 2012

Revised: October 2012

Published: February 2013

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Abstract

The X-ray phase contrast imaging technique relies on the measurement of the Fresnel diffraction intensity patterns associated to a phase shift induced by the object. The simultaneous recovery of the phase and of the absorption is an ill-posed nonlinear inverse problem. In this work, we investigate the resolution of this problem with nonlinear Tikhonov regularization and with a joint sparsity constraint regularization. The regularization functionals are minimized with a Gauss-Newton method and with a fixed point iterative method based on a surrogate functional. The algorithms are evalutated using simulated noisy data. The joint sparsity regularization gives better reconstructions for high noise levels.

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Mathematics Subject Classification: Primary: 65J22, 65J20, 65K10; Secondary: 52A41.

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