Regularized Newton methods for x-ray phase contrast and general imaging problems

2016-03-21 | journal article; research paper. A publication with affiliation to the University of Göttingen.

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​Regularized Newton methods for x-ray phase contrast and general imaging problems​
Maretzke, S. ; Bartels, M. ; Krenkel, M.; Salditt, T.   & Hohage, T. ​ (2016) 
Optics Express24(6) pp. 6490​-6506​.​ DOI: https://doi.org/10.1364/OE.24.006490 

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Authors
Maretzke, Simon ; Bartels, Matthias ; Krenkel, Martin; Salditt, Tim ; Hohage, Thorsten 
Abstract
Like many other advanced imaging methods, x-ray phase contrast imaging and tomography require mathematical inversion of the observed data to obtain real-space information. While an accurate forward model describing the generally nonlinear image formation from a given object to the observations is often available, explicit inversion formulas are typically not known. Moreover, the measured data might be insufficient for stable image reconstruction, in which case it has to be complemented by suitable a priori information. In this work, regularized Newton methods are presented as a general framework for the solution of such ill-posed nonlinear imaging problems. For a proof of principle, the approach is applied to x-ray phase contrast imaging in the near-field propagation regime. Simultaneous recovery of the phase-and amplitude from a single near-field diffraction pattern without homogeneity constraints is demonstrated for the first time. The presented methods further permit all-at-once phase contrast tomography, i.e. simultaneous phase retrieval and tomographic inversion. We demonstrate the potential of this approach by three-dimensional imaging of a colloidal crystal at 95nm isotropic resolution. (C) 2016 Optical Society of America
Issue Date
21-March-2016
Journal
Optics Express 
Organization
Institut für Numerische und Angewandte Mathematik ; Fakultät für Physik ; Institut für Röntgenphysik 
Working Group
RG Salditt (Structure of Biomolecular Assemblies and X-Ray Physics) 
RG Hohage (Inverse Problems) 
ISSN
1094-4087
Subject(s)
x-ray imaging

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