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Applied Mathematics and Mechanics

, Volume 29, Issue 1, pp 101–112 | Cite as

Algorithm for phase contrast X-ray tomography based on nonlinear phase retrieval

  • Ni Wen-lei  (倪文磊)Email author
  • Zhou Tie  (周铁)
Article

Abstract

A new algorithm for phase contrast X-ray tomography under holographic measurement was proposed in this paper. The main idea of the algorithm was to solve the nonlinear phase retrieval problem using the Newton iterative method. The linear equations for the Newton directions were proved to be ill-posed and the regularized solutions were obtained by the conjugate gradient method. Some numerical experiments with computer simulated data were presented. The efficiency, feasibility and the numerical stability of the algorithm were illustrated by the numerical experiments. Compared with the results produced by the linearized phase retrieval algorithm, we can see that the new algorithm is not limited to be only efficient for the data measured in the near-field of the Fresnel region and thus it has a broader validity range.

Key words

phase contrast tomography holographic measurement phase retrieval 

Chinese Library Classification

O29 O434.19 

2000 Mathematics Subject Classification

65R32 78A46 92C55 

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Copyright information

© Editorial Committee of Appl. Math. Mech. and Springer-Verlag 2008

Authors and Affiliations

  1. 1.LMAM, School of Mathematical SciencesPeking UniversityBeijingP. R. China

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