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.
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Communicated by GUO Mao-zheng
Project supported by the National Basic Research Program of China (No. 2003CB716101), the National Natural Science Foundation of China (No. 60532080), the Science Foundation of Chinese Ministry of Education (No. 306017), the Science Foundation of Engineering Research Institute of Peking University, and the Science Foundation of Microsoft Research of Asia.
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Ni, Wl., Zhou, T. Algorithm for phase contrast X-ray tomography based on nonlinear phase retrieval. Appl. Math. Mech.-Engl. Ed. 29, 101–112 (2008). https://doi.org/10.1007/s10483-008-0112-8
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DOI: https://doi.org/10.1007/s10483-008-0112-8