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In-line phase tomography using nonlinear phase retrieval. (English) Zbl 1324.92014

Summary: With hard \(X\)-rays synchrotron beams, phase contrast for inline phase tomography can be obtained with the measurement of the Fresnel diffraction intensity patterns associated to a phase shift induced by the object. We have studied the resolution of this inverse problem with an iterative nonlinear method. The phase retrieval algorithm was tested for a 3D Shepp-Logan phantom in the presence of noise. The nonlinear scheme outperforms the linear method. Both the high and low frequency ranges of the phase retrieved are improved and the method is less sensitive to noise. In future work, the method will be tested on experimental data. The method is expected to open new perspectives for the study of biological samples.

MSC:

92C55 Biomedical imaging and signal processing
47J06 Nonlinear ill-posed problems
47J25 Iterative procedures involving nonlinear operators
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