Abstract
Measurements achieved with ptychographic imaging are a special case of diffraction measurements. They are generated by illuminating small parts of a sample with, e.g., a focused Xray beam. By shifting the sample, a set of farfield diffraction patterns of the whole sample is then obtained. From a mathematical point of view those measurements are the squared modulus of the windowed Fourier transform of the sample. Thus, we have a phase retrieval problem for local Fourier measurements. A direct solver for this problem was introduced by Iwen, Viswanathan and Wang in 2016 and improved by Iwen, Preskitt, Saab and Viswanathan in 2018. Motivated by the applied perspective of ptychographic imaging, we present a generalization of this method and compare the different versions in numerical experiments. The new method proposed herein turns out to be more stable, particularly in the case of missing data.
Original language  English 

Pages (fromto)  292300 
Number of pages  9 
Journal  Mathematics and Computers in Simulation 
Volume  176 
Early online date  2019 Nov 16 
DOIs  
Publication status  Published  2020 Oct 
Subject classification (UKÄ)
 Computational Mathematics
 Other Physics Topics
Keywords
 Diffraction imaging
 Image reconstruction
 Phase retrieval
 Ptychography
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