A direct solver for the phase retrieval problem in ptychographic imaging
| Autor: | Rayan Saab, Nada Sissouno, Frank Filbir, Wolfgang zu Castell, Mark A. Iwen, Florian Boßmann, Maik Kahnt, Christian G. Schroer |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Diffraction
General Computer Science Phase Retrieval Ptychography Image Reconstruction Diffraction Imaging Computer science 010103 numerical & computational mathematics 02 engineering and technology Iterative reconstruction 01 natural sciences Theoretical Computer Science symbols.namesake FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Mathematics - Numerical Analysis 0101 mathematics Numerical Analysis Applied Mathematics Computational mathematics Numerical Analysis (math.NA) Solver Sample (graphics) Fourier transform Modeling and Simulation symbols 020201 artificial intelligence & image processing Phase retrieval Algorithm |
| Zdroj: | Math. Comput. Simul. 176, 292-300 (2020) |
| ISSN: | 0378-4754 |
| DOI: | 10.1016/j.matcom.2019.11.003 |
| Popis: | 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 X-ray beam. By shifting the sample, a set of far-field 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. (C) 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect