Well conditioned ptychograpic imaging via lost subspace completion

Ptychography, a special case of the phase retrieval problem, is a popular method in modern imaging. Its measurements are based on the shifts of a locally supported window function. In general, direct recovery of an object from such measurements is known to be an ill-posed problem. Although for some...

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Bibliographic Details
Published in:arXiv.org 2020-04
Main Authors: stner, Anton, Krahmer, Felix, Melnyk, Oleh, Sissouno, Nada
Format: Article
Language:English
Subjects:
Algorithms
Conditioning
Ill posed problems
Phase retrieval
Regularization
Window functions
Online Access:Get full text
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Summary:Ptychography, a special case of the phase retrieval problem, is a popular method in modern imaging. Its measurements are based on the shifts of a locally supported window function. In general, direct recovery of an object from such measurements is known to be an ill-posed problem. Although for some windows the conditioning can be controlled, for a number of important cases it is not possible, for instance for Gaussian windows. In this paper we develop a subspace completion algorithm, which enables stable reconstruction for a much wider choice of windows, including Gaussian windows. The combination with a regularization technique leads to improved conditioning and better noise robustness.
ISSN:2331-8422
DOI:10.48550/arxiv.2004.04458