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13 - Suggestions for Improvements

from Part III - Further Properties of Hybrid Iterative Algorithms and Suggestions for Improvement

Published online by Cambridge University Press:  21 April 2022

Alexander H. Barnett
Affiliation:
Flatiron Institute
Charles L. Epstein
Affiliation:
Flatiron Institute
Leslie Greengard
Affiliation:
Courant Institute
Jeremy Magland
Affiliation:
Flatiron Institute
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Summary

In this chapter, we consider several ideas that might lead to improved reconstructions in coherent diffraction imaging. To avoid the conditions that render the inverse problem ill conditioned, and the usual iterative algorithms nonconvergent, we consider approaches that entail (1) a modification of the sample preparation, (2) a new experimental modality, which uses a noniterative holographic Hilbert transform method to reconstruct the image, or (3) a geometric Newton-type algorithm. The final section describes the detailed implementation of the holographic Hilbert transform method. All of these proposals are illustrated with numerical experiments.

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Chapter
Information
Geometry of the Phase Retrieval Problem
Graveyard of Algorithms
, pp. 249 - 291
Publisher: Cambridge University Press
Print publication year: 2022

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