Title
Phase Retrieval for Characteristic Functions of Convex Bodies and Reconstruction from Covariograms
Document Type
Article
Publication Date
4-2011
Keywords
Algorithm, autocorrelation, convex body, covariogram, image analysis, least squares, phase retrieval, quasicrystal, set covariance
Abstract
The Phase Retrieval Problem of Fourier analysis involves determining a function f on Rn from the modulus |f�| of its Fourier transform f�. This problem arises naturally and frequently in various areas of science, such as X-ray crystallography, electron microscopy, optics, astronomy, and remote sensing, in which only the magnitude of the Fourier transform can be measured and the phase is lost.
Publication Title
Journal of the American Mathematical Society
Volume
24
Issue
2
First Page
293
Last Page
343
Required Publisher's Statement
First published in The Journal of the American Mathematical Society in Volume 24, Number 2, 2011, published by the American Mathematical Society)
Recommended Citation
Bianchi, Gabriele; Gardner, Richard J.; and Kiederlen, Markus, "Phase Retrieval for Characteristic Functions of Convex Bodies and Reconstruction from Covariograms" (2011). Mathematics Faculty Publications. 22.
https://cedar.wwu.edu/math_facpubs/22
Subjects - Topical (LCSH)
Convex bodies; Convex polytopes; Algorithms; Geometric tomography; Analysis of covariance
Genre/Form
articles
Type
Text
Rights
Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.
Language
English
Format
application/pdf
