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)

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

Included in

Mathematics Commons

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