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Proceedings Paper

Cramér-Rao bounds for variance of Fourier magnitude measurements
Author(s): Richard Holmes; Brandoch Calef; David Gerwe; Jean Dolne; Peter Crabtree
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Paper Abstract

Many imaging modalities measure magnitudes of Fourier components of an object. Given such data, reconstruction of an image from data that is also noisy and sparse is especially challenging, as may occur in some forms of intensity interferometry, Fourier telescopy, and speckle imaging. In such measurements, the Fourier magnitudes must be positive, and moreover must be less than 1 given the usual normalization, scaling the magnitudes so that the magnitude is one at zero spatial frequency in the u-v plane data. The Cramér-Rao formalism is applied to single Fourier magnitude measurements to ascertain whether a reduction in variance is possible given these constraints. An extension of the Cramér-Rao formalism is used to address the value of relatively general prior information. The impact of this knowledge is also shown for simulated image formation for a simple disk, with varying measurement SNR and sampling in the (u,v) plane.

Paper Details

Date Published: 17 September 2013
PDF: 12 pages
Proc. SPIE 8877, Unconventional Imaging and Wavefront Sensing 2013, 88770H (17 September 2013); doi: 10.1117/12.2026971
Show Author Affiliations
Richard Holmes, Boeing LTS Inc. (United States)
Brandoch Calef, Boeing LTS Inc. (United States)
David Gerwe, Boeing Phantom Works (United States)
Jean Dolne, Boeing Phantom Works (United States)
Peter Crabtree, Air Force Research Lab. (United States)

Published in SPIE Proceedings Vol. 8877:
Unconventional Imaging and Wavefront Sensing 2013
Jean J. Dolne; Thomas J. Karr; Victor L. Gamiz, Editor(s)

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