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Proceedings Paper

Fresnelets: a new wavelet basis for digital holography
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Paper Abstract

We present a new class of wavelet bases---Fresnelets---which is obtained by applying the Fresnel transform operator to a wavelet basis of L2. The thus constructed wavelet family exhibits properties that are particularly useful for analyzing and processing optically generated holograms recorded on CCD-arrays. We first investigate the multiresolution properties (translation, dilation) of the Fresnel transform that are needed to construct our new wavelet. We derive a Heisenberg-like uncertainty relation that links the localization of the Fresnelets with that of the original wavelet basis. We give the explicit expression of orthogonal and semi-orthogonal Fresnelet bases corresponding to polynomial spline wavelets. We conclude that the Fresnel B-splines are particularly well suited for processing holograms because they tend to be well localized in both domains.

Paper Details

Date Published: 5 December 2001
PDF: 6 pages
Proc. SPIE 4478, Wavelets: Applications in Signal and Image Processing IX, (5 December 2001); doi: 10.1117/12.449721
Show Author Affiliations
Michael Liebling, Swiss Federal Institute of Technology/Lausanne (Switzerland)
Thierry Blu, Swiss Federal Institute of Technology/Lausanne (Switzerland)
Michael A. Unser, Swiss Federal Institute of Technology/Lausanne (Switzerland)

Published in SPIE Proceedings Vol. 4478:
Wavelets: Applications in Signal and Image Processing IX
Andrew F. Laine; Michael A. Unser; Akram Aldroubi, Editor(s)

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