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Proceedings Paper

Portraits of frames: overcomplete representations with applications to image processing
Author(s): Akram Aldroubi
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Paper Abstract

We present two methods for generating frames of a Hilbert space H. The first method uses bounded operators on H to transform a frame into another frame of H1 C H. The other method uses bounded linear operators on l2 to generate frames of H. We characterize all the mappings that transform frames into other frames. We also show how to construct all frames of a given Hilbert space H starting from any given frame. We show how to apply the theory to obtain shift-invariant tight frames, and shift-invariant tight multiresolution. We also show how to obtain scaling function and wavelets with prescribed properties. Finally, we discuss the noise reduction properties of frames.

Paper Details

Date Published: 1 November 1993
PDF: 8 pages
Proc. SPIE 2034, Mathematical Imaging: Wavelet Applications in Signal and Image Processing, (1 November 1993); doi: 10.1117/12.162073
Show Author Affiliations
Akram Aldroubi, National Institutes of Health (United States)

Published in SPIE Proceedings Vol. 2034:
Mathematical Imaging: Wavelet Applications in Signal and Image Processing
Andrew F. Laine, Editor(s)

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