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Proceedings Paper

Random rounding in redundant representations
Author(s): Bernhard G. Bodmann; Stanley P. Lipshitz
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Paper Abstract

This paper investigates the performance of randomly dithered first and higher-order sigma-delta quantization applied to the frame coefficients of a vector in a infinite-dimensional Hilbert space. We compute the mean square error resulting from linear reconstruction with the quantized frame coefficients. When properly dithered, this computation simplifies in the same way as under the assumption of the white-noise hypothesis. The results presented here are valid for a uniform mid-tread quantizer operating in the no-overload regime. We estimate the large-redundancy asymptotics of the error for each family of tight frames obtained from regular sampling of a bounded, differentiable path in the Hilbert space. In order to achieve error asymptotics that are comparable to the quantization of oversampled band-limited functions, we require the use of smoothly terminated frame paths.

Paper Details

Date Published: 13 September 2007
PDF: 12 pages
Proc. SPIE 6701, Wavelets XII, 670103 (13 September 2007); doi: 10.1117/12.730798
Show Author Affiliations
Bernhard G. Bodmann, Univ. of Waterloo (Canada)
Stanley P. Lipshitz, Univ. of Waterloo (Canada)

Published in SPIE Proceedings Vol. 6701:
Wavelets XII
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)

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