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Proceedings Paper

Extension of the Karhunen-Loeve transform for wavelets and perfect reconstruction filterbanks
Author(s): Michael A. Unser
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Paper Abstract

Most orthogonal signal decompositions, including block transforms, wavelet transforms, wavelet packets, and perfect reconstruction filterbanks in general, can be represented by a paraunitary system matrix. This paper considers the general problem of finding the optimal P X P paraunitary transform that minimizes the approximation error when a signal is reconstructed from a reduced number of components Q < P. This constitutes a direct extension of the Karhunen-Loeve transform which provides the optimal solution for block transforms (unitary system matrix). General solutions are presented for the optimal representation of arbitrary wide sense stationary processes. This work also investigates a variety of suboptimal schemes using FIR filterbanks. In particular, it is shown that low-order Daubechies wavelets and wavelet packets (D2 and D3) are near optimal for the representation of Markov-1 processes.

Paper Details

Date Published: 1 November 1993
PDF: 12 pages
Proc. SPIE 2034, Mathematical Imaging: Wavelet Applications in Signal and Image Processing, (1 November 1993); doi: 10.1117/12.162087
Show Author Affiliations
Michael A. Unser, 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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