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   -> Volume 6, Issue 7


Preprint: L^2 Oracles for Semiorthogonal Wavelets
 
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Oliver Staadt (staadt@inf.ethz.ch)
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PostPosted: Fri Jul 11, 1997 3:33 pm    
Subject: Preprint: L^2 Oracles for Semiorthogonal Wavelets
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#5 Preprint: L^2 Oracles for Semiorthogonal Wavelets

Title: L^2 Optimal Oracles and Compression Strategies
for Semiorthogonal Wavelets

Author: Markus H. Gross

URLs: ftp://ftp.inf.ethz.ch/pub/publications/tech-reports/2xx/254.ps.gz
ftp://ftp.inf.ethz.ch/pub/publications/tech-reports/2xx/254.pdf
http://www.inf.ethz.ch/department/IS/cg/html/publi.html

Abstract:
This paper discusses the problem of optimal coefficient rejection for
approximations with semiorthogonal wavelets. A rejection strategy, a
so-called oracle, computes the significance of an individual wavelet
coefficient and is essential for lossy compression schemes. The oracles
proposed in this paper are based on the L2 norm of the underlying
functional space. The report starts with an error analysis in
semiorthogonal settings and presents a scheme to compute the fractional
energy in each complement space of a given iteration m. However, as
opposed to orthogonal settings the mini-mization of the overall
approximation error while rejecting K out of N wavelets cannot be solved
by sorting of the coefficients. Moreover, geometric interpretations of
this global optimization task relate to common combinatorial problems of
linear algebra and computational geometry. As a result, we propose a
greedy construction scheme for an L2 oracle, which computes the
conditional significance of individual wavelet coefficients and which
operates in quadratic time. The compression strategy is first derived
for 1D functions and extended to 2D nonstandard tensor product
functions. Some results on real world data sets compare the oracle with
standard rejection schemes for orthogonal bases.

|Oliver Staadt e-mail: staadt@inf.ethz.ch |
|Computer Graphics Group phone: +41-1-632-7122 |
|Computer Science Department fax: +41-1-632-1172 |
|Swiss Federal Institute of Technology ETH Zurich, CH |
|URL: http://www.inf.ethz.ch/personal/staadt |
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