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Preprint: Noise suppression and signal compression using ...
 
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saito@sdr.slb.com (Naoki Saito)
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PostPosted: Mon Dec 02, 2002 12:55 pm    
Subject: Preprint: Noise suppression and signal compression using ...
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Preprint: Noise suppression and signal compression using ...

Preprint and reprint are available

The following preprint is available via an anonymous ftp to pascal.math.yale.edu
and the filename is "/pub/wavelets/snssc.ps.z". This is a compressed postscript
file by gzip, so you need gunzip program to uncompress it.

Title: Simultaneous Noise Suppression and Signal Compression using a Library of
Orthonormal Bases and the Minimum Description Length Criterion}

Author: Naoki Saito

Abstract: We describe an algorithm to estimate a discrete signal from
its noisy observation, using a library of orthonormal bases (consisting of
various wavelets, wavelet packets, and local trigonometric bases) and the
information-theoretic criterion called minimum description length (MDL).
The key to effective random noise suppression is that the signal component in
the data may be represented efficiently by one or more of the bases in the
library, whereas the noise component cannot be represented efficiently by any
basis in the library. The MDL criterion gives the best compromise between the
fidelity of the estimation result to the data (noise suppression) and the
efficiency of the representation of the estimated signal (signal compression):
it selects the ``best" basis and the ``best" number of terms to be retained
out of various bases in the library in an objective manner.
Because of the use of the MDL criterion, our algorithm is free from any
parameter setting or subjective judgments.
This method has been applied usefully to various geophysical datasets containing
many transient features.

Also, the following REPRINT is available upon request via email or postcard to
Naoki Saito.

Title: Multiresolution Representations Using The Auto-Correlation Functions
of Compactly Supported Wavelets

Author: Naoki Saito and Gregory Beylkin

Journal: IEEE Trans. Signal Proc., special issue on wavelets and signal
processing, Vol. 41, No. 12, pp.3584-3590, 1993.

Abstract: We propose a shift-invariant multiresolution representation of
signals or images using dilations and translations of the auto-correlation
functions of compactly supported wavelets. Although these functions do not
form an orthonormal basis, their properties make them useful for signal and
image analysis.
Unlike wavelet-based orthonormal representations, our representation
has (1) symmetric analyzing functions, (2) shift-invariance, (3)
associated iterative interpolation schemes, (4) a simple algorithm
for finding the locations of the multiscale edges as zero-crossings.

We also develop a non-iterative method for reconstructing signals
from their zero-crossings (and slopes at these zero-crossings) in our
representation.
This method reduces the reconstruction problem to that of solving a
system of linear algebraic equations.

Naoki Saito

Schlumberger-Doll Research and Dept. of Mathematics, Yale University
Email: saito@ridgefield.sdr.slb.com
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