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   -> Volume 7, Issue 10


Preprint: Translation-invariant denoising from I. Cohen et al.
 
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Israel Cohen (cohen-israel@cs.yale.edu)
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PostPosted: Tue Sep 29, 1998 8:33 pm    
Subject: Preprint: Translation-invariant denoising from I. Cohen et al.
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#4 Preprint: Translation-invariant denoising from I. Cohen et al.

Preprints on translation-invariant denoising and robust
time-frequency representations:

1) Adaptive Suppression of Wigner Interference-Terms
Using Shift-Invariant Wavelet Packet Decompositions

Israel Cohen, Shalom Raz and David Malah
Department of Electrical Engineering
Technion - Israel Institute of Technology
Haifa 32000, Israel

Abstract:

The Wigner distribution (WD) possesses a number of desirable
mathematical properties relevant to time-frequency analysis. However,
the presence of interference terms renders the WD of multicomponent
signals extremely difficult to interpret. In this work, we propose
adaptive suppression of interference terms using the {it
Shift-Invariant Wavelet Packet Decomposition}. A prescribed signal is
expanded on its best basis and transformed into the Wigner
domain. Subsequently, the interference terms are eliminated by
adaptively thresholding the cross WD of interactive basis functions,
according to their amplitudes and distance in an idealized
time-frequency plane. We define a distance measure that weighs the
Euclidean distance with the local distribution of the signal. The
amplitude and distance thresholds control the cross-term interference,
the useful properties of the distribution, and the computational
complexity. The properties of the resultant {em modified Wigner
distribution/} (MWD) are investigated, and its performance in
eliminating interference terms, while still retaining high energy
resolution, is compared with that of other existing approaches. It is
shown that the proposed MWD is directly applicable to resolving
multicomponent signals. Each component is determined as a partial sum
of basis-functions over a certain equivalence class in the
time-frequency plane.

Keywords: Shift-invariance; Best-basis; Wavelets; Wavelet-packets;
Wigner distribution; Time-frequency; Interference terms

Technical Report, CC PUB No. 245, Technion - Israel Institute of
Technology, Haifa, Israel, June 1998 (to appear in Signal Processing).
http://www-sipl.technion.ac.il/wavelet.html

2) Translation-invariant denoising using the minimum description
length criterion

Israel Cohen, Shalom Raz and David Malah
Department of Electrical Engineering
Technion - Israel Institute of Technology
Haifa 32000, Israel

Abstract:

A translation-invariant denoising method, based on the {it Minimum
Description Length/} (MDL) criterion and tree-structured best-basis
algorithms is presented. A collection of signal models is generated
using an {it extended/} library of orthonormal wavelet-packet bases,
and an additive cost function, approximately representing the MDL
principle, is derived. We show that the minimum description length of
the noisy observed data is achieved by utilizing the {it
Shift-Invariant Wavelet Packet Decomposition/} (SIWPD) and
thresholding the resulting coefficients. This approach is extendable
to local trigonometric decompositions, and corresponding procedures to
optimize either the library of bases or the filter banks used at each
node of the expansion-tree are described. The signal estimator is
efficiently combined with a {it modified Wigner distribution/},
yielding robust time-frequency representations, characterized by high
resolution and suppressed interference-terms. The proposed method is
compared to alternative existing methods, and its superiority is
demonstrated by synthetic and real data examples.

Technical Report, CC PUB No. 246, Technion - Israel Institute of Technology,
Haifa, Israel, June 1998 (submitted to Signal Processing).
http://www-sipl.technion.ac.il/wavelet.html

Dr. Israel Cohen cohen-israel@cs.yale.edu
Yale University Tel: +(203) 432-1287
Department of Computer Science Fax: +(203) 432-0593
P.O. Box 208285
New Haven, CT 06520-8285
All times are GMT + 1 Hour
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