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   -> Volume 7, Issue 3


Preprint: Signal and Image Denoising
 
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Vasily Strela (strela@pascal.Dartmouth.EDU)
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PostPosted: Wed Mar 11, 1998 1:26 am    
Subject: Preprint: Signal and Image Denoising
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#4 Preprint: Signal and Image Denoising

Signal and Image Denoising via Wavelet Thresholding:
Orthogonal and Biorthogonal, Scalar and Multiple Wavelet Transforms

by V. Strela (Dartmouth College, NH, USA, strela@cs.dartmouth.edu)
and A. T. Walden (Imperial College, London, UK, a.walden@ic.ac.uk)

Imperial College, Statistics Section, Technical Report TR-98-01

Abstract

In this paper we discuss wavelet thresholding in the context of scalar
orthogonal, scalar biorthogonal, multiple orthogonal and multiple
biorthogonal wavelet transforms. Two types of multiwavelet
thresholding are considered: scalar and vector. Both of them take into
account the covariance structure of the transform. The form of the
universal threshold is carefully formulated. The results of numerical
simulations in signal and image denoising are presented.

Multiwavelets outperform scalar wavelets for three out of four noisy
1D test signals, and the Chui-Lian scaling functions and wavelets
combined with repeated row preprocessing appears to be a good general
method. Vector thresholding does not always outperform scalar
thresholding.

Multiwavelets generally outperform scalar wavelets for image denoising
for all four noisy 2D test images, and the results are visually very
impressive. Only for `Lenna' and `fingerprints' with signal to noise
ratios of 2 do scalar wavelets perform best. As for 1D signal
processing, Chui-Lian scaling functions and wavelets combined with
repeated row preprocessing appears to be a good general method.

For both 1D and 2D cases, the reconstructed signals derived from such
a good general method demonstrate much reduced noise levels ---
typically 50\% of the standard deviation of the original noise.

Tha paper can be downloaded from
http://math.dartmouth.edu/~strela/
or
http://www.ma.ic.ac.uk/~atw/
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