The Wavelet Digest Homepage
Return to the homepage
Search the complete Wavelet Digest database
Help about the Wavelet Digest mailing list
About the Wavelet Digest
The Digest The Community
 Latest Issue  Back Issues  Events  Gallery
The Wavelet Digest
   -> Volume 7, Issue 9


Preprint: Preprints on nonorthogonal wavelet denoising (Berkner)
 
images/spacer.gifimages/spacer.gif Reply into Digest
Previous :: Next  
Author Message
Kathrin Berkner (berkner@math.rice.edu)
Guest





PostPosted: Tue Aug 25, 1998 3:34 pm    
Subject: Preprint: Preprints on nonorthogonal wavelet denoising (Berkner)
Reply with quote

#1 Preprint: Preprints on nonorthogonal wavelet denoising (Berkner)

1) Smoothness estimates for soft-threshold denoising via translation invariant
wavelet transforms

Kathrin Berkner and Raymond O. Wells, Jr.
Computational Mathematics Laboratory
Rice University
Houston, TX 77005-1892

Abstract:

In this paper we study a generalization of the Donoho-Johnstone
denoising model for the case of the translation invariant wavelet
transform. Instead of soft-thresholding coefficients of the classical
orthogonal discrete wavelet transform, we study soft-thresholding of
the coefficients of the translation invariant discrete wavelet
transform. This latter transform is not an orthogonal
transformation. As a first step we construct a level-dependent
threshold to remove all the noise in the wavelet domain.
Subsequently, we use the theory of interpolating wavelet transforms to
characterize the smoothness of an estimated denoised function. Based
on the fact that the inverse of the translation invariant discrete
transform includes averaging over all shifts, we use smoother
autocorrelation functions in the representation of the estimated
denoised function in place of Daubechies scaling functions.

CML report 98-01
http://cml.rice.edu/98.html
email: berkner@math.rice.edu

2) A Correlation-Dependent Model for Denoising via Nonorthogonal Wavelet
Transforms

Kathrin Berkner and Raymond O. Wells, Jr.
Computational Mathematics Laboratory
Rice University
Houston, TX 77005-1892

Abstract:

In many applications it is desirable to study nonorthogonal wavelet
transforms. A translation-invariant wavelet transform is a
nonorthogonal variant of the classical wavelet transform which plays
an important role in denoising algorithms. However, it has been
observed in many experiments that the thresholding scheme for the
orthogonal DWT should be slightly modified for use in the
translation-invariant setting. These observations motivate us to study
denoising schemes for nonorthogonal wavelet transforms. In this paper
we derive a thresholding scheme for denoising that incorporates
correlations between nonorthogonal wavelet coefficients and specify
these thresholds for translation-invariant and biorthogonal wavelet
systems. The new scheme includes a scale- and wavelet-dependent
threshold which is larger than the one normally used in combination
with the orthogonal discrete wavelet transform.

CML report 98-07
http://cml.rice.edu/98.html
email: berkner@math.rice.edu
All times are GMT + 1 Hour
Page 1 of 1

 
Jump to: 
 


disclaimer - webmaster@wavelet.org
Powered by phpBB

This page was created in 0.026797 seconds : 18 queries executed : GZIP compression disabled