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   -> Volume 6, Issue 3


Preprint: Preprints from H-Y Gao on shrinkage denoising
 
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gao@statsci.com (Hong-Ye Gao)
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PostPosted: Sat Feb 15, 1997 1:56 am    
Subject: Preprint: Preprints from H-Y Gao on shrinkage denoising
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#2 Preprint: Preprints from H-Y Gao on shrinkage denoising

Preprints on wavelet shrinkage denoising are available by anonymous ftp:

ftp ftp.statsci.com
cd /pub/gao

Title: Wavelet Shrinkage Smoothing For Heteroscedastic Data
Author: Hong-Ye Gao
File: wsshd.ps.Z
Abstract:

We extend Donoho and Johnstone's wavelet shrinkage smoothing
technique (known as WaveShrink) to handle data with heteroscedastic
noise. We first show that if the noise variances are known,
WaveShrink estimate achieves the same near-optimal convergence rate
as in the white noise case. We then propose a procedure for
estimating the noise variances. Our procedure is based on applying
running MAD (Median Absolute Deviation from the median) to the
non-decimated finest level wavelet coefficients. We apply our
technique to various numerical examples.

Title: Wavelet Shrinkage DeNoising Using Non-Negative Garrote
Author: Hong-Ye Gao
File: garrote.ps.Z
Abstract:

In this paper, we combine Donoho and Johnstone's Wavelet Shrinkage
denoising technique (known as WaveShrink) with Breiman's
non-negative garrote. We show that the non-negative garrote
shrinkage estimate enjoys the same asymptotic convergence rate as
the hard and the soft shrinkage estimates. For finite sample
simulations, non-negative garrote performs better (smaller
mean-square-error) than both hard and soft, and comparable to the
firm shrinkage. We derive the minimax thresholds for the
non-negative garrote. We study the threshold selection procedure
based on Stein's Unbiased Risk Estimate (SURE) for both
non-negative garrote and soft shrinkages.

Title: Threshold Selection in WaveShrink
Author: Hong-Ye Gao
File: threshold.ps.Z
Abstract:

Donoho and Johnstone's wavelet shrinkage denoising technique (known
as WaveShrink) consists three steps: (1) transform data into
wavelet domain; (2) shrink the wavelet coefficients; and (3)
transform the shrunk coefficients back. The choice of shrinkage
function and thresholds in step (2) plays an important role for
WaveShrink both theoretically and in practice. In this paper, we
discuss the issue of threshold selection in WaveShrink. We first
review the threshold selection procedure based minimax thresholds
and Stein's Unbiased Risk Estimate (SURE). We then propose a new
threshold selection procedure based on combining Coifman and
Donoho's cycle-spinning and SURE. We call our new procedure
SPINSURE. We use examples to show that SPINSURE is numerically
more stable than SURE: smaller standard deviation and smaller
range. Various comparisons with the ideal and minimax thresholds
are also presented.
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