Abstract

In medical images, noise suppression is a particularly delicate and difficult task. A tradeoff between noise reduction and the preservation of actual image features has to be made in a way that enhances the diagnostically relevant image content. The method of wavelet thresholding has been used extensively for denoising medical images. The idea is to transform the data into the wavelet basis, in which the large coefficients are mainly the signal and the smaller ones represent the noise. By suitably modifying these coefficients, the noise can be removed from the data. In this paper, we evaluate several two-dimensional denoising procedures using medical test images corrupted with additive Gaussian noise. Our results, using the peak-signal-to-noise ratio as a measure of the quality of denoising, show that the NormalShrink method outperforms the other wavelet-based techniques (VisuShrink, BayesShrink). We also demonstrate that garrote shrinkage offers advantages over both hard and soft shrinkage.

References

1.
Chang
,
S. G.
and
Vetterli
,
M.
, “
Spatial Adaptive Wavelet Thresholding for Image Denoising
”,
Proc. of IEEE Int. Conf. On Image Processing
,
1997
.
2.
Chambolle
,
A.
,
DeVore
,
R. A.
,
Lee
,
N.-Y.
, and
Lucier
,
B. J.
, “
Nonlinear Wavelet Image Processing: Variational Problems, Compression and Noise Removal through Wavelet Shrinkage
,”
IEEE Trans. Image Processing
 1057-7149 https://doi.org/10.1109/83.661182, Vol.
7
,
1998
, pp.
319
335
.
3.
Donoho
,
D. L.
, “
Wavelet Thresholding and W.V.D.: A 10-minute Tour
,”
Int. Conf. on Wavelets and Applications
,
Toulouse, France
,
06
1992
.
4.
Donoho
,
D. L.
and
Johnstone
,
I. M.
, “
Ideal Spatial Adaptation via Wavelet Shrinkage
,”
Biometrika
 0006-3444 https://doi.org/10.2307/2337118, Vol.
81
,
1994
, pp.
425
455
.
5.
Donoho
,
D. L.
, “
De-Noising by Soft-Threshholding
,”
IEEE Trans. Information Theory
 0018-9448, Vol.
41
, No.
3
,
05
1995
.
6.
Shao
,
X.
and
Cherkassky
,
V.
, “
Model Selection for Wavelet-based Signal Estimation
,”
Proc. IEEE Int. Joint Conf. on Neural Networks
,
Anchorage, AK
,
1998
.
7.
Grace Chang
,
S.
,
Yu
,
Bin
, and
Vetterli
,
M.
, “
Adaptive Wavelet Thresholding for Image Denoising and Compression
,”
IEEE Trans. Image Processing
 1057-7149 https://doi.org/10.1109/83.862633, Vol.
9
,
09
2000
, pp.
1532
1546
.
8.
Kaur
,
Lakhwinder
,
Gupta
,
Savita
, and
Chauhan
,
R. C.
, “
Image Denoising using Wavelet Thresholding
,”
Third Conference on Computer Vision, Graphics and Image Processing
,
India
, Dec. 16–18, 2002.
9.
Gupta
,
Savita
and
Kaur
,
Lakhwinder
, “
Wavelet Based Image Compression using Daubechies Filters
,”
In Proc. 8th National conference on communications
,
I.I.T.
Bombay
, NCC-2002.
10.
Vetterli
,
M.
and
Kovacevic
,
J.
, “
Wavelets and Subband Coding
,”
Englewood Cliffs, NJ
,
Prentice Hall
,
1995
.
11.
Bruce
,
A.
and
Gao
,
H.-Y.
, “
WaveShrink: Shrinkage Functions and Thresholds
,”
Proc. SPIE
 0277-786X, Vol.
2569
,
1995
, pp.
270
281
.
12.
Breiman
,
L.
, “
Better Subset Regression Using the Non-negative Garrote
,”
Technometrics
 0040-1706, Vol.
37
, No.
4
,
1995
, pp.
373
384
.
13.
Gao
,
H.-Y.
and
Bruce
,
A. G.
, “
WaveShrink with Firm Shrinkage
,”
Statistica Sinica
 1017-0405, Vol.
7
,
1997
, pp.
855
874
.
14.
Gao
,
H.-Y.
, “
Wavelet Shrinkage Denoising Using the Non-Negative Garrote
,”
Journal of Computational and Graphical Statistics
 1061-8600, Vol.
7
, No.
4
,
1998
, pp.
469
488
.
15.
Donoho
,
D. L.
and
Johnstone
,
I. M.
, “
Adapting to Unknown Smoothness via Wavelet Shrinkage
,”
Journal of the American Statistical Association
 0003-1291 https://doi.org/10.2307/2291512, Vol.
90
, No.
432
,
1995
, pp.
1200
1224
.
16.
Stein
,
C.
, “
Estimation of the Mean of a Multivariate Normal Distribution
,”
The Annals of Statistics
 0090-5364, Vol.
9
,
1981
, pp.
1135
1151
.
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