© The Institution of Engineering and Technology
Noise filtering is a common step in image processing, and is particularly effective in improving the subjective quality of images. A large number of techniques have been developed, many of which concentrate on the problem of removing noise without damaging small structures such as edges. One recent approach that demonstrates empirical merit is the non-local means (NLM) algorithm. However, in order to use noise filtering algorithms in quantitative or clinical image analysis tasks an understanding of their behaviour that goes beyond subjective appearance must be developed. The purpose of this study is to investigate the statistical basis of NLM in order to attempt to understand the conditions required for its use. The theory is illustrated on synthetic data and clinical magnetic resonance images of the brain.
References
-
-
1)
-
R.J. Barlow
.
(1989)
Statistics – a guide to the use of statistical methods in the physical sciences.
-
2)
-
H. Gudjbartson ,
S. Patz
.
The Rician distribution of noisy MRI data.
Magn. Reson. Med.
,
6 ,
910 -
914
-
3)
-
M. Mahmoudi ,
G. Sapiro
.
Fast image and video denoising via nonlocal means of similar neighbourhoods.
IEEE Signal Process. Lett.
,
12 ,
839 -
842
-
4)
-
Bromiley, P.A., Thacker, N.A., Courtney, P.: `Non-parametric image subtraction for MRI', Proc. MIUA 2001, 2001, Birmingham, p. 105–108.
-
5)
-
Thacker, N.A., Lacey, A.J., Bromiley, P.A.: `Validating MRI field homogeneity correction using image information measures', Proc. BMVC'02, 2002, p. 626–635.
-
6)
-
A. Buades ,
B. Coll ,
J.M. Morel
.
A review of image denoising algorithms, with a new one.
Multiscale Model. Simul.
,
490 -
530
-
7)
-
A.P. Dempster ,
N.M. Laird ,
D.B. Rubin
.
Maximum likelihood from incomplete data via the EM algorithm.
J. Ro. Soci.
,
1 -
38
-
8)
-
Tomasi, C., Manduchi, R.: `Bilateral filtering of gray and color images', Proc. Sixth IEEE Int. Conf. on Computer Vision, 4–7 January 1998, Bombay, India, p. 839–846.
-
9)
-
Manjon, J.V., Robles, M., Thacker, N.A.: `Multispectral MRI de-noising using non-local means', Proc. MIUA 2007, 2007, Aberystwyth, p. 41–46.
-
10)
-
D. Barash
.
A fundamental relationship between bilateral filtering, adaptive smoothing and the nonlinear diffusion equation.
IEEE Trans. PAMI
,
6 ,
844 -
847
-
11)
-
D. Comaniciu ,
P. Meer
.
Mean shift: A robust approach toward feature space analysis.
IEEE Trans. PAMI
,
5 ,
603 -
619
-
12)
-
R.D. Nowak
.
Rician noise removal for magnetic resonance imaging.
IEEE Trans. Image Process.
,
10 ,
1408 -
1419
-
13)
-
E. Vul ,
C. Harris ,
P. Winkielman ,
H. Pashler
.
Puzzlingly high correlations in fMRI studies of emotion, personality, and social cognition.
Perspect. Psycholo. Sci.
,
3 ,
274 -
290
-
14)
-
P. Perona ,
J. Malik
.
Scale-space and edge detection using anisotropic diffusion.
IEEE Trans. PAMI
,
7 ,
629 -
639
-
15)
-
W.H. Press ,
S.A. Teukolsky ,
W.T. Vetterling ,
B.P. Flannery
.
(1996)
Numerical recipes in C.
-
16)
-
J.V. Manjon ,
J. Carbonell-Caballero ,
J.J. Lull ,
G. Gracian-Marti ,
L. Marti-Bonmati ,
M. Robles
.
MRI denoising using non-local means.
Med. Image Analy.
,
514 -
523
-
17)
-
Thacker, N.A., Pokrić, M., Williamson, D.C.: `Noise filtering and testing illustrated using a multi-dimensional partial volume model of MR data', Proc. BMVC, 2004, Kingston, London, p. 909–919.
-
18)
-
P.A. Bromiley ,
N.A. Thacker ,
P. Courtney
.
Non-parametric image subtraction using grey level scattergrams.
Image and Vision Comput.
,
609 -
617
-
19)
-
Coupe, P., Yger, P., Barillot, C.: `Fast non local means denoising for 3D MR images', Medical Image Computing and Computer-Assisted Intervention – MICCAI 2006, 2006, p. 33–40, (LNCS, 4191).
-
20)
-
S.I. Olsen
.
Estimation of noise in images: an evaluation.
CVGIP: Graph. Models Image Process.
,
319 -
323
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cvi.2008.0076
Related content
content/journals/10.1049/iet-cvi.2008.0076
pub_keyword,iet_inspecKeyword,pub_concept
6
6