Nasim:
The
true noise can be calculated by measuring noise in the background, but you have
to be careful. Because MRI intensities are magnitudes, noisy signals are
described by Rician statistics, which were described by S. O. Rice in a 1944
technical paper. In the absence of any true signal, the statistics
are also called the Rayleigh distribution. If SIG is the true SD of the
signal in each quadrature channel, the average
measured signal intensity of pure noise is SIG*sqrt(pi/2) ~
1.253*SIG, and the measured SD of the signal intensity of pure noise is
SIG*sqrt[2-(pi/2)] ~ 0.655*SIG. Therefore, you have to
do one of the following calculations:
1)
Measure the average value in a ROI where there is no image artifact (ghosting,
etc.), and divide by sqrt(pi/2) ~ 1.253.
2)
Measure the standard deviation (SD) in the ROI, and divide by sqrt[2-(pi/2)] ~
0.655.
For
example, in a DTI paper that should appear soon in Magn Reson Med, we found a
mean value of 24.1 and a SD of 17.2, yielding estimated noise levels of
24.1/1.253 = 19.2 and 17.2/0.655 = 26.3. The two numbers will rarely agree
exactly. Ideally, you would report both noise calculations. If you
want to report a single number, I suggest taking the average of these two
calculations, unless you have reason to believe that one is more accurate than
the other.
If you
draw a ROI in tissue rather than noise, you add tissue heterogeneity to the true
noise. If your tissue noise is less than or equal to your background
noise, it is safe to use it. If the tissue noise is greater than the
background noise, I suggest using the background noise.
The
following references provide more information.
Edelstein
WA, Bottomley PA, Pfeifer LM. A signal-to-noise calibration procedure for NMR
imaging systems. Med Phys
1984;11:180-185.
Henkelman
RM. Measurement of signal intensities in the presence of noise in MR
images. Med Phys
1985;12:232-233. [Published
correction: Med Phys 1986;13:544]
Bernstein
MA, Thomasson DM, Perman WH. Improved detectability in low signal-to-noise ratio
magnetic resonance images by means of a phase-corrected real
reconstruction. Med Phys
1989;16:813-817.
McGibney
G, Smith MR. An unbiased signal-to-noise ratio measure for magnetic resonance
images. Med Phys
1993;20:1077-1078.
Gudbjartsson
H, Patz S. The Rician distribution of noisy MRI data. Magn Reson Med 1995;34:910-914. [Letter,
related letter, and response: Magn Reson Med 1996;36:331-333]
Dietrich O, Heiland S, Sartor K. Noise correction
for the exact determination of apparent diffusion coefficients at low SNR.
Magn Reson Med 2001;45:448-453.
--
Peter B. Kingsley, MRI
Physicist [log in to unmask]
Department of Radiology / MRI
North Shore University Hospital
300 Community Drive, Manhasset, NY 11030,
USA
Tel (516)
562-2842 Fax (516) 562-3561
Hi all,
I would like to know is there any consensus on how to define noise when
you are doing Region of Interest (ROI) based analysis and you want to
determine noise so that you could define SNR in a ROI?
In some papers I see they define a ROI in the background and measure
noise as the mean of that ROI and consider it as noise value every where in
the image. On the other hand in some other papers they use the standard
deviation of the values on the desired ROI as noise.
Thanks
Nasim
Do you Yahoo!?
Yahoo! Small Business - Try
our new resources site!