Posted by
Frederic V. Hessman on
Jul 11, 2007; 2:32pm
URL: http://imagej.273.s1.nabble.com/SNR-estimation-of-a-single-image-tp3698855p3698858.html
> In order to test robustness of an image processing algorithm, I
> want to estimate the signal to noise ratio of my images. It
> concerns a very rough approximation since I merely want to take
> Poisson noise into account, hence making abstraction of detector
> noise, dark noise etc. (at least for now)
> I want to be able to compare with synthetic images (originally
> without noise) in which I gradually raise the Poisson noise. When
> considering the original noiseless image as O, the current image as
> C and i the voxel number I approximate the signal-noise ratio in
> these synthetic images using (Manders et al., 1993):
>
> SNR=20log(sqrt(sum(Ci)²/sum(Ci-Oi)²))
>
> Since there is no original image for real images, this formula
> doesn't apply. I have found several definitions of defining SNR,
> but none of them seem to give values that correspond with what I
> retrieve after using the first formula on the synthetic images. The
> most common way seems to be using the standard deviation of a
> region with 'no' signal to estimate noise and using the dynamic
> range or maximum of the signal. But this seems rather arbitrary and
> dependent on the chosen region. Is there a way of approximating the
> noise and SNR of a single image - so not by recording the image
> several times - without having to select a signal-free ROI and what
> would be the most reliable definition?
> Many thanks in advance.
Without knowing the gain g of the current image (the number of
photoelectrons per camera intensity unit) there will be no point in
doing Poisson statistics. Ignoring detector read-out noise, bias,
and dark current (as you said), the signal-to-noise is
S/N = S/sqrt(S/g) = sqrt(gS)
(the conversion to db's is trivial but unnecessary, like expressing
the exposure times in fortnights). If you don't have the gain, you
have no idea about the noise and will make a mistake of a factor of
sqrt(g): for typical gains in the range of 2-5, this is not a small
effect. The gain is easy to measure: take a series of images with
high intensities and measure the slope of the variance versus signal
relation, which is the gain.
Calculating S/N from comparisons with synthetic images seems like a
very dangerous route - lots of possibilities for systematic errors -
especially since you should be able to compute the TRUE S/N from
knowing what your images are about. With no gain, I'd simply use the
local standard deviations in regions with no image structure - at
least they are measured from the data.
Rick
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Dr. Frederic V. Hessman
[hidden email]
Institut für Astrophysik Tel. +49-551-39-5052
Friedrich-Hund-Platz 1 Fax +49-551-39-5043
37077 Goettingen Room F04-133
http://www.Astro.physik.Uni-Goettingen.de/~hessman------------------------------------------------------------------------
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