Dear all
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. Kind regards, winnok ______ ir. Winnok De Vos Research Assistant dep. Molecular Biotechnology Faculty of Bioscience Engineering Ghent University Coupure links 653 9000 Ghent Belgium tel 0032.(0)9.264.59.71 fax 0032.(0)9.264.62.19 www.molecularbiotechnology.ugent.be |
> 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 ------------------------------------------------------------------------ ------------------------ 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 ------------------------------------------------------------------------ ------------------------- MONET: a MOnitoring NEtwork of Telescopes http://monet.Uni-Goettingen.de ------------------------------------------------------------------------ ------------------------- |
In reply to this post by Winnok H. De Vos
Dear all
Thank you for your replies. I had also thought of using deconvolved images as noise free images (estimation of original), but decided not to since the deconvolution 'erodes' objects by the PSF, hence causing objects to be smaller and have different intensities. It might be possible to normalize the latter, but I fear the shape adjustment will cause a bias in noise calculation. It seems the best way must be to use the relation of the detector gain (CCD or PMT) with the photon flux. But as I want to compare with the synthetic images which are independent of detector characteristics, I would prefer a way to directly compare the images purely from image variables. A variance estimation over small neighbourhoods throughout the image might roughly give an idea of noise, but then again might be skewed by border regions? Winnok ______ ir. Winnok De Vos Research Assistant dep. Molecular Biotechnology Faculty of Bioscience Engineering Ghent University Coupure links 653 9000 Ghent Belgium tel 0032.(0)9.264.59.71 fax 0032.(0)9.264.62.19 www.molecularbiotechnology.ugent.be ----- Original Message ----- From: "Alessandro Esposito" <[hidden email]> To: <[hidden email]> Sent: Friday, July 13, 2007 11:05 AM Subject: Re: SNR estimation of a single image Search the CONFOCAL archive at http://listserv.acsu.buffalo.edu/cgi-bin/wa?S1=confocal It could be useful the following: "The Role of Photon Statistics in Fluorescence Anisotropy Imaging" by Lidke et al. They use multiple images of the same object to compute a variance from which you may infer the number of collected photons in the assumption that only poissonian noise is present. Cheers, Alessandro -- Dr. Alessandro Esposito Laser Analytics Group - Department of Chemical Engineering University Cambridge CV: home.quantitative-microscopy.org Web: wikiscope.org |
Just be careful : Lidke et al. suggest (page 1238)
"A defocused object is an easy and suitable test image. A background dark level is measured and subtracted from the series. To rule out fluctuations of the light source, one normalizes every image by its integrated intensity. The mean intensity and variance is computed per pixel over the series. A plot of the variance versus intensity yields a line with slope equal to the gain..." This is basically what I suggested, but DON'T normalize the images before calculating the mean intensity and variance: if you do, you'll mess up your result (I'm not sure what Lidke et al. originally meant by this). You don't have to worry about "fluctuations of the light source" anyway, since if the level changes, so will the Poisson noise. Rick On 13 Jul 2007, at 4:07 pm, winnok ugent wrote: > Dear all > > Thank you for your replies. > I had also thought of using deconvolved images as noise free images > (estimation of original), but decided not to since the > deconvolution 'erodes' objects by the PSF, hence causing objects to > be smaller and have different intensities. It might be possible to > normalize the latter, but I fear the shape adjustment will cause a > bias in noise calculation. > It seems the best way must be to use the relation of the detector > gain (CCD or PMT) with the photon flux. > But as I want to compare with the synthetic images which are > independent of detector characteristics, I would prefer a way to > directly compare the images purely from image variables. > A variance estimation over small neighbourhoods throughout the > image might roughly give an idea of noise, but then again might be > skewed by border regions? > > Winnok > > > ______ > ir. Winnok De Vos > Research Assistant > > dep. Molecular Biotechnology > Faculty of Bioscience Engineering > Ghent University > Coupure links 653 > 9000 Ghent > Belgium > > tel 0032.(0)9.264.59.71 > fax 0032.(0)9.264.62.19 > www.molecularbiotechnology.ugent.be > ----- Original Message ----- From: "Alessandro Esposito" > <[hidden email]> > To: <[hidden email]> > Sent: Friday, July 13, 2007 11:05 AM > Subject: Re: SNR estimation of a single image > > > Search the CONFOCAL archive at > http://listserv.acsu.buffalo.edu/cgi-bin/wa?S1=confocal > > It could be useful the following: > > "The Role of Photon Statistics in Fluorescence Anisotropy Imaging" > by Lidke > et al. > > They use multiple images of the same object to compute a variance > from which > you may infer the number of collected photons in the assumption > that only > poissonian noise is present. > > Cheers, > > Alessandro > -- > Dr. Alessandro Esposito > Laser Analytics Group - Department of Chemical Engineering > University Cambridge > CV: home.quantitative-microscopy.org > Web: wikiscope.org ------------------------------------------------------------------------ ------------------------ 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 ------------------------------------------------------------------------ ------------------------- MONET: a MOnitoring NEtwork of Telescopes http://monet.Uni-Goettingen.de ------------------------------------------------------------------------ ------------------------- |
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