I have an image with Poisson noise, I need to estimate the noise level in this image(average and variance)
Is anyone know a known algorithm that does this,
Personally, I have not found.
I would be grateful if you answer me.
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Can you specify what 'Poisson noise' is in this case? Each pixel x_i is distributed as Poisson(lambda_i) where lambda_i is your pixel intensity? – Memming Sep 15 '13 at 14:09
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The scintigraphic images are affected by Poisson noise in nature. In the literature they approximate the Poisson model with Gaussian, which is to estimate the variance and the average noise. But I have not found a suitable algorithm makes it :( – manuala Sep 15 '13 at 18:25
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So my assumption is correct then. You want to estimate the underlying intensity function. – Memming Sep 15 '13 at 18:28
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I am no expert in scintigraphic images, but I presume that you want to estimate the density of the source which are emitting radioactive signals with Poisson statistics.
Note that for Poisson observation, mean and variance are equal.
Estimating the intensity of an inhomogeneous Poisson observation is a well known problem. I recommend Bayesian methods. Here are some pointers:
- Miller MI, Roysam B. Bayesian image reconstruction for emission tomography incorporating Good's roughness prior on massively parallel processors. Proc Natl Acad Sci U S A. 1991 Apr 15;88(8):3223-7. http://www.ncbi.nlm.nih.gov/pubmed/2014243
- Nguyen MK, Guillemin H, Duvaut P. Bayesian MAP restoration of scintigraphic images. ICASSP 1999 http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=757577
Memming
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Thank you for your answer, but you can better explain, Is that you know a well-defined approach – manuala Sep 15 '13 at 19:46
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Thank you for documentation, The second article is a very good example for the restoration of scintigraphic images, it uses Bayesian Maximum A Posteriori (MAP). – manuala Sep 24 '13 at 17:43
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I wanted to estimate the variance of the noise, but it does not explain the estimation algorithm. Can you provide me the matlab code please – manuala Sep 24 '13 at 17:43
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@manuala the variance of the noise is same as the mean for Poisson observation. All you need to estimate is the mean. – Memming Sep 24 '13 at 18:12
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Yes but I have not found the estimation algorithm, can you help me in this direction or give me a link to a matlab code please :) – manuala Sep 24 '13 at 19:40
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@manuala you won't find some matlab code that solves your specific problem. You need extra assumptions about smoothness that only you would know. Good luck. – Memming Sep 24 '13 at 20:01
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Hi, thank you for your help, I just want to know if the algorithm Expectation-Maximization (EM) technique for maximum-likelihood estimation can estimate the Poisson noise variance ?? I would be grateful if you can answer me – manuala Sep 28 '13 at 15:11
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@manuala you can accept this answer and ask a separate question with more details. – Memming Sep 28 '13 at 15:23
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You tell me that the Expectation Maximization (EM) algorithm can estimate the noise variance of an image corrupted by Poisson noise. After you will find the matlab code of the EM algorithm http://www.mathworks.com/matlabcentral/fileexchange/8636-emgm Can you explain me or give me some change for this code so I can calculate the vainance noise pleaseee – manuala Sep 30 '13 at 15:10