Bayesian Inference for Determining Data and Noise Variance in Image Denoising

[Loures]

Hello,
I am working do determine an optimum threshold for wavelt transform image denoise. I have the following quesstion. considering a vector of a data d*:
d*= d + noise
where the noise is zero mean and with variance sigma ~(0,sigma) and the signal "d" has variance sigma_x.
I have to infer the noise variance sigma and the signal variance sigma_x.
How can I do it followin g the Bayesian Methodology of Inference.
I have experience with Bayesian inference, but never have feced this problem.
Thank you,
Loures

 

[Valkarie]

In order to use Bayesian inference to determine the noise variance sigma and the signal variance sigma_x, you need to define a prior distribution for each variable. Depending on what information you have, you can choose an appropriate prior. For example, if you assume that both sigma and sigma_x are positive numbers, you can use a Gamma distribution as your prior. Once you have defined the prior, you can then use Bayes' theorem to calculate the posterior distribution of the two variables, given the data d*. You can then use this posterior distribution to calculate the mean and variance of sigma and sigma_x.