Additive and multiplicative versions of the maximum a posteriori algorithm with median root prior

It is a well-known fact that the maximum likelihood expectation maximization (MLEM) algorithm applied to either the original image or the image rescaled with the sensitivity, produces the same result. However, if an a posteriori function is maximized instead of the likelihood function, this rescaling procedure produces a different outcome. This abstract concentrates on the difference between these procedures applied in the maximum a posteriori (MAP) algorithm with the median root prior (MRP). It will be shown that depending on the way the prior is utilised, it is possible to achieve more noise reduction in the low sensitivity regions. The disadvantage being the fact that the weight prior, beta, must be tuned according to the maximum in the sensitivity.