Before revision:  This random vector is augmented by a random regularization parameter for the linear part. A probability distribution function for this augmented random vector knowing the measurements is derived . We explain how this derivation is related to the maximum likelihood regularization parameter selection [ Galatsanos and Katsaggelos,
After revision:  A dilation parameter alpha is used to scale the regularity of the linear unknown and is also modeled as a random variable. A posterior probability distribution for (m; alpha) is derived following an approach related to the maximum likelihood regularization parameter selection [ Galatsanos and Katsaggelos,