On the estimation of hyperparameters in Bayesian approach of solving inverse problems

The author proposes a new view on the estimation of hyperparameters (the parameters of the prior law) when a Bayesian approach with maximum entropy (ME) priors is used to solve the inverse problems which arise in signal and image reconstruction and restoration problems. In particular, he compares two methods; the expectation maximization (EM) algorithm which aims to find the marginalized maximum likelihood (MML) estimate and the generalized maximum likelihood (GML). Some simulation results with application in image restoration are provided to show the performance of the GML method. The convergence of the present implementation of the GML method depends essentially on the initialization of the hyperparameters and the image. If one starts with good initial values, the GML works satisfactorily.<>