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

Authors:
Ali Mohammad-Djafari
Affiliations:
Laboratoire des Signaux et Systèmes, CNRS, ESE, UPS, École Supérieure d'Électricité, Gif-sur-Yvette, France
Venue:
ICASSP'93 Proceedings of the 1993 IEEE international conference on Acoustics, speech, and signal processing: image and multidimensional signal processing - Volume V
Year:
1993

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Abstract

In this paper we propose a new view on the estiriiation of the 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 we compare two methods; the Expectation Maximization (EM) algorithm who 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 performances of the GML method.