Hyperparameter estimation for satellite image restoration using a MCMC maximum-likelihood method

The satellite image deconvolution problem is ill-posed and must be regularized. Herein, we use an edge-preserving regularization model using a ' function, involving two hyperparameters. Our goal is to estimate the optimal parameters in order to automatically reconstruct images. We propose to use the Maximum Likelihood Estimator (MLE), applied to the observed image. We need sampling from prior and posterior distributions. Since the convolution prevents from using standard samplers, we have developed a modiied Geman-Yang algorithm, using an auxiliary variable and a cosine transform. We present a Markov Chain Monte Carlo Maximum Likelihood (MCMCML) technique which is able to simultaneously achieve the estimation and the reconstruction.