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

摘要

The satellite image deconvolution problem is ill-posed and must be regularized. Herein, we use an edge-preserving regularization model using a ϕ 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 use of standard samplers, we have developed a modified 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.