Image restoration using an estimated Markov model
Signal Processing
Simulated annealing: theory and applications
Simulated annealing: theory and applications
Simultaneous Parameter Estimation and Segmentation of Gibbs Random Fields Using Simulated Annealing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Constrained Restoration and the Recovery of Discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Variational Method in Image Recovery
SIAM Journal on Numerical Analysis
Unsupervised deconvolution of sparse spike trains using stochasticapproximation
IEEE Transactions on Signal Processing
Deterministic edge-preserving regularization in computed imaging
IEEE Transactions on Image Processing
Estimation of Markov random field prior parameters using Markov chain Monte Carlo maximum likelihood
IEEE Transactions on Image Processing
Nonlinear image recovery with half-quadratic regularization
IEEE Transactions on Image Processing
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Satellite images can be corrupted by an optical blur and electronic noise. Blurring is modeled by convolution, with a known linear operator H, and the noise is supposed to be additive, white and Gaussian, with a known variance. The recovery problem is ill-posed and therefore must be regularized. Herein, we use a regularization model which introduces a function, avoiding noise amplification while preserving image discontinuities (i.e. edges) of the restored image. This model involves two hyperparameters. Our goal is to estimate the optimal parameters in order to reconstruct images automatically. In this paper, we propose to use the Maximum Likelihood estimator, applied to the observed image. To evaluate the derivatives of this criterion, we must estimate expectations by sampling (samples are extracted from a Markov chain). These samples are images whose probability takes into account the convolution operator. Thus, it is very difficult to obtain them directly by using a standard sampler. We have developed a new algorithm for sampling, using an auxiliary variable based on Geman-Yang algorithm, and a cosine transform. We also present a new reconstruction method based on this sampling algorithm. We detail the Markov Chain Monte Carlo Maximum Likelihood (MCMCML) algorithm which ables to simultaneously estimate the parameters, and to reconstruct the corrupted image.