Unsupervised joint deconvolution and segmentation method for textured images: a Bayesian approach and an advanced sampling algorithm
Résumé
The paper tackles the problem of joint deconvolution and segmentation of textured images. The images are composed of regions containing a patch of texture that belongs to a set of K possible classes. Each class is described by a Gaussian random field with parametric power spectral density whose parameters are unknown. The class labels are modelled by a Potts field driven by a granularity coefficient that is also unknown. The method relies on a hierarchical model and a Bayesian strategy to jointly estimate the labels, the K textured images in addition to hyperparameters: the signal and the noise levels as well as the texture parameters and the granularity coefficient. The capability to estimate the latter is an important feature of the paper. The estimates are designed in an optimal manner as a risk minimizer that yields the marginal posterior maximizer for the labels and the posterior mean for the rest of the unknowns. They are computed based on a convergent procedure from samples of the posterior obtained through an advanced MCMC algorithm: Perturbation-Optimization step and Fisher Metropolis-Hastings step within a Gibbs loop. Various numerical evaluations provide encouraging results despite the strong difficulty of the problem.
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