This paper presents a new method for super-resolution (SR) reconstruction of a high-resolution (HR) image from several lowresolution (LR) images. The HR image is assumed to be composed of homogeneous regions. Thus, the a priori distribution of the pixels is modeled by a finite mixture model (FMM) and a Potts Markov model (PMM) for the labels. The whole a priori model is then a hierarchical Markov model. The LR images are assumed to be obtained from the HR image by lowpass filtering, arbitrarily translation, decimation, and finally corruption by a random noise. The problem is then put in a Bayesian detection and estimation framework, and appropriate algorithms are developed based on Markov chain Monte Carlo (MCMC) Gibbs sampling. At the end, we have not only an estimate of the HR image but also an estimate of the classification labels which leads to a segmentation result.

Abstract.This communication presents an extension to a super-resolution (SR) method we previously exposed in [1]. SR techniques involve several low-resolution (LR) images in the reconstruction's process of a high-resolution (HR) image. The LR images are assumed to be obtained from the HR image through optical and sensor blurs, shift movement and decimation operators, and finally corruption by a random noise. Moreover, the HR image is assumed to be composed of a finite number of homogeneous regions. Thus, we associate to each pixel of the HR image a classification variable which is modeled by a Potts Markov field. The SR problem is then expressed as a Bayesian joint estimation of the HR image pixel values, its classification labels variable, and the problem's hyperparameters. These estimations are performed using an appropriate algorithm based on hybrid Markov Chain Monte-Carlo (MCMC) Gibbs sampling.In this study, we distinguish two kinds of region's homogeneity: the first one follows a constant model, and the second a bilinear model. Our previous work [1] only deals with constant model. Finally we conclude this work showing simulation results obtained with synthetic and real data.

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