Super-Resolution Using Hidden Markov Model and Bayesian Detection Estimation Framework
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Super-Resolution Using Hidden Markov Model and Bayesian Detection Estimation Framework Fabrice Humblot1, 2 and Ali Mohammad-Djafari2 1 DGA/DET/SCET/CEP/ASC/GIP, 2 LSS/UMR8506
94114 Arcueil, France (CNRS-Sup´elec-UPS), 91192 Gif-sur-Yvette Cedex, France
Received 12 December 2004; Revised 22 May 2005; Accepted 27 May 2005 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. Copyright © 2006 F. Humblot and A. Mohammad-Djafari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1.
INTRODUCTION
This paper concerns super-resolution (SR) reconstruction of an image from a few low-resolution (LR) images in order to gain a better detection on faintly contrasted and isolated specks having a size of almost one pixel in a picture. In this paper we deal more particularly with the SR process. The SR reconstruction consists in producing a highresolution (HR) image from a set of LR images. These LR images can be taken from a video sequence. They must come out from a moving scene: the movement and nonredundant information are what make SR process possible. So, the obtained HR picture contains more useful information than one of the LR pictures taken in the initial video sequence. One of the main steps in a SR reconstruction process is the registration of the different LR images. It is defined as the way of matching two or more pictures showing the same scene from different viewpoints, from different sensors, or at different times. To get a good SR reconstruction, it is essential to know accurately the transformation that enables to go from one LR picture to another. Our work context allows us to limit the field of possible transformations between two pictures to the global translatory motion. Indeed, it does not seem unrealistic to have a stabilized and controlled camera to obtain the initial LR video sequence. We can imagine that the movement of the camera during the image acquisition
is limited to global translational move, and that there is no zoom effect (equivalent to homothety transformation) and no rotation of the camera axis. To deal with this proble
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