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Hierarchical Bayesian sparse image reconstruction with application to MRFM

Dobigeon, Nicolas and Tourneret, Jean-Yves and Hero, Alfred O. Hierarchical Bayesian sparse image reconstruction with application to MRFM. (2009) IEEE Transactions on Signal Processing, vol. 1 (n° 9). pp. 2059-2070. ISSN 1053-587X

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Official URL: http://dx.doi.org/10.1109/TIP.2009.2024067

Abstract

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g., by maximizing the estimated posterior distribution. In our fully Bayesian approach, the posteriors of all the parameters are available. Thus, our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of the proposed hierarchical Bayesian sparse reconstruction method is illustrated on synthetic data and real data collected from a tobacco virus sample using a prototype MRFM instrument.

Item Type:Article
Additional Information:Thanks to IEEE editor. The publisher's version is available at http://www.signalprocessingsociety.org/publications/periodicals/tsp/
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution: Université de Toulouse > Université de Toulouse I-Sciences Sociales - UT1
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT
Other partners > University of Michigan - U-M (USA)
Université de Toulouse > Université Paul Sabatier-Toulouse III - UPS
French research institutions > Centre National de la Recherche Scientifique - CNRS
Laboratory name:
Statistics:download
Deposited By: Nicolas DOBIGEON
Deposited On:13 Oct 2009 15:47

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