VARIATIONAL POSTERIOR DISTRIBUTION APPROXIMATION IN BAYESIAN EMISSION TOMOGRAPHY RECONSTRUCTION USING A GAMMA MIXTURE PRIOR

Rafael Molina, Antonio López, José Manuel Martín, Aggelos K. Katsaggelos

2007

Abstract

Following the Bayesian framework we propose a method to reconstruct emission tomography images which uses gamma mixture prior and variational methods to approximate the posterior distribution of the unknown parameters and image instead of estimating them by using the Evidence Analysis or alternating between the estimation of parameters and image (Iterated Conditional Mode (ICM)) approach. By analyzing the posterior distribution approximation we can examine the quality of the proposed estimates. The method is tested on real Single Positron Emission Tomography (SPECT) images.

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  18. In algorithm 3 we need to calculate the quantities E [x j]qk(x), E [log(pc pG(x j | ßc, ac))]qk+1(x),qk+1(ß),qk(p),
  19. E [1/ßc]qk+1(ß) and E [log Ai, jx j]qk+1(x).
  20. To calculate E [x j]qk(x) we note that (see Eq. 8)
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Paper Citation


in Harvard Style

Molina R., López A., Manuel Martín J. and K. Katsaggelos A. (2007). VARIATIONAL POSTERIOR DISTRIBUTION APPROXIMATION IN BAYESIAN EMISSION TOMOGRAPHY RECONSTRUCTION USING A GAMMA MIXTURE PRIOR . In Proceedings of the Second International Conference on Computer Vision Theory and Applications - Volume 3: Bayesian Approach for Inverse Problems in Computer Vision, (VISAPP 2007) ISBN 978-972-8865-75-7, pages 165-173. DOI: 10.5220/0002066001650173


in Bibtex Style

@conference{bayesian approach for inverse problems in computer vision07,
author={Rafael Molina and Antonio López and José Manuel Martín and Aggelos K. Katsaggelos},
title={VARIATIONAL POSTERIOR DISTRIBUTION APPROXIMATION IN BAYESIAN EMISSION TOMOGRAPHY RECONSTRUCTION USING A GAMMA MIXTURE PRIOR},
booktitle={Proceedings of the Second International Conference on Computer Vision Theory and Applications - Volume 3: Bayesian Approach for Inverse Problems in Computer Vision, (VISAPP 2007)},
year={2007},
pages={165-173},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002066001650173},
isbn={978-972-8865-75-7},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Second International Conference on Computer Vision Theory and Applications - Volume 3: Bayesian Approach for Inverse Problems in Computer Vision, (VISAPP 2007)
TI - VARIATIONAL POSTERIOR DISTRIBUTION APPROXIMATION IN BAYESIAN EMISSION TOMOGRAPHY RECONSTRUCTION USING A GAMMA MIXTURE PRIOR
SN - 978-972-8865-75-7
AU - Molina R.
AU - López A.
AU - Manuel Martín J.
AU - K. Katsaggelos A.
PY - 2007
SP - 165
EP - 173
DO - 10.5220/0002066001650173