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Towards Automatic Selection of the Regularization Parameters in Emission Tomgraphy by Fourier Synthesis

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Computer Vision and Mathematical Methods in Medical and Biomedical Image Analysis (MMBIA 2004, CVAMIA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3117))

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Abstract

The problem of image reconstruction in emission tomography in an ill-posed inverse problem. The methodology FRECT (Fourier regularized computed tomography) allows not only for a priori analysis of the stability of the reconstruction process but also for an exact definition of the resolution in the slices. Its natural regularization parameter, namely the cutoff frequency ν of the filter underlying the definition of the FRECT solution, can be calibrated by estimating the condition number for a range of values of ν. We first outline the methodology FRECT. We then discuss the numerical strategies which can be implemented in order to estimate the condition numbers of large matrices. Finally, we present a few results obtained in the context of SPECT reconstructions, and discuss the possibility to determine automatically the best possible cutoff frequency from the analysis of the stability.

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Author information

Authors and Affiliations

  1. Dpt. des Sciences Mathématiques, Université de Montpellier 2, Place Eugène Bataillon, 31 095, Montpellier Cedex 5, France

    P. Maréchal

  2. Faculté de médecine de Montpellier, Service de médecine nucléaire, CHU Lapeyronie, 371 av. du Doyen Gaston Giraud, 34 295, Montpellier Cedex 5, France

    D. Mariano-Goulart

  3. CERFACS, 42 av. Gaspard Coriolis, 31057, Toulouse Cedex, France

    L. Giraud & S. Gratton

Authors
  1. P. Maréchal
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  2. D. Mariano-Goulart
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  3. L. Giraud
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  4. S. Gratton
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Iowa, 52242, Iowa City, IA, USA

    Milan Sonka

  2. Computational Biomedicine Lab, University of Houston, Houston, TX

    Ioannis A. Kakadiaris

  3. Center for Machine Perception, Czech Technical University, 121 35, Prague 2, Czech Republic

    Jan Kybic

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© 2004 Springer-Verlag Berlin Heidelberg

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Maréchal, P., Mariano-Goulart, D., Giraud, L., Gratton, S. (2004). Towards Automatic Selection of the Regularization Parameters in Emission Tomgraphy by Fourier Synthesis. In: Sonka, M., Kakadiaris, I.A., Kybic, J. (eds) Computer Vision and Mathematical Methods in Medical and Biomedical Image Analysis. MMBIA CVAMIA 2004 2004. Lecture Notes in Computer Science, vol 3117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27816-0_6

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  • DOI: https://doi.org/10.1007/978-3-540-27816-0_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22675-8

  • Online ISBN: 978-3-540-27816-0

  • eBook Packages: Springer Book Archive

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