Bayesian 3D X-ray computed tomography image reconstruction with a scaled Gaussian mixture prior model

Wang, Li; Gac, Nicolas; Mohammad-Djafari, Ali

doi:10.1063/1.4906022

Title: Bayesian 3D X-ray computed tomography image reconstruction with a scaled Gaussian mixture prior model

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Abstract

In order to improve quality of 3D X-ray tomography reconstruction for Non Destructive Testing (NDT), we investigate in this paper hierarchical Bayesian methods. In NDT, useful prior information on the volume like the limited number of materials or the presence of homogeneous area can be included in the iterative reconstruction algorithms. In hierarchical Bayesian methods, not only the volume is estimated thanks to the prior model of the volume but also the hyper parameters of this prior. This additional complexity in the reconstruction methods when applied to large volumes (from 512{sup 3} to 8192{sup 3} voxels) results in an increasing computational cost. To reduce it, the hierarchical Bayesian methods investigated in this paper lead to an algorithm acceleration by Variational Bayesian Approximation (VBA) [1] and hardware acceleration thanks to projection and back-projection operators paralleled on many core processors like GPU [2]. In this paper, we will consider a Student-t prior on the gradient of the image implemented in a hierarchical way [3, 4, 1]. Operators H (forward or projection) and H{sup t} (adjoint or back-projection) implanted in multi-GPU [2] have been used in this study. Different methods will be evalued on synthetic volume 'Shepp and Logan' in terms of qualitymore »« less

Authors:

Wang, Li; Gac, Nicolas; Mohammad-Djafari, Ali ^[1]

Laboratoire des Signaux et Systèmes 3, Rue Joliot-Curie 91192 Gif sur Yvette (France)

Publication Date:: Tue Jan 13 00:00:00 EST 2015

OSTI Identifier:: 22390872

Resource Type:: Journal Article

Journal Name:: AIP Conference Proceedings

Additional Journal Information:: Journal Volume: 1641; Journal Issue: 1; Conference: MAXENT 2014: Conference on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Clos Luce, Amboise (France), 21-26 Sep 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; APPROXIMATIONS; COMPUTERIZED TOMOGRAPHY; IMAGE PROCESSING; IMAGES; ITERATIVE METHODS; MATHEMATICAL MODELS; MIXTURES; NONDESTRUCTIVE TESTING; PROJECTION OPERATORS; VARIATIONAL METHODS; X RADIATION

Citation Formats


                    Wang, Li, Gac, Nicolas, and Mohammad-Djafari, Ali. Bayesian 3D X-ray computed tomography image reconstruction with a scaled Gaussian mixture prior model.  United States: N. p., 2015. 
        Web.  doi:10.1063/1.4906022.

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                    Wang, Li, Gac, Nicolas, & Mohammad-Djafari, Ali. Bayesian 3D X-ray computed tomography image reconstruction with a scaled Gaussian mixture prior model.  United States.  https://doi.org/10.1063/1.4906022

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                    Wang, Li, Gac, Nicolas, and Mohammad-Djafari, Ali. 2015.  
        "Bayesian 3D X-ray computed tomography image reconstruction with a scaled Gaussian mixture prior model".  United States.  https://doi.org/10.1063/1.4906022.

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@article{osti_22390872,

  title        = {Bayesian 3D X-ray computed tomography image reconstruction with a scaled Gaussian mixture prior model},

  author       = {Wang, Li and Gac, Nicolas and Mohammad-Djafari, Ali},

  abstractNote = {In order to improve quality of 3D X-ray tomography reconstruction for Non Destructive Testing (NDT), we investigate in this paper hierarchical Bayesian methods. In NDT, useful prior information on the volume like the limited number of materials or the presence of homogeneous area can be included in the iterative reconstruction algorithms. In hierarchical Bayesian methods, not only the volume is estimated thanks to the prior model of the volume but also the hyper parameters of this prior. This additional complexity in the reconstruction methods when applied to large volumes (from 512{sup 3} to 8192{sup 3} voxels) results in an increasing computational cost. To reduce it, the hierarchical Bayesian methods investigated in this paper lead to an algorithm acceleration by Variational Bayesian Approximation (VBA) [1] and hardware acceleration thanks to projection and back-projection operators paralleled on many core processors like GPU [2]. In this paper, we will consider a Student-t prior on the gradient of the image implemented in a hierarchical way [3, 4, 1]. Operators H (forward or projection) and H{sup t} (adjoint or back-projection) implanted in multi-GPU [2] have been used in this study. Different methods will be evalued on synthetic volume 'Shepp and Logan' in terms of quality and time of reconstruction. We used several simple regularizations of order 1 and order 2. Other prior models also exists [5]. Sometimes for a discrete image, we can do the segmentation and reconstruction at the same time, then the reconstruction can be done with less projections.},

  doi          = {10.1063/1.4906022},

  url          = {https://www.osti.gov/biblio/22390872},
  journal      = {AIP Conference Proceedings},

  issn         = {0094-243X},

  number       = 1,

  volume       = 1641,

  place        = {United States},

  year         = {Tue Jan 13 00:00:00 EST 2015},

  month        = {Tue Jan 13 00:00:00 EST 2015}

}

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