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Bayesian 3D X-ray Computed Tomography with a Hierarchical Prior Model for Sparsity in Haar Transform Domain

Laboratoire des signaux et système, Centralesupelec, CNRS, 3 Rue Joliot Curie, 91192 Gif sur Yvette, France
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Entropy 2018, 20(12), 977; https://doi.org/10.3390/e20120977
Received: 26 October 2018 / Revised: 3 December 2018 / Accepted: 11 December 2018 / Published: 16 December 2018
(This article belongs to the Special Issue Probabilistic Methods for Inverse Problems)
In this paper, a hierarchical prior model based on the Haar transformation and an appropriate Bayesian computational method for X-ray CT reconstruction are presented. Given the piece-wise continuous property of the object, a multilevel Haar transformation is used to associate a sparse representation for the object. The sparse structure is enforced via a generalized Student-t distribution ( S t g ), expressed as the marginal of a normal-inverse Gamma distribution. The proposed model and corresponding algorithm are designed to adapt to specific 3D data sizes and to be used in both medical and industrial Non-Destructive Testing (NDT) applications. In the proposed Bayesian method, a hierarchical structured prior model is proposed, and the parameters are iteratively estimated. The initialization of the iterative algorithm uses the parameters of the prior distributions. A novel strategy for the initialization is presented and proven experimentally. We compare the proposed method with two state-of-the-art approaches, showing that our method has better reconstruction performance when fewer projections are considered and when projections are acquired from limited angles. View Full-Text
Keywords: X-ray computed tomography; inverse problem; sparsity; hierarchical structure; generalized Student-t distribution; Haar transformation X-ray computed tomography; inverse problem; sparsity; hierarchical structure; generalized Student-t distribution; Haar transformation
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Wang, L.; Mohammad-Djafari, A.; Gac, N.; Dumitru, M. Bayesian 3D X-ray Computed Tomography with a Hierarchical Prior Model for Sparsity in Haar Transform Domain. Entropy 2018, 20, 977.

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