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

Abstract : 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 ( Stg ), 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.
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Li Wang, Ali Mohammad-Djafari, Nicolas Gac, Mircea Dumitru. Bayesian 3D X-ray Computed Tomography with a Hierarchical Prior model for Sparsity in Haar Transform domain. Entropy, MDPI, 2018, Special Issue "Probabilistic Methods for Inverse Problems", ⟨10.3390/e20120977⟩. ⟨hal-01950706⟩

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