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

• Main Authors: Li Wang, Ali Mohammad-Djafari, Nicolas Gac, Mircea Dumitru
• Format: Article
• Language: English
• Published: MDPI AG 2018-12-01
• Series: Entropy
• Subjects: X-ray computed tomography; inverse problem; sparsity; hierarchical structure; generalized Student-<i>t</i> distribution; Haar transformation
• Online Access: https://www.mdpi.com/1099-4300/20/12/977

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-<i>t</i> distribution (<inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="script">S</mi> <msub> <mi>t</mi> <mi>g</mi> </msub> </mrow> </semantics> </math> </inline-formula>), 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.