X-ray Computed Tomography using a Sparsity Enforcing Prior Model Based on Haar Transformation in a Bayesian Framework

Issue title: An overview of Tomography and Applications

Guest editors: Paolo Dulio, Andrea Frosini and Grzegorz Rozenberg

Article type: Research Article

Authors: Wang, Li^{; *; †} | Mohammad-Djafari, Ali | Gac, Nicolas

Affiliations: Laboratoire des Signaux et Système, CentraleSupélec, CNRS, Université Paris Sud, Université Paris-Saclay, 3, Rue Joliot-Curie, 91192 Gif-sur-Yvette, France. li.wang@lss.supelec.fr, djafari@lss.supelec.fr, nicolas.gac@lss.supelec.fr

Correspondence: [†] Address for correspondence: Laboratoire des Signaux et Système, CentraleSupélec, CNRS, Université Paris Sud, Université Paris-Saclay, 3, Rue Joliot-Curie, 91192 Gif-sur-Yvette, France

Note: [*] Thanks to China Scholarship Council for funding

Abstract: X-ray Computed Tomography (CT) has become a hot topic in both medical and industrial applications in recent decades. Reconstruction by using a limited number of projections is a significant research domain. In this paper, we propose to solve the X-ray CT reconstruction problem by using the Bayesian approach with a hierarchical structured prior model basing on the multilevel Haar transformation. In the proposed model, the multilevel Haar transformation is used as the sparse representation of a piecewise continuous image, and a generalized Student-t distribution is used to enforce its sparsity. The simulation results compare the performance of the proposed method with some state-of-the-art methods.

Keywords: Computed Tomography (CT), Bayesian Approach, Hierarchical Model, Generalized Student-t distribution, Joint Maximum A Posterior (JMAP)

DOI: 10.3233/FI-2017-1594

Journal: Fundamenta Informaticae, vol. 155, no. 4, pp. 449-480, 2017