Computed tomography reconstruction based on a hierarchical model and variational Bayesian method

International audienceIn order to improve the quality of X-ray Computed Tomography (CT) reconstruction for Non Destructive Testing (NDT), we propose a hierarchical prior modeling with a Bayesian approach. In this paper we present a new hierarchical structure for the inverse problem of CT by using a multivariate Student-t prior which enforces sparsity and preserves edges. This model can be adapted to the piecewise continuous image reconstruction problems. We demonstrate the feasibility of this method by comparing with some other state of the art methods. In this paper, we show simulation results in 2D where the image is the middle slice of the Shepp-Logan object but the algorithms are adapted to the big data size problem, which is one of the principal difficulties in the 3D CT reconstruction problem