A 3D Bayesian Computed Tomography Reconstruction Algorithm with Gauss-Markov-Potts Prior Model and its Application to Real Data

Iterative reconstruction methods in Computed Tomography (CT) are known to provide better image quality than analytical methods but they are not still applied in many fields because of their computational cost. In the last years, Graphical Processor Units (GPU) have emerged as powerful devices in order to parallelize calculations, but the efficiency of their use is conditionned on applying algorithms that can be massively parallelizable. Moreover, in non-destructive testing (NDT) applications, a segmentation of the reconstructed volume is often needed in order to have an accurate diagnosis on the material health, but performing a segmentation after the reconstruction introduces uncertainties in the diagnosis from both the reconstruction and the segmentation algorithms. In this paper, we propose an iterative reconstruction method for 3D CT that performs a joint reconstruction and segmentation of the controlled object in NDT for industrial applications. The method is based on a 3D Gauss-Markov-Potts prior model in Bayesian framework, which has shown its effective use in many image restoration and super-resolution problems. First, we briefly describe this model, before deriving the expression of the joint posterior distribution of all the unknowns. Next, an effective maximization of this distribution is presented. We use a ray-driven projector and a voxel-driven backprojector implemented on GPU. The algorithm is developed so it can be massively parallelized. * The authors are grateful to Lionel Gay and Nicolas Cochennec for having provided the real IQI phantom used to test the method. They would also like to thank Thomas Boulay for his contribution to the implementation of the projector and the backprojector on GPU. 2 C. Chapdelaine, A. Mohammad-Djafari, N. Gac, E. Parra / 3D Bayesian CT with Gauss-Markov-Potts prior model Finally, we present our results on simulated and real phantoms. In addition, we investigate further reconstruction quality indicators in order to compare our results with other methods.