Variational Bayesian approach in model-based iterative reconstruction for 3D X-ray computed tomography with Gauss-Markov-Potts prior

Camille Chapdelaine (1) , Ali Mohammad-Djafari (1) , Nicolas Gac (1) , Estelle Parra-Denis (2)

1 L2S - Laboratoire des signaux et systèmes
2 Safran Tech

3D X-ray Computed Tomography (CT) is used in medicine and non-destructive testing 1 (NDT) for industry to visualize the interior of a volume and control its healthiness. Compared to 2 analytical reconstruction methods, model-based iterative reconstruction (MBIR) methods obtain 3 high-quality reconstructions while reducing the dose. Nevertheless, usual Maximum-A-Posteriori 4 (MAP) estimation does not enable to quantify the uncertainties on the reconstruction, which can 5 be useful for the control performed afterwards. Herein, we propose to estimate these uncertainties 6 jointly with the reconstruction by computing Posterior Mean (PM) thanks to Variational Bayesian 7 Approach (VBA). We present our reconstruction algorithm using a Gauss-Markov-Potts prior model 8 on the volume to reconstruct. For PM calculation in VBA, the uncertainties on the reconstruction are 9 given by the variances of the posterior distribution of the volume. To estimate these variances in our 10 algorithm, we need to compute diagonal coefficients of the posterior covariance matrix. Since this 11 matrix is not available in 3D X-ray CT, we propose an efficient solution to tackle this difficulty, based 12 on the use of a matched pair of projector and backprojector. In our simulations using the Separable 13 Footprint (SF) pair, we compare our PM estimation with MAP estimation. Perspectives for this work 14 are applications to real data as improvement of our GPU implementation of SF pair. 15

Mots clés: Computed Tomography; Gauss-Markov-Potts; variational Bayesian approach; Separable

Domaines: Traitement du signal et de l'image [eess.SP]

Camille Chapdelaine, Ali Mohammad-Djafari, Nicolas Gac, Estelle Parra-Denis. Variational Bayesian approach in model-based iterative reconstruction for 3D X-ray computed tomography with Gauss-Markov-Potts prior. MaxEnt 2019 : Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Jun 2019, Garching/Munich, Germany. ⟨10.3390/proceedings2019033004⟩. ⟨hal-02132706⟩