In order to enhance image quality for controlling the interior of a volume in industry, model-based iterative reconstruction (MBIR) methods in 3D X-ray Computed Tomography (CT) have shown their efficiency compared to analytical reconstruction methods. MBIR methods enforce a prior model on the volume to reconstruct and make fusion of the information contained in the prior model and the projection data. The projections have many uncertainties which have very different origins in 3D CT. They are taken into account in MBIR methods but, despite of their different origins, they are in general gathered in only one term in the forward model. In this paper, we propose to derive a new forward model by adding a further error term in the Poisson statistics of photon-count, corresponding to the deviation of the monochromatic model with respect to the actual polychromacy of the rays. A Taylor expansion of the Poisson log-likelihood leads us to a new algebraic forward model accounting for two terms of uncertainties : we call it the error- splitting forward model. Different prior models are assigned to each of distinguished uncertainties : measurement uncertainties are modeled as Gaussian, while linear model uncertainties are modeled as heavy-tailed to bring robustness to the reconstruction process. We give strategies to fix the parameters of the error-splitting forward model. Next, we use it in a full MBIR method with Gauss-Markov-Potts prior model on the volume, in order to reconstruct piecewise-constant objects for non-destructive testing in industry. Compared to the conventional forward model, we show in our experiments that the use of the error-splitting forward model with Gauss-Markov-Potts prior combines better robustness and accuracy.

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

Countries with access to large bodies of water often aim to protect their maritime transport by employing maritime surveillance systems. However, the number of available sensors (e.g., cameras) is typically small compared to the to-be-monitored targets, and their Field of View (FOV) and range are often limited. This makes improving the situational awareness of maritime transports challenging. To this end, we propose a method that not only distributes multiple sensors but also plans paths for them to observe multiple targets, while minimizing the time needed to achieve situational awareness. In particular, we provide a formulation of this sensor allocation and path planning problem which considers the partial awareness of the targets' state, as well as the unawareness of the targets' trajectories. To solve the problem we present two algorithms: 1) a greedy algorithm for assigning sensors to targets, and 2) a distributed multi-agent path planning algorithm based on regret-matching learning. Because a quick convergence is a requirement for algorithms developed for high mobility environments, we employ a forgetting factor to quickly converge to correlated equilibrium solutions. Experimental results show that our combined approach achieves situational awareness more quickly than related work.