Variational Bayesian Kalman filtering in dynamical tomography

The problem of dynamical tomography consists in reconstructing a temporal sequence of images from their noisy projections. For this purpose, a recursive algorithm is usually used, like for instance the Kalman Filter (KF), due to the dynamical structure of the problem. However, since it needs the inverse of innovation matrix, KF may suffer from a huge computational cost in cases of images with very high dimensions. To solve this issue, we develop a new suboptimal version of the KF based on a Variational Bayesian (VB) approach. The proposed Variational Bayesian KF (VBKF) algorithm is compared to the KF with simulations in a small problem (images 32×32). As expected, the image quality of VBKF is as good as the KF and the VBKF algorithm is four times faster than the KF. Furthermore, in realistic high dimensional problems in which the practical implementation of KF becomes impossible, the VBKF gives an attractive alternative since it can be millions times faster than the KF