TY - GEN
T1 - Variational Bayesian Kalman filtering in dynamical tomography
AU - Ait-El-Fquih, Boujemaa
AU - Rodet, Thomas
PY - 2011
Y1 - 2011
N2 - 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 32x32). 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.
AB - 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 32x32). 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.
UR - http://www.scopus.com/inward/record.url?scp=80051622445&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2011.5947230
DO - 10.1109/ICASSP.2011.5947230
M3 - Conference contribution
AN - SCOPUS:80051622445
SN - 9781457705397
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 4004
EP - 4007
BT - 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
ER -