Tomographic imaging of dynamic objects with the ensemble Kalman filter

Authors:
Mark D. Butala;Richard A. Frazin;Yuguo Chen;Farzad Kamalabadi
Affiliations:
Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL;Department of Atmospheric, Oceanic and Space Sciences, University of Michigan, Ann Arbor, MI;Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL;Department of Electrical and Computer Engineering and Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL
Venue:
IEEE Transactions on Image Processing
Year:
2009

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Abstract

We address the image formation of a dynamic object from projections by formulating it as a state estimation problem. The problem is solved with the ensemble Kalman filter (EnKF), a Monte Carlo algorithm that is computationally tractable when the state dimension is large. In this paper, we first rigorously address the convergence of the EnKF. Then, the effectiveness of the EnKF is demonstrated in a numerical experiment where a highly variable object is reconstructed from its projections, an imaging modality not yet explored with the EnKF. The results show that the EnKF can yield estimates of almost equal quality as the optimal Kalman filter but at a fraction of the computational effort. Further experiments explore the rate of convergence of the EnKF, its performance relative to an idealized particle filter, and implications of modeling the system dynamics as a random walk.