A Natural Approach to the Numerical Integration of Riccati Differential Equations
SIAM Journal on Numerical Analysis
Estimation with Applications to Tracking and Navigation
Estimation with Applications to Tracking and Navigation
Cardiac Motion Extraction from Images by Filtering Estimation Based on a Biomechanical Model
FIMH '09 Proceedings of the 5th International Conference on Functional Imaging and Modeling of the Heart
Recovery of myocardial kinematic function without the time history of external loads
EURASIP Journal on Advances in Signal Processing - Image processing and analysis in biomechanics
Effective estimation in cardiac modelling
FIMH'07 Proceedings of the 4th international conference on Functional imaging and modeling of the heart
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A sampled-data filtering framework is presented for cardiac motion recovery from periodic medical image sequences. Cardiac dynamics is a continuously evolving physiological process, whereas the imaging data can provide only sampled measurements at discrete time instants. Stochastic multi-frame filtering frameworks are constructed to couple the continuous cardiac dynamics with the discrete measurements, and to deal with the parameter uncertainty of the biomechanical constraining model and the noisy nature of the imaging data in a coordinated fashion. The state estimates are predicted according to the continuous-time state equation between observation time points, and then updated with the new measurements obtained at discrete time instants, yielding physically more meaningful and more accurate estimation results. Both continuous-discrete Kalman filter and sampled-data H∞ filter are applied, and the H∞ scheme can give robust estimation results when the noise statistics is not available a priori. The sampled-data estimation strategies are validated through synthetic data experiments to illustrate their advantages and on canine MR phase contrast images to show their clinical relevance.