Sampled-Data Filtering Framework for Cardiac Motion Recovery: Optimal Estimation of Continuous Dynamics From Discrete Measurements

Quantitative and noninvasive estimation of cardiac kinematics has significant physiological and clinical implications. In this paper, a sampled-data filtering framework is presented for the recovery of cardiac motion and deformation functions from periodic medical image sequences. Cardiac dynamics is a continuously evolving physical/physiological process, whereas the imaging data can provide only sampled measurements at discrete time instants. Given such a hybrid paradigm, stochastic multiframe filtering frameworks are constructed to couple the continuous dynamics with the discrete measurements, and to coordinately deal with the parameter uncertainty of the biomechanical constraining model and the noisy nature of the imaging data. The state estimates are predicted according to the continuous-time biomechanically constructed state equation between observation time points, and then updated with the new imaging-derived measurements at discrete time instants, yielding physically more meaningful and more accurate estimation results. Both continuous-discrete Kalman filter and sampled-data H_infin filter are applied for motion recovery. While Kalman filter is the optimal estimator under Gaussian noises, the H_infin scheme can give robust estimation results when the types and levels of model uncertainties and data disturbances are not available a priori. The strategies are validated through synthetic data experiments to illustrate their advantages and on canine MR phase contrast images and human MR tagging data to show their clinical potential.