In medical imaging and image analysis, the goals of a variety of problems, including cardiac motion estimation and dynamic PET reconstruction, are essentially to recover meaningful physiological information of the underlying biological processes from medical imaging data. For such problems, an optimal estimation framework using biological guidance and sampled-data filtering has been developed, and has been applied to the specific cardiac and PET information recovery problems....[ Read more ]

In medical imaging and image analysis, the goals of a variety of problems, including cardiac motion estimation and dynamic PET reconstruction, are essentially to recover meaningful physiological information of the underlying biological processes from medical imaging data. For such problems, an optimal estimation framework using biological guidance and sampled-data filtering has been developed, and has been applied to the specific cardiac and PET information recovery problems.

Biological models are incorporated in the framework to provide physiological guidance for the information recovery, with biomechanical models used for cardiac motion estimation, and tracer kinetic models adopted for dynamic PET reconstruction, so that it is possible to go beyond the limits imposed by data qualities. Sampled-data filtering is proposed to properly couple continuous biological dynamics with discrete imaging-derived observations, where the information recovery is formulated as a state estimation problem in a continuous-discrete hybrid paradigm. In sampled-data filtering, state estimates are predicted according to the original continuous-time state equation between observation time points and updated with new measurements at discrete time instants, yielding physiologically more meaningful and more accurate estimation results. Both continuous-discrete Kalman filter and sampled-data H_∞ filter are developed in the framework, corresponding to MMSE and mini-max optimization criteria respectively. The filtering framework can also deal with system and data uncertainties coordinately.

With guidance from appropriate biological models and through several transforms, both the cardiac motion estimation and the dynamic PET reconstruction problems can be formulated as the state estimation problem in a hybrid paradigm, and sampled-data filtering strategies are applied for the information recovery, where the H_∞ strategy is particularly suited to dynamic PET data with complicated statistics and low SNR. The strategies are validated through synthetic data experiments to illustrate their advantages and on different real data sets to show their clinical potential.