State-space reconstruction of pet parametric maps

The primary goal of dynamic Positron Emission Tomography (PET) is to quantify the physiological and biological processes through tracer kinetics analysis. However, the process is difficult and complicated because of the compromising imaging data quality, i.e. either longer scans with good counting statistics but poor temporal resolution, or noisy shorter scans with good temporal resolution. In this paper, we explore the usage of state space principles for physiological parameter estimation in dynamic PET imaging. The system equation is constructed from particular tracer kinetic models, with the number and relationship between tissue compartments dictated by the physiological and biochemical properties of the process under study. And the observation equation on measurement data is formed based on the specific types of imaging or image-derived data. Once the Poisson distributed PET data are converted to Gaussian ones through the Anscombe transformation, an extended Kalman filter is adopted to estimate the tracer kinetics parameters from the system and observations. More appropriate estimation strategies which better take care of the PET statistics are also under development. The framework is tested on simulated digital phantom data, and the results are of sufficient accuracy and robustness.