A Natural Approach to the Numerical Integration of Riccati Differential Equations
SIAM Journal on Numerical Analysis
Statistical approaches in quantitative positron emissiontomography
Statistics and Computing
PET image reconstruction: a robust state space approach
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
Simultaneous estimation of physiological parameters and the input function - in vivo PET data
IEEE Transactions on Information Technology in Biomedicine
Dynamic Dual-Tracer PET Reconstruction
IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
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Dynamic PET reconstruction is a challenging issue due to the spatio-temporal nature and the complexity of the data. Conventional frame-by-frame approaches fail to explore the temporal information of dynamic PET data, and may lead to inaccurate results due to the low SNR of data. Due to the ill-conditioning of image reconstruction, proper prior knowledge should be incorporated to constrain the reconstruction. In this paper, we propose a tracer kinetics guided reconstruction framework for dynamic PET imaging. The dynamic reconstruction problem is formulated in a state-space representation, where compartment model serves as a continuous-time system equation to describe the tracer kinetic processes, and the imaging data is expressed as discrete sampling of the system states in a measurement equation. The reconstruction problem has therefore become a state estimation problem in a continuous-discrete hybrid paradigm, and sampled-data H∞ filtering is applied to for the estimation. As H∞ filtering makes no assumptions on the system and measurement statistics, robust reconstruction results can be obtained for dynamic PET imaging where the statistical properties of measurement data and system uncertainty are not available a priori.