An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
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We describe a method for computing a continuous time estimate of dynamic changes in tracer density using list mode PET data. The tracer density in each voxel is modeled as an inhomogeneous Poisson process whose rate function can be represented using a cubic B-spline basis. An estimate of these rate functions is obtained by maximizing the likelihood of the arrival times of each detected photon pair over the control vertices of the spline. By resorting the list mode data into a standard sinogram plus a "timogram" that retains the arrival times of each of the events, we are able to perform efficient computation that exploits the symmetry inherent in the ordered sinogram. The maximum likelihood estimator uses quadratic temporal and spatial smoothness penalties and an additional penalty term to enforce non-negativity. Corrections for scatter and randoms are described and the results of studies using simulated and human data are included.