Novel scatter compensation of list-mode PET data using spatial and energy dependent corrections

With the widespread use of positron emission tomography (PET) crystals with greatly improved energy resolution (e.g., 11.5% with LYSO as compared to 20% with BGO) and of list-mode acquisitions, the use of the energy of individual events in scatter correction schemes becomes feasible. We propose a novel scatter approach that incorporates the energy of individual photons in the scatter correction and reconstruction of list-mode PET data in addition to the spatial information presently used in clinical scanners. First, we rewrite the Poisson likelihood function of list-mode PET data including the energy distributions of primary and scatter coincidences and show that this expression yields an MLEM reconstruction algorithm containing both energy and spatial dependent corrections. To estimate the spatial distribution of scatter coincidences we use the single scatter simulation (SSS). Next, we derive two new formulae which allow estimation of the 2-D (coincidences) energy probability density functions (E-PDF) of primary and scatter coincidences from the 1-D (photons) E-PDFs associated with each photon. We also describe an accurate and robust object-specific method for estimating these 1-D E-PDFs based on a decomposition of the total energy spectra detected across the scanner into primary and scattered components. Finally, we show that the energy information can be used to accurately normalize the scatter sinogram to the data. We compared the performance of this novel scatter correction incorporating both the position and energy of detected coincidences to that of the traditional approach modeling only the spatial distribution of scatter coincidences in 3-D Monte Carlo simulations of a medium cylindrical phantom and a large, nonuniform NCAT phantom. Incorporating the energy information in the scatter correction decreased bias in the activity distribution estimation by ~20% and ~40% in the cold regions of the large NCAT phantom at energy resolutions 11.5% and 20% at 511 keV, respectively, compared to when using the spatial information alone.