A Kernel Density Estimator-Based Maximum A Posteriori Image Reconstruction Method for Dynamic Emission Tomography Imaging

A novel maximum a posteriori (MAP) method for dynamic single-photon emission computed tomography image reconstruction is proposed. The prior probability is modeled as a multivariate kernel density estimator (KDE), effectively modeling the prior probability non-parametrically, with the aim of reducing the effects of artifacts arising from inconsistencies in projection measurements in low-count regimes where projections are dominated by noise. The proposed prior spatially and temporally limits the variation of time-activity functions (TAFs) and attracts similar TAFs together. The similarity between TAFs is determined by the spatial and range scaling parameters of the KDE-like prior. The resulting iterative image reconstruction method is evaluated using two simulated phantoms, namely the extended cardiac-torso (XCAT) heart phantom and a simulated Mini-Deluxe Phantom. The phantoms were chosen to observe the effects of the proposed prior on the TAFs based on the vicinity and abutments of regions with different activities. Our results show the effectiveness of the proposed iterative reconstruction method, especially in low-count regimes, which provides better uniformity within each region of activity, significant reduction of spatiotemporal variations caused by noise, and sharper separation between different regions of activity than expectation maximization and an MAP method employing a more traditional Gibbs prior.