Constrained mixture modeling for the estimation of kinetic parameters in dynamic PET

The estimation and analysis of kinetic parameters in dynamic PET is frequently confounded by noise and partial volume effects. We propose a new constrained model of dynamic PET to address these limitations. The proposed formulation incorporates an explicit partial volume model in which each image voxel is represented as a mixture of different pure tissue types with distinct temporal dynamics. A two stage algorithm is proposed to solve the resulting problem. In the first stage, a sparse signal processing method is applied to estimate the rate parameters for the different tissue compartments from the noisy PET time series. In the second stage, tissue fractions and the linear parameters of different time activity curves (TACs) are estimated using a combination of sparsity, spatial-regularity, and fractional mixture constraints. A block coordinate descent (BCD) algorithm is combined with a manifold search to robustly estimate these parameters. The method is evaluated with both simulated and experimental dynamic PET data.