Adaptive Spatially Variant Optimization of a Temporal Spline Basis for Dynamic PET Reconstruction

In this paper we try to find an optimal temporal basis to reconstruct dynamic list-mode PET data. The goal of this method is to avoid over-fitting of and to avoid the introduction of too much bias in the reconstructed Time Activity Curves (TACs). The optimal basis is estimated from the list-mode data during reconstruction. In particular we have evaluated the Akaike Information Criterion (AIC) as objective function for the determination of the optimal number of temporal B-spline basis functions. The optimal number is spatially variant and is determined for different physiological regions in the image. The required segmentation based on the image sequences clusters the pixels of different physiological regions. We have evaluated different clustering methods. Numerical experiments of simulated cardiac PET data showed that the method based on an initial Non-negative Matrix Factorization (NMF) which includes a Poissonian noise model performed the best. Our results show that the AIC based determination of the optimal number of basis functions was useful for dynamic PET reconstruction, especially for an accurate reconstruction of the blood input curves.