Filtered sampling for PET

Abstract

In tomography reconstruction, the relationship between the finite-element representation of the objective function and the expected number of hits in detectors - or in other words, the particle transport - is described by the system matrix. With the evolution of high-performance hardware, precise on-the-fly estimation of the system matrix becomes more and more feasible, which allows the use of patient-dependent data and makes it unnecessary to deal with the compression of enormous matrices. On-the-fly system matrix generation requires the online approximation of high dimensional integrals, which is usually attacked by Monte Carlo quadrature and importance sampling. Determining the number of samples used by the estimators belongs to the classical tradeoff problem between accuracy and computational time. However, the approximation error mainly comes from the measurement noise and high frequency components of the measured object that cannot be captured using a given sample density. In this paper, we propose the application of filtered sampling for the forward projection step of iterative ML-EM based PET reconstruction to decrease the variance of the integrand and thus to reduce the error of integral estimation for a given set of samples. The input of the forward projection is filtered using a low-pass filter, which reduces noise and increases the probability that samples do not miss high frequency peaks - e.g. a point source. The iteration thus converges to a modified fixed point, from which the original function can be extracted by applying the same filter. The presented model is built into the TeraTomo™ system.