Estimation of detector response function for PET from point source measurements: Effect of point source configuration

The accuracy of the system model in an iterative reconstruction algorithm greatly affects the quality of reconstructed positron emission tomography images. For efficient computation in reconstruction, the system model in PET can be factored into a product of geometric projection and detector response function, where the former is often computed based on analytical calculation, and the latter is estimated using Monte Carlo simulations. Direct measurement of detector response function is difficult in practice because of the requirement of a collimated source. We have developed a method to estimate the 2D detector blurring matrix from point source measurements. A monotonically convergent iterative algorithm was derived to estimate the radial and angular components of the detector blurring matrix while taking into account of the detector block structure and rotational symmetry of modern PET scanners. In this work, we investigate the effect of point source configurations on the detector blurring matrix estimation. The objective is to obtain accurate estimate of the detector response function while reducing the amount of data needed during the measurement. We found that the detector blurring matrix estimation can be viewed as a limited-angle tomography problem. Monte Carlo simulation was used to evaluate the accuracy of the estimated blurring matrices. The number and position of discrete point source measurements as well as the sampling distance and acquisition time was varied. The Monte Carlo simulation results show that sampling distance of the point source has a significant impact on the estimation of the detector blurring matrix and the accuracy of the estimated blurring matrix is spatially variant. The results also show that placing point sources outside the reconstructed field of view is beneficial in some cases.