Iterative image reconstruction for positron emission tomography based on a detector response function estimated from point source measurements

The accuracy of the system model in an iterative reconstruction algorithm greatly affects the quality of reconstructed positron emission tomography (PET) images. For efficient computation in reconstruction, the system model in PET can be factored into a product of a geometric projection matrix and sinogram blurring matrix, where the former is often computed based on analytical calculation, and the latter is estimated using Monte Carlo simulations. Direct measurement of a sinogram blurring matrix is difficult in practice because of the requirement of a collimated source. In this work, we propose a method to estimate the 2D blurring kernels from uncollimated point source measurements. Since the resulting sinogram blurring matrix stems from actual measurements, it can take into account the physical effects in the photon detection process that are difficult or impossible to model in a Monte Carlo (MC) simulation, and hence provide a more accurate system model. Another advantage of the proposed method over MC simulation is that it can easily be applied to data that have undergone a transformation to reduce the data size (e.g., Fourier rebinning). Point source measurements were acquired with high count statistics in a relatively fine grid inside the microPET II scanner using a high-precision 2D motion stage. A monotonically convergent iterative algorithm has been derived to estimate the detector blurring matrix from the point source measurements. The algorithm takes advantage of the rotational symmetry of the PET scanner and explicitly models the detector block structure. The resulting sinogram blurring matrix is incorporated into a maximum a posteriori (MAP) image reconstruction algorithm. The proposed method has been validated using a 3 x 3 line phantom, an ultra-micro resolution phantom and a 22Na point source superimposed on a warm background. The results of the proposed method show improvements in both resolution and contrast ratio when compared with the MAP reconstruction with a MC-based sinogram blurring matrix, and one without a detector response model. The reconstruction time is unaffected by the new method since the blurring component takes a relatively small part of the overall reconstruction time. The proposed method can be applied to other PET scanners for human and animal imaging.