Advancements to the planogram frequency-distance rebinning algorithm.

In this paper we consider the task of image reconstruction in positron emission tomography (PET) with the planogram frequency-distance rebinning (PFDR) algorithm. The PFDR algorithm is a rebinning algorithm for PET systems with panel detectors. The algorithm is derived in the planogram coordinate system which is a native data format for PET systems with panel detectors. A rebinning algorithm averages over the redundant four-dimensional set of PET data to produce a three-dimensional set of data. Images can be reconstructed from this rebinned three-dimensional set of data. This process enables one to reconstruct PET images more quickly than reconstructing directly from the four-dimensional PET data. The PFDR algorithm is an approximate rebinning algorithm. We show that implementing the PFDR algorithm followed by the (ramp) filtered backprojection (FBP) algorithm in linogram coordinates from multiple views reconstructs a filtered version of our image. We develop an explicit formula for this filter which can be used to achieve exact reconstruction by means of a modified FBP algorithm applied to the stack of rebinned linograms and can also be used to quantify the errors introduced by the PFDR algorithm. This filter is similar to the filter in the planogram filtered backprojection algorithm derived by Brasse et al. The planogram filtered backprojection and exact reconstruction with the PFDR algorithm require complete projections which can be completed with a reprojection algorithm. The PFDR algorithm is similar to the rebinning algorithm developed by Kao et al. By expressing the PFDR algorithm in detector coordinates, we provide a comparative analysis between the two algorithms. Numerical experiments using both simulated data and measured data from a positron emission mammography/tomography (PEM/PET) system are performed. Images are reconstructed by PFDR+FBP (PFDR followed by 2D FBP reconstruction), PFDRX (PFDR followed by the modified FBP algorithm for exact reconstruction) and planogram filtered backprojection image reconstruction algorithms. We show that the PFDRX algorithm produces images that are nearly as accurate as images reconstructed with the planogram filtered backprojection algorithm and more accurate than images reconstructed with the PFDR+FBP algorithm. Both the PFDR+FBP and PFDRX algorithms provide a dramatic improvement in computation time over the planogram filtered backprojection algorithm.