Three-dimensional Fourier-based reprojection analytic reconstruction from histoprojections for high-resolution time-of-flight positron emission tomography scanners

Purpose: In spite of the general acceptance of iterative reconstruction for clinical use, analytic algorithms provide an important alternative tool due to their linearity, unbiased performance, and predictability for quantitative imaging and quality control studies. On modern time-of-flight (TOF) positron emission tomography scanners with excellent timing resolution, substantial angular compression of (histoprojection) data is possible without loss of resolution, but this also brings challenges for analytical algorithms. We propose TOF and non-TOF Fourier-based analytic approaches that appropriately handle the data sparsity on modern TOF systems. Approach: The proposed TOF algorithm (3D-DIFTOF—direct inversion Fourier transform for TOF) works directly on histoprojection data. The proposed Fourier-based approaches for histoprojection data are further extended to include non-TOF reconstruction (TOF-binned 3D-DIFT), which is particularly useful in time calibration procedures due to its insensitivity to time calibration errors. TOF information is used here to extend available histoprojection data to a larger number of views, essential for artifact-free non-TOF reconstruction. The proposed algorithms are compared with standard analytic techniques on Siemens scanners—space-based confidence-weighted TOF FBP and non-TOF DIFT. Results: 3D-DIFTOF reconstruction demonstrates both improved NEMA-based resolution and contrast versus background variability trade-offs. Similarly, the TOF-binned 3D-DIFT approach shows improved contrast-noise trade-offs over the standard non-TOF approach and is well suited for timing calibration. Conclusions: Our results demonstrate that the proposed 3D-DIFTOF technique provides an improved and more faithful characterization of image resolution compared with standard space-based analytic reconstructions. The proposed tools also provide accurate translation of sparse TOF data available on clinical scanners to upsampled data for non-TOF algorithms.