3D Fourier-Based Re-Projection Analytic Reconstruction from Histo-Projections for High Resolution TOF Scanners

The new SiPM-based Siemens scanner (Vision) achieves time resolution below 250 ps. Due to the redundancy of TOF information, TOF data can be substantially angularly compressed without loss of resolution. This allows TOF data to be partitioned into histo-projections with a significantly reduced number of transverse and oblique views for TOF reconstruction. Nevertheless, backward extension to a larger number of azimuthal views is required for the FORE+FBP analytic algorithm, which is used on the Siemens scanners. The 3D Fourier-based re-projection TOF reconstruction algorithm, based on the central slice theorem, is capable of reconstructing images from angularly sparse TOF data. The basic theory behind this TOF analytic algorithm was developed over the past decade; nevertheless, it has not been applied in the histo-projection data format due to the required interpolation operations. This work is dedicated to the implementation of the histo-projection based 3D-DIFTOF (Direct Inversion Fourier Transform) TOF algorithm. Presented results using experimental data demonstrate that the Fourier-domain interpolations within 3D-DIFTOF implementation preserve the spatial resolution of the data, as compared to the image-domain interpolations within the TOF FORE+FBP algorithm, which do affect the reconstructed spatial resolution. Consequently, the 3D-DIFTOF algorithm is a good candidate for the analytical reconstruction of TOF compressed data from modern scanners with high spatial and TOF resolution.