A fast 3D reconstruction algorithm for inverse-geometry CT based on an exact PET rebinning algorithm

Inverse-geometry CT (IGCT) employs a large area x-ray source array opposite a small area detector array. The system is expected to provide sub-second volumetric imaging with isotropic resolution and no cone-beam effects. Due to the large amount of data, it is desirable to have an exact 3D reconstruction algorithm that is fast. Currently known IGCT algorithms are either slow, due to 3D backprojection, and/or require a reprojection step, or are inexact. Defrise et al. developed an exact Fourier rebinning algorithm (FORE-J) for 3D PET. This algorithm first rebins the 3D PET data into in-plane sinograms and then reconstructs the series of axial slices using any 2D method. FORE-J is fast, exact, and efficiently uses all of the acquired PET data. We modified this algorithm to adapt it to the IGCT geometry. Experiments were performed using a numerical "Defrise" phantom consisting of high-intensity discs spaced in z to assess the accuracy of the modified algorithm as well as highlight any cone-beam effects. A noise simulation was performed to analyze the noise properties of FORE-J and the modified algorithm. The modified algorithm is very fast and slightly more accurate than the original algorithm with a very small noise penalty in the central axial slices.

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