Fourier-based forward and back-projectors in iterative fan-beam tomographic image reconstruction

Fourier-based forward and back-projection methods have the potential to reduce computation demands in iterative tomographic image reconstruction. Interpolation errors are a limitation of conventional Fourier-based projectors. Recently, the min-max optimized Kaiser-Bessel interpolation within the nonuniform fast Fourier transform (NUFFT) approach has been applied in parallel-beam image reconstruction, whose results show lower approximation errors than conventional interpolation methods. However, the extension of min-max NUFFT approach to fan-beam data has not been investigated. We have extended the min-max NUFFT framework to the fan-beam tomography case, using the relationship between the fan-beam projections and corresponding projections in parallel-beam geometry. Our studies show that the fan-beam Fourier-based forward and back-projection methods can significantly reduce the computation time while still providing comparable accuracy as their space-based counterparts.