Resampling density values on R-lines into density values on a Cartesian grid

Three dimensional cone-beam reconstruction methods based on the differentiated backprojection accurately reconstruct objects only along measured lines. Thus, the values on a Cartesian grid need to be interpolated from the known data. The quality of the final reconstruction result depends on the chosen interpolation method. In this work, we discuss three solutions to this interpolation problem, compare them, quantify their resolution property and discuss their computational effort. Two of these solutions are original. Methods are tested on simulated data of the ForBild head and thorax phantoms. Three different source trajectories are investigated: helix, saddle and circle-plus-line. Our results suggest that a carefully chosen interpolation method considerably reduces the computational effort in the reconstruction algorithm while maintaining the image quality.