Comparison of interpolation functions to improve a rebinning-free CT-reconstruction algorithm.

The robust algorithm OPED for the reconstruction of images from Radon data has been recently developed. This reconstructs an image from parallel data within a special scanning geometry that does not need rebinning but only a simple re-ordering, so that the acquired fan data can be used directly for the reconstruction. However, if the number of rays per fan view is increased, there appear empty cells in the sinogram. These cells need to be filled by interpolation before the reconstruction can be carried out. The present paper analyzes linear interpolation, cubic splines and parametric (or "damped") splines for the interpolation task. The reconstruction accuracy in the resulting images was measured by the Normalized Mean Square Error (NMSE), the Hilbert Angle, and the Mean Relative Error. The spatial resolution was measured by the Modulation Transfer Function (MTF). Cubic splines were confirmed to be the most recommendable method. The reconstructed images resulting from cubic spline interpolation show a significantly lower NMSE than the ones from linear interpolation and have the largest MTF for all frequencies. Parametric splines proved to be advantageous only for small sinograms (below 50 fan views).