A new reprojection method based on a comparison of popular reprojection models

Reprojection is of interest in several applications such as iterative tomographic reconstruction, dose-calculation in radiotherapy and 3D-display volume-rendering. All numerical implementations of reprojection result in varying degrees of errors. Popular reprojection methods were compared using 128×128 2D-noiseless-numerical uniform-disk and Shepp–Logan phantoms to evaluate errors in external-border, interior and overall regions of the reprojected sinogram, in order to investigate a new method for increasing their accuracy on all regions. Root mean squared errors (RMSE) (with calculated projection as reference) were used. No method gives the least errors in all regions. Smoothing projectors decrease noise but introduce important errors in the border region, whereas other projectors increase errors inside the reprojected sinogram. The overall-error is a trade-off between interior and border errors. The conventional ray-driven (R1) and the bilinear-interpolated pixel driven with 5×5 sub-pixels (L5) provide the highest accuracy for border and interior regions, respectively. These results motivate the implementation of a new reprojection method that uses R1 to project pixels near borders in the sinogram and L5 for the others. Feature borders were localized using the spatial derivatives of sinogram count profile. This method provides the least errors for all regions. The performance of the new method was investigated on iterative reconstruction tasks with MLEM. Results show that the new method can promise more accuracy in terms of RMSE and aliasing reduction of the reconstructed images.