Abstract
We here present 
which is an exact method for 3D reconstruction from cone-beam projection data. The new method is compared to the LINCON method which is known to be fast and to give good image quality. Both methods have 
complexity and are based on Grangeat's result which states that the derivative of the Radon transform of the object function can be obtained from cone-beam projections.
One disadvantage with LINCON is that the rather computationally intensive chirp z-transform is frequently used. In , FFT and interpolation in the Fourier domain are used instead, which are less computationally demanding. The computation tools involved in are solely FFT, 1D eight-point interpolation, multiplicative weighting and tri-linear interpolation. We estimate that will be 2-2.5 times faster than LINCON.
The interpolation filter belongs to a special class of filters developed by us. It turns out that the filter must be very carefully designed to keep a good image quality. Visual inspection of experimental results shows that the image quality is almost the same for LINCON and the new method . However, it should be remembered that can never give better image quality than LINCON, since is designed to approximate LINCON as well as possible.