Two-dimensional detectors for cone-beam exposure are now introduced in medical as well as industrial computer tomography. This thesis starts with a review of basic 2D reconstruction algorithms and the first proposal for cone-beam tomography due to Feldkamp et al.

Exact reconstruction is possible only if complete projection data are avail­ able. We make an attempt to compile and present a number of completeness conditions proposed in the literature. The completeness conditions restrict the choice of X-ray source trajectories for exact 3D reconstruction. One such trajectory is a helix. The helix trajectory has the advantage of being very simple to generate in a tomography system. We have investigated the possibility to use the exact reconstruction method of Grangeat with the helical source trajectory.     ·

The Grangeat method consists of two phases. In the first phase the derivative of the Radon space is calculated and in the second phase the object is reconstructed from these data. In between the two phases a Radon space interpolation step is necessary. The use of a helical source trajectory complicates this interpolation, however, in that the mapping equations from output to input coordinates are no longer easily solved. As a remedy to this problem we propose the use of a method we call forward interpolation. Moreover, this method seems to be applicable to arbitrary source trajectories.

Experiments using our helical trajectory forward interpolation reconstruction algorithm show that the image quality is almost the same as for a similar algorithm using a dual circular trajectory and conventional interpolation.

Unfortunately, sometimes the object to be reconstructed is not limited in size. Instead, the complete projections extend beyond the available detector at least in same direction. This is typically the case in medical applications where a patient cannot be covered from head to toe by a reasonably sized detector. In such a case it is no longer possible to generate untruncated projections. We present preliminary results from a method for solving this long object problem using a filtered backprojection technique.