High performance cone-beam spiral backprojection with voxel-specific weighting

Cone-beam spiral backprojection is computationally highly demanding. At first sight, the backprojection requirements are similar to those of cone-beam backprojection from circular scans such as it is performed in the widely used Feldkamp algorithm. However, there is an additional complication: the illumination of each voxel, i.e. the range of angles the voxel is seen by the x-ray cone, is a complex function of the voxel position. In general, one needs to multiply a voxel-specific weight w(x, y, z, α) prior to adding a projection from angle α to a voxel at position x, y, z. Often, the weight function has no analytically closed form and must be numerically determined. Storage of the weights is prohibitive since the amount of memory required equals the number of voxels per spiral rotation times the number of projections a voxel receives contributions and therefore is in the order of up to 1012 floating point values for typical spiral scans. We propose a new algorithm that combines the spiral symmetry with the ability of today’s 64 bit operating systems to store larg