Application of spherical harmonics to cone beam image reconstruction

Cone beam geometry has become popular in both SPECT and transmission computed tomography especially in imaging of relatively small organs. A direct image reconstruction technique developed by Grangeat (1991) is based on the relationship between cone-beam projections and the first derivative of the Radon transform. This paper describes this relationship using an expansion in spherical harmonics and develops a new method for calculating the first derivative of the Radon transform from the cone-beam projections. The algorithm works as follows: First, expansion in spherical harmonics is obtained for cone-beam projections. Then, a simple transformation is applied to the corresponding expansion coefficients. Finally, the values of the first derivative of the Radon transform are calculated by evaluating the expansion with the transformed coefficients. Computer simulations verified that this approach combined with Radon inversion formula allows to achieve high quality image reconstruction