ANALYTICAL INVERSION-FORMULA FOR UNIFORMLY ATTENUATED FAN-BEAM PROJECTIONS

A convolution backprojection algorithm was derived by Tretiak and Metz to reconstruct two-dimensional (2-D) transaxial slices from uniformly attenuated parallel-beam projections. Using transformation of coordin ates, this algorithm can be modified to obtain a formulation useful to reconstruct uniformly attenuated fan-beam projections. Unlike that fo r parallel-beam projections, this formulation does not produce a filte red backprojection reconstruction algorithm but instead has a formulat ion that is an inverse integral operator with a spatially varying kern el, This algorithm thus requires more computation time than does the f iltered backprojection reconstruction algorithm for the uniformly atte nuated parallel-beam case. However, the fan-beam reconstructions demon strate the same image quality as that of parallel-beam reconstructions .