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It is shown here that the fast digital convolution technique used for parallel x-ray beams can be used also to reconstruct a density function for diverging x-ray beams. This technique when combined with what was called previously a generalized Â¿Â¿Â¿-filter yields good accuracy, a flexibility to cope with noise and a substantial reduction in the x-ray dosage. Finite field transforms and zero-order interpolation can be used also to improve the speed of the x-ray reconstruction process. Tests based on these methods are performed on an ideal phantom. A detailed comparison is made between a system using diverging beams, and a system using parallel beams with simulated data.