A Modified Reconstruction Filter for Diverging X-Ray Beams

The 3-D reconstruction of a density function for diverging X-ray beams, based on the direct convolution algorithm, was developed by Lakshminarayanan. In this method, the reconstruction of a section of an object was obtained as the average, over all source positions, of the backprojected data convolved with an appropriate filter function. In this note, a modification of Lakshminarayanan's filter is proposed. The modified filter has less undesirable high-frequency components, yet it retains the convolution property. It is shown that the new filter has less oscillatory response across the edge of highly absorbent structures (e. g., bones). Finally, it is shown how the modified fan-beam filter can be FFT implemented.