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Because of the potential for more rapid data collection, newer scanners for reconstructive tomography are implemented in a "fan-beam" geometry. In these implementations there is a source that emits a fan-shaped pattern of radiation. A detector located on the opposite side of the scanned object provides data that depend on the attenuation density of the object integrated along a ray in the fan joining the source and detector. Increased speed is realized by the use of not just a single detector but, rather, a circular array of detectors that collect data simultaneously along several rays in the fan. Original procedures for constructing tomographic sections from fan-beam data rely on the use of existing algorithms for parallel-beam data, which can be used by rearranging the fan-beam data into a parallel-beam format. (1,2) However, in this format the data suffer from a nonuniformity in sampling due to the nonlinear relationship between the fan-beam and parallel-beam coordinate systems. Partly for this reason, as well as for the conservation of data storage and potential speed benefits, algorithms that make direct use of fan-beam data have been derived by a number of investigators. (3,4,5) Published fan-beam algorithms assume that the output of all detectors in the fan are sampled simultaneously at discrete source angles as the source rotates about the object. The samples so derived at each source angle are processed together in a filtering operation which is followed by an "inverse square-law" back projection to yield the tomographic section after all source angles have been completed. We have investigated the implications of processing each detector output independently as the source rotates and then combining these processed detector outputs at the completion of all data collection to form the section. For a geometry in which the detector array rotates with the source, we have found that this can be accomplished without the back projection operation by using the emerging technology of adaptive transversal filters.
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