Zusammenfassung
Recently, an exact reconstruction method for helical CT was published
by A. Katsevich. The algorithm is of the filtered backprojection
type and is, therefore, computationally efficient. Moreover, during
backprojection, only data are used which correspond to an illumination
interval of 180 degrees as seen from the object-point. We propose
a new reconstruction method, which is applicable to data obtained
with a 3-Pi acquisition IEEE Trans. Med. Imaging 19, 848-863 (2000).
The method uses the same filter types as the Katsevich algorithm,
but the directions and the number of the filter lines are chosen
differently. For the derivation of the new algorithm, we analyze
the relationship of the Katsevich method and radon inversion. A certain
radon plane can intersect with the backprojection interval related
to a 3-Pi acquisition either once, three, or five times. In analogy
to the definition of quasiexactness introduced by Kudo et al. for
a 1-Pi acquisition, we use the term quasiexactness for algorithms
on a 3-Pi acquisition, if radon planes with one or three intersections
within the backprojection interval are treated correctly. Using the
results on the relationship with radon inversion, we can prove that
our algorithm is quasiexact in this sense. We use simulation results
in order to demonstrate that the algorithm yields excellent image
quality.
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