Microlocal analysis of an FBP algorithm for truncated spiral cone beam data

In this article we propose an FBP-type algorithm for inversion of spiral cone beam data, study its theoretical properties, and illustrate performance of the algorithm by numerical examples. In particular it is shown that the algorithm does not reconstruct f exactly, but computes the result of applying a pseudo-differential operator (PDO) with singular symbol to f. Away from critical directions the amplitude of this PDO is homogeneous of order zero in the dual variable, bounded, and approaches one as the pitch of the spiral goes to zero. Numerical experiments presented in the article show that even when the pitch is relatively large, the accuracy of reconstruction is quite high. On the other hand, under certain circumstances, the algorithm produces artifacts typical of all FBP-type algorithms.