A general inversion formula for cone beam CT

We present a new cone beam inversion formula based on a general weighting function n. The formula is theoretically exact and is represented by a 2D integral. If the source trajectory C is complete (and satisfies two other very mild assumptions), then the simplest uniform weight gives a convolution-based FBP algorithm. This choice is not always optimal from the practical point of view. The uniform weight works well for closed trajectories, but the resulting algorithm does not solve the long object problem if C is not closed. In the latter case one has to use the flexibility in choosing n and find the weight that gives an inversion formula with the desired properties. In particular, this can be done for spiral CT. It turns out that the inversion algorithms for spiral CT proposed earlier by the author are particular cases of the new formula. As a further application of the new formula we present a 3PI algorithm for spiral CT, which is theoretically exact and of the FBP type with shift-invariant filtering.