Filtered Backprojection for Divergent Beams

An alternative to the parallel mode of data collection is when data are collected so that they naturally divide into subsets containing estimated ray sums for lines diverging from a single point. Our standard projection data are of this type. There are two basic approaches to designing an FBP-type algorithm for such data. The first is to find an FBP-type implementation of the Radon inversion formula that is appropriate for the divergent mode of data collection. The second is to use interpolation in the (l,θ) space to estimate ray sums for sets of parallel lines from the measured ray sums for sets of divergent lines (this process is called rebinning) and then apply the parallel beam FBP method. In this chapter we concentrate on the first of these methods. We also return to the topic of window selection in the context of the divergent beam FBP method.