Cone-Beam Image Reconstruction by Moving Frames

In this paper, we present a new algorithmic paradigm for cone-beam image reconstruction. The new class of algorithms, referred to as cone-beam reconstruction by moving frames, enables numerical implementation of exact cone-beam inversion using its intrinsic geometry. In particular, our algorithm allows a 3-D discrete approach to the differentiation-backprojection operator on the curved manifolds appearing in all analytical cone-beam inverse formulations. The enabling technique, called the method of moving frames, has been popular in the computer vision community for many years [3]. Although cone-beam image reconstruction has come from a different origin and has been until now developed along very different lines from computer vision algorithms, we can find analogies in their line-and-plane geometry. We demonstrate how the moving frame technique can be made into a ubiquitous and powerful computational tool for designing and implementing more robust and more accurate cone-beam reconstruction algorithms.