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Box Spline Projection in Non-Parallel Geometry

The pixel- and voxel-basis are common choices for image discretization in the context of computed tomography (CT). They can also be viewed as first-order box splines – a class of functions with closed-form X-ray and Radon transforms that can be computed efficiently. In this paper we derive a method for exact projection of box splines in a non-parallel geometry that can be used in fan-beam and cone-beam tomographic image reconstruction algorithms. We also provide efficient computational procedures for evaluation of the basis function in the projection domain.