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We present a convolutional spline framework for highly efficient and accurate computation of forward model for image reconstruction in fan-beam geometry in X-ray computed tomography. The efficiency of computations makes this framework suitable for large-scale optimization algorithms with on-the-fly, memory-less, computations of the forward and back-projection. Our experiments demonstrate the improvements in accuracy as well as efficiency of our model, specifically for first-order box splines (i.e., pixel-basis) compared to recently developed methods for this purpose, namely Look-up Table-based Ray Integration (LTRI) and Separable Footprints (SF) in 2-D.

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.