A Convolutional Forward and Back-Projection Model for Fan-Beam Geometry

Iterative methods for tomographic image reconstruction have great potential for enabling high quality imaging from low-dose projection data. The computational burden of iterative reconstruction algorithms, however, has been an impediment in their adoption in practical CT reconstruction problems. We present an approach for highly efficient and accurate computation of forward model for image reconstruction in fan-beam geometry in X-ray CT. The efficiency of computations makes this approach 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.