The FDK algorithm with an expanded definition domain for cone-beam reconstruction preserving oblique line integrals

The FDK algorithm is a widely used filtered-backprojection (FBP) algorithm for 3D image reconstruction from circular cone-beam projections. In this paper, we redefine the x-ray transform and expand the definition domain of FDK reconstruction to all points in 3D space. We prove that the FDK reconstruction, in this expanded definition domain, preserves the value of integrals along oblique lines in an angular range larger than the original FDK reconstruction proven by Rodet et al. Based on this result, an efficient FBP-type method is proposed to synthesize radiographs from cone-beam projections. Finally, numerical experiments are done to validate this stereogram synthesis algorithm.

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