Katsevich-type algorithms for variable radius spiral cone-beam CT

To solve the long object problem, an exact and efficient algorithm has been recently developed by Katsevich. While the Katsevich algorithm only works with standard helical cone-beam scanning, there is an important need for nonstandard spiral cone-beam scanning. Specifically, we need a scanning spiral of variable radius for our newly proposed electron-beam CT/micro-CT prototype. In this paper, for variable radius spiral cone-beam CT we construct two Katsevich-type cone-beam reconstruction algorithms in the filtered backprojection (FBP) and backprojected filtration (BPF) formats, respectively. The FBP algorithm is developed based on the standard Katsevich algorithm, and consists of four steps: data differentiation, PI-tine determination, slant filtration and weighted backprojection. The BPF algorithm is designed based on the scheme by Zou and Pan, and also consists four steps: data differentiation, PI-fine determination, weighted backprojection and inverse Hilbert transform. Numerical experiments are conducted with mathematical phantoms