Affiliations: Department of Biomedical Engineering, Shanghai Jiao
Tong University, Shanghai, 200030, China | LMAM, School of Mathematical Sciences, Peking
University, Beijing 100871, China | Department of Radiology, University of Iowa, Iowa
City, IA 52242, USA
Abstract: In this paper, we propose a helical cone-beam scanning configuration
of triple symmetrically located X-ray sources, and study minimum detection
windows to extend the traditional Tam-Danielsson window for exact image
reconstruction. For three longitudinally displaced scanning helices of the same
radius and a source location on any helix, the corresponding minimum detection
window is bounded by the most adjacent turns respectively selected from the
other two helices. The height of our proposed minimum detector window is only
1/3 of that in the single helix case. Associated with proposed minimum
detection windows, we define the inter-helix PI-line and establish its
existence and uniqueness property: through any point inside the triple helices,
there exists one and only one inter-helix PI-line for any pair of the helices.
Furthermore, we prove that cone-beam projection data from such a triple-source
helical scan are sufficient for exact image reconstruction. Although there are
certain redundancies among those projection data, the redundant part cannot be
removed by shrinking the detector window without violating the data sufficiency
condition. Those results are important components for development of exact or
quasi-exact image reconstruction algorithms in the case of triple-source
helical cone-beam scanning in the future.
