Detector plane and coordinate system for the triple-source FBP CBCT based on an inter-helix PI-line. x – y – z is the 3-D fixed-coordinate system,
the 3-D rotated coordinate system for the source a1(t),
the 1-D coordinate system for the inter-helix PI-line
, and u1 – v1 the 2-D coordinate system on the corresponding detector plane of a1(t). The actual direction of the Hilbert filtering is along the cone-beam projection of
on the detector plane, shown as the dashed–dotted line.