Fig. 3.

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, ${\mathbf{d}}_1^1-{\mathbf{d}}_2^1-{\mathbf{d}}_3^1$ the 3-D rotated coordinate system for the source a₁(t), $x_{\pi \overline{1,2}}$ the 1-D coordinate system for the inter-helix PI-line $\overline{{\mathbf{a}}_1^s{\mathbf{a}}_2^e}$, 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 $\overline{{\mathbf{a}}_1^s{\mathbf{a}}_2^e}$ on the detector plane, shown as the dashed–dotted line.