Abstract
Recently, 3D image fusion reconstruction using a FDK algorithm along three-orthogonal circular isocentric orbits has been proposed. On the other hand, we know that 3D image reconstruction based on three-orthogonal circular isocentric orbits is sufficient in the sense of Tuy data sufficiency condition. Therefore the datum obtained from three-orthogonal circular isocentric orbits can derive an exact reconstruction algorithm. In this paper, an exact weighted-FBP algorithm with three-orthogonal circular isocentric orbits is derived by means of Katsevich's equations of filtering lines based on a circle trajectory and a modified weighted form of Tuy's reconstruction scheme.
Highlights
The cone-beam scanning configuration with a circular trajectory remains one of the most popular scanning configuration and has been widely employed for data acquisition in 3-D X-ray computed tomography (CT), because it allows for operating at a high rotating speed due to its symmetry, avoiding the need to axially translate the patient, such as in helical or step-and-shoot CT [1, 2]
We know that 3D image reconstruction based on three-orthogonal circular isocentric orbits is sufficient in the sense of Tuy data sufficiency condition
The features of our inversion formula can be summarized as follow: using some properties of the cone-beam transform to derive the inversion formula, a proper choice of the weighting function, deriving equations of the filtering lines and describing geometric properties of filtering lines in the planar detector plane
Summary
The cone-beam scanning configuration with a circular trajectory remains one of the most popular scanning configuration and has been widely employed for data acquisition in 3-D X-ray computed tomography (CT), because it allows for operating at a high rotating speed due to its symmetry, avoiding the need to axially translate the patient, such as in helical or step-and-shoot CT [1, 2]. The features of our inversion formula can be summarized as follow: using some properties of the cone-beam transform to derive the inversion formula, a proper choice of the weighting function, deriving equations of the filtering lines and describing geometric properties of filtering lines in the planar detector plane. Provided that nx (s, σ) fulfilled the completeness condition: nx (s, σ) = 1, a.e.inσ ∈ S2 This inversion formula tells us Tuy’s data sufficiency conditions for an accurate reconstruction of a ROI from cone-beam projections. These conditions are: σ · y(s) = σ · x and σ · y 0 (s) 6= 0. The equation of the filtering line on the planar-detector is given by: u(cos λ − sin s) sin λ cos s sin λ (28)
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