]>A Reconstruction Approach for Imaging in 3D Cone Beam Vector Field Tomography : Algorithm 1
Given   : Measured data 𝐃 1 𝐟 ( 𝛼 , 𝜔 ) for 𝛼 ∈ Γ , 𝜔 ∈ 𝑆 2
Output    : Approximation 𝐟 𝛾 to 𝐟
Compute:
    (1) 𝐠 ( 𝛼 , 𝜔 ) = 𝐃 1 𝐟 ( 𝛼 , 𝜔 ) 𝜔
    (2) ( 𝐟 𝛾 ) 𝑗 ( 𝑥 ) = 𝐠 , 𝐕 𝑗 𝛾 ( 𝑥 ) 𝐿 2 ( Γ × 𝑆 2 , ℝ 3 )
            = ∫ Γ ∫ 𝑆 2 𝐠 ( 𝛼 , 𝜔 ) , 𝐕 𝑗 𝛾 ( 𝑥 ; 𝛼 , 𝜔 ) d 𝑆 ( 𝜔 ) d 𝛼
    = ∫ Γ ∫ 𝑆 2 𝐃 1 𝐟 ( 𝛼 , 𝜔 ) 𝜔 𝑗 𝑣 𝛾 ( 𝑥 ; 𝛼 , 𝜔 ) d 𝑆 ( 𝜔 ) d 𝛼
                      for 𝑗 ∈ { 1 , 2 , 3 }
Algorithm 1: For cone beam VFT.