Learned Primal Dual Reconstruction for PET

. 2021 Nov 24;7(12):248. doi: 10.3390/jimaging7120248

Algorithm 1 Learned Primal-Dual reconstruction.

1:
Given: g, $N_{LPD}$
2:
Set: $R (\cdot) = \frac{A^{*} (\cdot)}{{| | A | |}^{2}}$
3:
$h^{(0)} = Ξ_{ϕ}^{0} (g)$
4:
$f_{g}^{(0)} = R (h^{(0)})$
5:
$f^{(0)} = Λ_{θ}^{0} (f_{g}^{(0)})$
6:
for $i = 1$ , ⋯, $N_{LPD} - 1$ do
7:
$h_{f}^{(i - 1)} = A (f^{(i - 1)})$
8:
$h^{(i)} = h^{(i - 1)} + Ξ_{ϕ}^{i} (g, h^{(0)}, \dots, h^{(i - 1)}, h_{f}^{(i - 1)})$
9:
$f_{g}^{(i)} = R (h^{(i)})$
10:
$f^{(i)} = f^{(i - 1)} + Λ_{θ}^{i} (f^{(0)}, \dots, f^{(i - 1)}, f_{g}^{(i)})$
11:
end for
12:
return $f^{(i)}$