Algorithm 3.

(Semi-Dynamic PAPA for MAP ECT Reconstruction)

Preparation: ∇fH, ∇bH, τ are defined in (13), (14) and (15), respectively. The parameters r and l are positive integers.

Initialization: f(0) = 1, b(0) = 0.

Run Algorithm 2 until k > l.

Set $S^{(l)}\leftarrow \text{diag }\left(\frac{f^{(l)}}{A^{\top }1}\right)$.

repeat

Step 1: $h^{(k)}\leftarrow P_{{ℝ}_{+}^d}(f^{(k)}-\tau S^{(l)}{\nabla }_{f}H(f^{(k)},b^{(k)}))$

Step 2: $b^{(k+1)}\leftarrow Q_{h^{(k)}}^r(b^{(k)})$

Step 3: $f^{(k+1)}\leftarrow P_{{ℝ}_{+}^d}(f^{(k)}-\tau S^{(l)}{\nabla }_{f}H(f^{(k)},b^{(k+1)}))$

until “convergence”