Parameters: M, maximum expansion order; K, iteration number; ɛ, difference between the projection images of the results in two adjacent iterations; λ, μ₀, d₀, b₀, parameters of ADMM algorithm; γ, η, adaptive updating parameters.

1: Calculate s_m by analytical algorithm, t ← 0, s⁽⁰⁾ ←s_m.

2: Compute ${\mathbf{S}}^{\left(0\right)}\left(\mathit{r}\right)$, ${\mathit{I}}_{\mathbf{rec}}^{\left(0\right)}\leftarrow {\mathit{P}}_{\widehat{\mathit{p}}}\left\{{\mathit{S}}^{\left(0\right)}\right\}$.

3: for k = 1, …, K do

4: t ← t + 1

5: for n_z = 1: N_z do

6: Obtain s^(t) by L-BFGS algorithm.

7: Compute ${\mathit{S}}^{(\mathit{t})}\left(\mathit{z}\right)$, set ${\mathit{S}}^{(\mathit{t})}\left({\mathit{z}}_{\mathbf{j}}\right)=0$ if ${\mathit{S}}^{(\mathit{t})}\left({\mathit{z}}_{\mathit{j}}\right)<0$.

8: ${\mathit{d}}_{\mathit{t}}\leftarrow \mathbf{s}\mathbf{h}\mathbf{r}\mathbf{i}\mathbf{n}\mathbf{k}\left(\mathit{\phi }\left({\mathit{s}}^{\left(\mathit{t}\right)}\right)+{\mathit{b}}_{\mathit{t}-1},\frac{1}{{\mathit{\mu }}_{\mathit{t}-1}}\right)$

9: ${\mathit{b}}_{\mathit{t}}\leftarrow {\mathit{b}}_{\mathit{t}-1}+\mathit{\phi }\left({\mathit{s}}^{\left(\mathit{t}\right)}\right)-{\mathit{d}}_{\mathit{t}}$

10: Update μ_t

11: end for

12: if $\frac{1}{{\mathit{N}}_{\mathit{x}}{\mathit{N}}_{\mathit{y}}}{\mathit{I}}_{\mathbf{rec}}^{\left(\mathit{t}\right)}-{\mathit{I}}_{\mathbf{rec}2}^{\left(\mathit{t}-1\right)2}\le \mathit{\epsilon }$, break;

13: end for

Parameters: σ, standard deviation of Gaussian noise; K_e, epochs;

l_r, learning rate

1 η ∼ U(0, 0.1):

2: for t = 1, …, K_e do

3: ξ ∼N(0, σ) η ←η + ξ,

4: calculate loss L_t

5: update Θ using Adam

6: end for

7: $\mathit{S}\leftarrow {\mathit{f}}_{\mathbf{\Theta }}\left(\mathit{\eta }\right)$