1:	β(1) ← 1; βred ← 0.99; α(1) ← 0.05; αred ← 0.9;
2:	tol ← 0.11; NTV ← 20; rmax ← 0.9;
3:	λ(1) ← 1; γ ← 4;
4:	MaxIteration ← 1000; Δfmin ← 2 × 10−4;
5:	f⃗(0) ← f⃗FDK	⊲ Use FDK image as the initial image
6:	for k ← 1, MaxIteration do	⊲ main loop
7:	for j ← 1,N do	⊲ POCS step via SART with positivity constraint.
8:	$f_{\mathrm{P}\mathrm{O}\mathrm{C}\mathrm{S}{,}_j}^{(k)}\leftarrow \text{max}\{f_j^{(k-1)}+\frac{{\beta }^{(k)}}{{\sum }_{i=1}^M{R}_{i,j}}\sum _{i=1}^M\frac{R_{i,j}}{{\sum }_{j=1}^N{R}_{i,j}}[p_i-{\left(\mathbf{R}{\overrightarrow{f}}^{(k-1)}\right)}_i],0\}$
9:	end for
10:	$\overrightarrow{\mathrm{\Delta }}{f}_{\mathrm{P}\mathrm{O}\mathrm{C}\mathrm{S}}^{(k)}\leftarrow {\overrightarrow{f}}_{\mathrm{P}\mathrm{O}\mathrm{C}\mathrm{S}}^{(k)}-{\overrightarrow{f}}^{(k-1)}$
11:	${\overrightarrow{f}}^{(k)}\leftarrow {\overrightarrow{f}}_{\mathrm{P}\mathrm{O}\mathrm{C}\mathrm{S}}^{(k)}$
12:	res(k) ← ‖p̃ − Rf⃗(k)‖
13:	if k = 1 then
14:	${\alpha }^{(1)}\leftarrow {\alpha }^{(1)}\times \Vert \overrightarrow{\mathrm{\Delta }}{f}_{\mathrm{P}\mathrm{O}\mathrm{C}\mathrm{S}}^{(1)}\Vert$	⊲ Initialize TV step size
15:	end if
16:	${\overrightarrow{f}}_{\text{Seg}}^{(k)}$ ← AnatomySegmentation (f⃗(k))
17:	for kTV ← 1,NTV do
18:	${\overrightarrow{df}}_{\mathrm{A}\mathrm{A}\mathrm{T}\mathrm{V}}\leftarrow \frac{-{\nabla }_{{\overrightarrow{f}}^{(k)}}\mathrm{T}\mathrm{V}\left({\overrightarrow{f}}^{(k)}\right)+{\mathrm{\lambda }}^{(k)}{\nabla }_{{\overrightarrow{f}}_{\text{Seg}}^{(k)}}\mathrm{T}\mathrm{V}\left({\overrightarrow{f}}_{\text{Seg}}^{(k)}\right)}{\Vert {\nabla }_{{\overrightarrow{f}}^{(k)}}\mathrm{T}\mathrm{V}\left({\overrightarrow{f}}^{(k)}\right)\Vert }$
19:	f⃗(k) ← f⃗(k) + α(k)d⃗fAATV
20:	end for
21:	$\overrightarrow{\mathrm{\Delta }}{f}_{\mathrm{A}\mathrm{A}\mathrm{T}\mathrm{V}}^{(k)}\leftarrow {\overrightarrow{f}}^{(k)}-{\overrightarrow{f}}_{\mathrm{P}\mathrm{O}\mathrm{C}\mathrm{S}}^{(k)}$
22:	if $\Vert {\overrightarrow{f}}^{(k)}-{\overrightarrow{f}}^{(k-1)}\Vert /\sqrt{N}<\mathrm{\Delta }{f}_{\text{min}}$ then	⊲ Stopping criterion
23:	break;
24:	else
25:	β(k+1) ← β(k) × βred	⊲ Calculate new step sizes
26:	if $\Vert \overrightarrow{\mathrm{\Delta }}{f}_{\mathrm{A}\mathrm{A}\mathrm{T}\mathrm{V}}^{(k)}\Vert >r_{\text{max}}\Vert \overrightarrow{\mathrm{\Delta }}{f}_{\mathrm{P}\mathrm{O}\mathrm{C}\mathrm{S}}^{(k)}\Vert$ and res(k) > tol then
27:	α(k+1) ← α(k) × αred
28:	end if
29:	${\mathrm{\lambda }}^{(k+1)}={\left[\frac{{\alpha }^{(k+1)}}{{\alpha }^{(1)}}\right]}^{1/\gamma }$
30:	end if
31:	end for
32:	return ${\overrightarrow{f}}_{\mathrm{P}\mathrm{O}\mathrm{C}\mathrm{S}}^{(k)}$