1:	$\epsilon :=\mu ·{\displaystyle \sum _{i=1}^{N_d}}\frac{0.5}{I_0(i)\times exp(-b_i)}$; Nmax: = 1000; L0 = 103, σ0 = 20, stop :=−0.999, $\theta :=\sqrt{{\sigma }_0/L_0}$, sL:= 1.3, Δ:=0.02ε control parameters
2:	h⃗0 : = f⃗0: = FDK or ART initial image
3:	for k=1, Nmax do main loop
4:	$\overrightarrow{d_{TV}}:=\nabla {\Vert \overrightarrow{h}\Vert }_{TV},\overrightarrow{d_{\mathit{data}}}:=M^T\left(M\overrightarrow{h}-\overrightarrow{b}\right)$;
5:	$\overrightarrow{h_{\mathit{ind}}}:=\{\begin{array}{cc}1,& h_i\ne 0\\ 0,& h_i=0\end{array},cos\alpha :=\frac{(\overrightarrow{h_{\mathit{ind}}}•\overrightarrow{d_{TV}})}{\mid \overrightarrow{h_{\mathit{ind}}}•\overrightarrow{d_{TV}}\mid }·\frac{(\overrightarrow{h_{\mathit{ind}}}•\overrightarrow{d_{\mathit{data}}})}{\mid \overrightarrow{h_{\mathit{ind}}}•\overrightarrow{d_{\mathit{data}}}\mid }$; (• denotes element-wise multiplication between two vectors)
6:	f⃗old:= f⃗, $\delta h:=0.5·{\Vert M\overrightarrow{h}-\overrightarrow{b}\Vert }_2^2$
7:	if δh >ε − Δ, λ: = 1/Δ; else λ: = 1/(ε − δh); end if; calculate the regularization weight outside and inside the feasible solution set, respectively.
8:	$\nabla F(\overrightarrow{f}):=\overrightarrow{d_{TV}}+\lambda ·\overrightarrow{d_{\mathit{data}}}$; gradient of the objective as a function of f⃗
9:	f⃗ := (h⃗ − L−1∇F)+ ; update image and set non-negativity
10:	while $F(\overrightarrow{f})>F(\overrightarrow{h})+\nabla F{(\overrightarrow{h})}^T(\overrightarrow{f}-\overrightarrow{h})+0.5L·{\Vert \overrightarrow{f}-\overrightarrow{h}\Vert }_2^2$
11:	L = sL · L;
12:	f⃗:= (h⃗ − L−∇F)+ ;
13:	end; backtracking to find the Lipschitz constant L
14:	$\sigma :=min\left[{\sigma }_{\mathit{old}},\frac{F(\overrightarrow{f_{\mathit{old}}})-F(\overrightarrow{h})-\nabla F{(\overrightarrow{h})}^T(\overrightarrow{f_{\mathit{old}}}-\overrightarrow{h})}{0.5·{\Vert \overrightarrow{f_{\mathit{old}}}-\overrightarrow{h}\Vert }_2^2}\right]$
15:	${\theta }_{\mathit{new}}:=0.5·\left(\frac{\sigma }{L}-{\theta }^2+\sqrt{{\left(\frac{\sigma }{L}-{\theta }^2\right)}^2+4{\theta }^2}\right)$
16:	β: = θ(1 − θ)/(θ2 + θnew)
17:	$\overrightarrow{h}:=\overrightarrow{f}+\beta (\overrightarrow{f}-\overrightarrow{f_{\mathit{old}}})$, θ: = θnew, σold: =σ;
18:	if $cos\alpha <\mathit{stop}\&\&0.5{\Vert M\overrightarrow{f}-\overrightarrow{b}\Vert }_2^2\le \epsilon$ stopping criteria
19:	return f⃗;
20:	break;
21:	end if;
22:	end for;