Table 1. Main steps of AFTV-SIR.

Algorithm of AFTV-SIR
Preparation:
Obtain ${\mu }_{\text{TV}}$ by performing Chambolle-Pock algorithm [40] on the noisy reconstruction ${\mu }_{\text{FBP}}$;
Compute the residual image $v_{\text{TV}}=\mu -{\mu }_{\text{TV}}$;
Compute the global variance ${\hat{\sigma }}^2$ and local variance $P_{v_{\text{TV}}}$;
Compute $\alpha$ with Eq. (17);
Initialization:
Given, $\lambda$, $\epsilon$, $N_{ite}$, $\tau$,
Set ${\mu }^0=0$, $t=0$
Main Loop:
while $t<N_{ite}$ and $d>\tau$
Update ${\mu }^t$ with ${\mu }^{t-1}$ using Eq. (8);
$d={\Vert {\mu }^t-{\mu }^{t-1}\Vert }_2^2/J;$
$t=t+1;$
end