Algorithm 1.

CMAA-TTV

Input: y, W, A, ${\mathbf{\text{x}}}^{(0)}=\text{FBP}(\mathbf{\text{y}}),{\mathbf{\text{Ω}}}_n=\mathbf{0},{\mathbf{\text{Z}}}_n=\mathbf{0},{\mathbf{\text{Γ}}}_n=\mathbf{0},r,{\tau }_n\left(\stackrel{\text{Δ}}{=}\beta {\kappa }_n\right),\mu ,\alpha =1.999,M=12.$
Output: the reconstructed PCT image x.
1:	for t = 0 to T − 1 do
2:	Update x by the relaxed OS-LALM:
	1):	initialization $\rho =1,{\widetilde{\mathbf{\text{x}}}}^{(0)}={\mathbf{\text{x}}}^{(t)},{\mathbf{\text{g}}}^{(0)}={\zeta }^{(0)}=M{\mathbf{\text{A}}}_m^T{\mathbf{\text{W}}}_m\left({\mathbf{\text{A}}}_m{\mathbf{\text{x}}}^{(0)}-{\mathbf{\text{y}}}_m\right),{\mathbf{\text{h}}}^{(0)}={\mathbf{\text{Ψ}}}_{\text{A}}^{(0)}{\mathbf{\text{x}}}^{(0)}-{\zeta }^{(0)}.$
	2):	for k = 0 to K − 1 do
	3):	for m = 0 to M − 1 do
	4):	r = kM + m,
	5):	${\mathbf{s}}^{(r+1)}=\rho \left({\mathbf{\text{Ψ}}}_{\text{A}}{\widetilde{\mathbf{\text{x}}}}^{(r)}-{\mathbf{h}}^{(r)}\right)+(1-\rho ){\mathbf{g}}^{(r)},$
	6):	${\tilde{\mathbf{x}}}^{(r+1)}={\left[{\tilde{\mathbf{x}}}^{(r)}-{\left(\rho {\mathbf{\text{Ψ}}}_{\text{A}}+{\mathbf{\text{Ψ}}}_R\right)}^{-1}\left({\mathbf{s}}^{(r+1)}+\nabla R_1\left(x^{(r)}\right)\right)\right]}_{+},$
	7):	${\zeta }^{(r+1)}=M{\mathbf{A}}_m^T{\mathbf{W}}_m\left({\mathbf{A}}_m{\tilde{\mathbf{x}}}^{(r+1)}-{\mathbf{y}}_m\right),$
	8):	${\mathbf{\text{g}}}^{(r+1)}=\frac{\rho }{\rho +1}\left(\alpha {\zeta }^{(r+1)}+(1-\alpha ){\mathbf{\text{g}}}^{(r)}\right)+\frac{1}{\rho +1}{\mathbf{\text{g}}}^{(r)},$
	9):	${\mathbf{h}}^{(r+1)}=\alpha \left({\mathbf{\text{Ψ}}}_{\text{A}}{\tilde{\mathbf{x}}}^{(r+1)}-{\zeta }^{(r+1)}\right)+(1-\alpha ){\mathbf{h}}^{(r)},$
	10):	decrease ρ using (15).
	11):	end for
	12):	end for
	13):	${\mathbf{x}}^{(t+1)}={\tilde{\mathbf{x}}}^{(KM)}.$
3:	Update Ωn by (18).
4:	Update Zn by (21).
5:	Update Γn by (22).
6:	end for