TABLE 1.

FADDM

Fast ADMM-W(y,E,D,λ,ρ,W)
1.	set f0 = 0
2.	set ${\overline{f}}_1=f_0$
3.	set s0 = 0
4.	set ${\overline{s}}_1=s_0$
5.	set k = 1
6.	while k ≤ K
7.	compute $c_k={\left(D^H{E}^{H}ED+\rho W^{H}W\right)}^{-1}\left(D^H{E}^{H}y+W^H\left(\rho {\overline{s}}_k+{\overline{f}}_k\right)\right)$
8.	compute $s_k={\text{MST}}_{\lambda /\rho }^{{ℝ}_{+}}\left(W{c}_k-1/\rho {\overline{f}}_k\right)$
9.	compute $f_k={\overline{f}}_k+\rho \left(s_k-W{c}_k\right)$
10.	compute $d_k=1/\rho {\Vert f_k-{\overline{f}}_k\Vert }_2^2+\rho {\Vert s_k-{\overline{s}}_k\Vert }_2^2$
11.	if k > 1 and if dk < dk−1
12.	compute ${\alpha }_{k+1}=(1+\sqrt{1+4{\alpha }_k^2})/2$
13.	compute ${\overline{s}}_{k+1}=s_k+\frac{\left({\alpha }_k\right)-1}{{\alpha }_{k+1}}\left(s_k-s_{k-1}\right)$
14.	compute ${\overline{f}}_{k+1}=f_k+\frac{\left({\alpha }_k\right)-1}{{\alpha }_{k+1}}\left(f_k-f_{k-1}\right)$
15.	else
16.	set ak+1 = 1
17.	set ${\overline{f}}_{k+1}=f_{k-1}$
18.	set ${\overline{s}}_{k+1}=s_{k-1}$
19.	set dk = dk−1
20.	end if-else
22.	set k = k + 1
22.	end while
23.	return ck and xk = Dck
24.	end procedure