Algorithm 3:

Block total-variation superiorization with DROP (TVS2-DROP)

1. set k=0
2. set xk=xFBP the initial FBP reconstruction, and βk=1
3. repeat for each block over 10 cycles
4.  set s to a subgradient of ϕ at xk
5.  if ∥s∥>0 set vk=−s∕∥s∥
6.  else set vk=s
7.  set continue=true
8.  while continue
9.   set yk=xk+βkvk
10.   calculate the merit function (total variation) withEq. 7, and if ϕ(yk)≤ϕ(xk)
11.    apply the projection operator Pt(k) to y (Eq.5)
12.    calculate the feasibility proximity with Eq. 6using histories from the current block, and if Pr(Pt(k)y)<Pr(xk)
13.     set xk+1=PMy
14.     set continue=false
15.    else set βk=βk∕2
16.   else set βk=βk∕2
17.  set k=k+1