  Iterative image reconstruction (IIR) algorithms in Computed Tomography (CT)
are based on algorithms for solving a particular optimization problem. Design
of the IIR algorithm, therefore, is aided by knowledge of the solution to the
optimization problem on which it is based. Often times, however, it is
impractical to achieve accurate solution to the optimization of interest, which
complicates design of IIR algorithms. This issue is particularly acute for CT
with a limited angular-range scan, which leads to poorly conditioned system
matrices and difficult to solve optimization problems. In this article, we
develop IIR algorithms which solve a certain type of optimization called convex
feasibility. The convex feasibility approach can provide alternatives to
unconstrained optimization approaches and at the same time allow for efficient
algorithms for their solution -- thereby facilitating the IIR algorithm design
process. An accelerated version of the Chambolle-Pock (CP) algorithm is adapted
to various convex feasibility problems of potential interest to IIR in CT. One
of the proposed problems is seen to be equivalent to least-squares
minimization, and two other problems provide alternatives to penalized,
least-squares minimization.
