  Properties of Superiorized Preconditioned Conjugate Gradient (SupPCG)
algorithms in image reconstruction from projections are examined. Least squares
(LS) is usually chosen for measuring data-inconsistency in these inverse
problems. Preconditioned Conjugate Gradient algorithms are fast methods for
finding an LS solution. However, for ill-posed problems, such as image
reconstruction, an LS solution may not provide good image quality. This can be
taken care of by superiorization. A superiorized algorithm leads to images with
the value of a secondary criterion (a merit function such as the total
variation) improved as compared to images with similar data-inconsistency
obtained by the algorithm without superiorization. Numerical experimentation
shows that SupPCG can lead to high-quality reconstructions within a remarkably
short time. A theoretical analysis is also provided.
