  We investigated the imaging performance of a fast convergent ordered-subsets
algorithm with subiteration-dependent preconditioners (SDPs) for positron
emission tomography (PET) image reconstruction. In particular, we considered
the use of SDP with the block sequential regularized expectation maximization
(BSREM) approach with the relative difference prior (RDP) regularizer due to
its prior clinical adaptation by vendors. Because the RDP regularization
promotes smoothness in the reconstructed image, the directions of the gradients
in smooth areas more accurately point toward the objective function's minimizer
than those in variable areas. Motivated by this observation, two SDPs have been
designed to increase iteration step-sizes in the smooth areas and reduce
iteration step-sizes in the variable areas relative to a conventional
expectation maximization preconditioner. The momentum technique used for
convergence acceleration can be viewed as a special case of SDP. We have proved
the global convergence of SDP-BSREM algorithms by assuming certain
characteristics of the preconditioner. By means of numerical experiments using
both simulated and clinical PET data, we have shown that the SDP-BSREM
algorithms substantially improve the convergence rate, as compared to
conventional BSREM and a vendor's implementation as Q.Clear. Specifically,
SDP-BSREM algorithms converge 35\%-50\% faster in reaching the same objective
function value than conventional BSREM and commercial Q.Clear algorithms.
Moreover, we showed in phantoms with hot, cold and background regions that the
SDP-BSREM algorithms approached the values of a highly converged reference
image faster than conventional BSREM and commercial Q.Clear algorithms.
