An Accelerated Penalized Maximum Likelihood Algorithm for Positron Emission Tomography

We develop a “fast” algorithm for obtaining regularized estimates of emission means in positron emission tomography (PET). The algorithm, which iteratively minimizes a penalized maximum likelihood (PML) objective function (i.e., negative log likelihood function plus a scaled penalty function), is based on a “pattern search” and a previously developed PML algorithm. As desired, the proposed accelerated PML (APML) algorithm guarantees nonnegative estimates and monotonically decreases the PML objective function with increasing iterations. For the case where the PML objective function is strictly convex, which is true for the class of penalty functions under consideration, we prove that the APML algorithm converges to the unique minimizer of the PML objective function. To demonstrate the utility of the APML algorithm, we applied it to real thorax phantom data and compared it to two existing PML algorithms.