Parallelization of the simulated annealing algorithm.

Abstract

Nuclear medicine imaging involves the introduction of a radiopharmaceutical into the body and the subsequent detection of the radiation emanating from the organ at which the procedure was directed. The data set resulting from such a procedure is generally very underdetermined, due to the dimensions of the imaging apparatus, and underconstrained due to the noise in the imaging process. A means by which more information can be obtained is through a form of imaging utilizing code-apertures. Although increasing the amount of information collected, coded-aperture imaging results in a multiplexing of the data. Demultiplexing the data requires a reconstruction process not required in conventional nuclear medicine imaging. The reconstruction process requires the optimization of an estimate to the object to be reconstructed. This optimization is done through the minimization of an energy functional. The minimization of such energy functionals requires the optimization of several parameters. Solution of this type problem is difficult because there are far too many degrees of freedom to permit an exhaustive search for an optimum, and in many cases no algorithms are known which will determine the exact optimum with significantly less work than exhaustive search. Instead, heuristic algorithms, such as the simulated annealing algorithm, have been employed and have proven effective in minimizing such energy functionals. Unfortunately, the simulated annealing algorithm, as characteristic of Monte Carlo algorithms, is very computer intensive; in fact, it is so intensive that insufficient computational power is often the chief hindrance to investigation of the algorithm. The simulated annealing algorithm, however, is amenable to parallel processing. The goal of the research in this dissertation is to investigate the parameters involved in implementing the simulated annealing algorithm in parallel; however, the form of the simulated annealing algorithm implemented here requires no annealing because the energy functionals investigated are quadratic in form. The parameters related to the parallelization of the simulated annealing algorithm include the decomposition of the reconstruction space among the processors, the formulation of the problem at the estimate level with the smallest task being a single perturbation trial evaluated on a local basis, and the communications required to keep all the processors as current as possible with changes made simultaneously to the estimate. Three objects, varying in size, shape and detail, are reconstructed utilizing the TRIMM parallel processor.