A GENERAL-CLASS OF PRECONDITIONERS FOR STATISTICAL ITERATIVE RECONSTRUCTION OF EMISSION COMPUTED-TOMOGRAPHY

A major drawback of statistical iterative image reconstruction for emi ssion computed tomography is its high computational cost, The ill-pose d nature of tomography leads to slow convergence for standard gradient -based iterative approaches such as the steepest descent or the conjug ate gradient algorithm, In this paper new theory and methods for a cla ss of preconditioners are developed for accelerating the convergence r ate of iterative reconstruction. To demonstrate the potential of this class of preconditioners, a preconditioned conjugate gradient (PCG) it erative algorithm for weighted least squares reconstruction (WLS) was formulated for emission tomography. Using simulated positron emission tomography (PET) data of the Hoffman brain phantom, it was shown that the convergence rate of the PCG can reduce the number of iterations of the standard conjugate gradient algorithm by a factor of 2-8 times de pending on the convergence criterion.