A fast preconditioned conjugate gradient algorithm for regularized WLS reconstruction for PET

In this paper, new theory and methods for a class of preconditioners are developed for accelerating the convergence rate of iterative reconstruction. A preconditioned conjugate gradient (PCG) iterative algorithm for weighted least squares reconstruction (WLS) is formulated for emission tomography. A linear regularization method is adopted and shown to be equivalent to penalized WLS reconstruction with quadratic penalty functions. Using simulated positron emission tomography (PET) data of the Hoffman brain phantom, it was shown that the convergence rate of the PCG using the new preconditioner is an order-of-magnitude faster compared to the standard conjugate gradient algorithm. It is also significantly faster than previously proposed preconditioners for emission tomography