Three penalized EM-type algorithms for PET image reconstruction

Based on Bayes theory, Green introduced the maximum a posteriori (MAP) algorithm to obtain a smoothing reconstruction for positron emission tomography. This algorithm is flexible and convenient for most of the penalties, but it is hard to guarantee convergence. For a common goal, Fessler penalized a weighted least squares (WLS) estimator by a quadratic penalty and then solved it with the successive over-relaxation (SOR) algorithm, however, the algorithm was time-consuming and difficultly parallelized. Anderson proposed another WLS estimator for faster convergence, on which there were few regularization methods studied. For three regularized estimators above, we develop three new expectation maximization (EM) type algorithms to solve them. Unlike MAP and SOR, the proposed algorithms yield update rules by minimizing the auxiliary functions constructed on the previous iterations, which ensure the cost functions monotonically decreasing. Experimental results demonstrated the robustness and effectiveness of the proposed algorithms.