TY - JOUR A2 - Dang, Chuangyin AU - Teng, Yueyang AU - Sun, Hang AU - Guo, Chen AU - Kang, Yan PY - 2016 DA - 2016/10/19 TI - ADMM-EM Method for -Norm Regularized Weighted Least Squares PET Reconstruction SP - 6458289 VL - 2016 AB - The L1-norm regularization is usually used in positron emission tomography (PET) reconstruction to suppress noise artifacts while preserving edges. The alternating direction method of multipliers (ADMM) is proven to be effective for solving this problem. It sequentially updates the additional variables, image pixels, and Lagrangian multipliers. Difficulties lie in obtaining a nonnegative update of the image. And classic ADMM requires updating the image by greedy iteration to minimize the cost function, which is computationally expensive. In this paper, we consider a specific application of ADMM to the L1-norm regularized weighted least squares PET reconstruction problem. Main contribution is derivation of a new approach to iteratively and monotonically update the image while self-constraining in the nonnegativity region and the absence of a predetermined step size. We give a rigorous convergence proof on the quadratic subproblem of the ADMM algorithm considered in the paper. A simplified version is also developed by replacing the minima of the image-related cost function by one iteration that only decreases it. The experimental results show that the proposed algorithm with greedy iterations provides a faster convergence than other commonly used methods. Furthermore, the simplified version gives a comparable reconstructed result with far lower computational costs. SN - 1748-670X UR - https://doi.org/10.1155/2016/6458289 DO - 10.1155/2016/6458289 JF - Computational and Mathematical Methods in Medicine PB - Hindawi Publishing Corporation KW - ER -