title: ADMM-EM Method forL1-Norm Regularized Weighted Least Squares PET Reconstruction.
abstract: TheL1-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 theL1-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.
authors.affiliation: Sino-Dutch Biomedical and Information Engineering School, Northeastern University, Shenyang 110004, China.
authors.forename: Yueyang
authors.identifier: 0000-0002-1487-8434
authors.initials: Y
authors.lastname: Teng
authors.affiliation: Sino-Dutch Biomedical and Information Engineering School, Northeastern University, Shenyang 110004, China.
authors.forename: Hang
authors.identifier: 0000-0002-4021-5722
authors.initials: H
authors.lastname: Sun
authors.affiliation: Shenyang Branch of Philips Healthcare (Suzhou) Co., Ltd., Shenyang 110004, China.
authors.forename: Chen
authors.identifier: 0000-0002-7315-2633
authors.initials: C
authors.lastname: Guo
authors.affiliation: Sino-Dutch Biomedical and Information Engineering School, Northeastern University, Shenyang 110004, China.
authors.forename: Yan
authors.identifier: 0000-0003-4563-144X
authors.initials: Y
authors.lastname: Kang
mesh_terms: D000465:Algorithms; D001921:Brain / Q000000981:diagnostic imaging*; D003198:Computer Simulation; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D016018:Least-Squares Analysis; D000069550:Machine Learning; D015233:Models, Statistical; D010363:Pattern Recognition, Automated; D049268:Positron-Emission Tomography; D011829:Radiation Dosage; D012984:Software