ADMM-EM method for \(L_1\)-norm regularized weighted least squares PET reconstruction
type: Item
instance of: scholarly article
title: ADMM-EM method for \(L_1\)-norm regularized weighted least squares PET reconstruction
zbMATH Open document ID: 1367.92066
DOI: 10.1155/2016/6458289
author: Yueyang Teng
author: Hang Sun
author: Chen Guo
author: Yan Kang
published in: Computational \& Mathematical Methods in Medicine
publication date: 2017-08-04T00:00:00Z
review text: Summary: The \(L_1\)-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 \(L_1\)-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.
Mathematics Subject Classification ID: 92C55
zbMATH DE Number: 6756917
zbMATH Keywords: \(L_1\)-norm regularization
zbMATH Keywords: Lagrangian multipliers
zbMATH Keywords: positron emission tomography
describes a project that uses: D-ADMM
MaRDI profile type: Publication
Wikidata QID: Q37385955
full work available at URL: https://doi.org/10.1155/2016/6458289
OpenAlex ID: W2532274247
cites work: Q4850052
cites work: A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
cites work: Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
cites work: Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
cites work: D-ADMM: A Communication-Efficient Distributed Algorithm for Separable Optimization
cites work: Tikhonov Regularization and Total Least Squares
cites work: Projected Landweber method and preconditioning
cites work: Block-wise Alternating Direction Method of Multipliers for Multiple-block Convex Programming and Beyond
cites work: A Statistical Model for Positron Emission Tomography
cites work: Bayesian regularization and nonnegative deconvolution for room impulse response estimation
cites work: On the convergence properties of the EM algorithm
cites work: A convergent non-negative deconvolution algorithm with Tikhonov regularization
cites work: Q5689624
cites work: Q5591247
cites work: Q4060241
description: scientific article; zbMATH DE number 6756917