CG Variants for General-Form Regularization with an Application to Low-Field MRI

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Abstract

In an earlier paper, we generalized the CGME (Conjugate Gradient Minimal Error) algorithm to the ℓ2-regularized weighted least-squares problem. Here, we use this Generalized CGME method to reconstruct images from actual signals measured using a low-field MRI scanner. We analyze the convergence of both GCGME and the classical Generalized Conjugate Gradient Least Squares (GCGLS) method for the simple case when a Laplace operator is used as a regularizer and indicate when GCGME is to be preferred in terms of convergence speed. We also consider a more complicated ℓ1-penalty in a compressed sensing framework.

Original languageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference
EditorsFred J. Vermolen, Cornelis Vuik
Place of PublicationCham
PublisherSpringer
Pages673-681
Number of pages9
ISBN (Electronic)978-3-030-55874-1
ISBN (Print)978-3-030-55873-4
DOIs
Publication statusPublished - 2021
EventEuropean Numerical Mathematics and Advanced Applications Conference 2019 - Hotel Zuiderduin , Egmond aan Zee, Netherlands
Duration: 30 Sep 20194 Oct 2019
https://www.enumath2019.eu/

Publication series

NameLecture Notes in Computational Science and Engineering
Volume139
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

ConferenceEuropean Numerical Mathematics and Advanced Applications Conference 2019
Abbreviated titleENUMATH 2019
CountryNetherlands
CityEgmond aan Zee
Period30/09/194/10/19
Internet address

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