Preconditioned block Kaczmarz methods for linear equations with an application to computed tomography.

IF 1.7 3区 医学 Q3 INSTRUMENTS & INSTRUMENTATION
Duo Liu, Wenli Wang, Gangrong Qu
{"title":"Preconditioned block Kaczmarz methods for linear equations with an application to computed tomography.","authors":"Duo Liu, Wenli Wang, Gangrong Qu","doi":"10.1177/08953996251317421","DOIUrl":null,"url":null,"abstract":"<p><strong>Background: </strong>Preconditioned Kaczmarz methods play a pivotal role in image reconstruction. A fundamental theoretical question lies in establishing the convergence conditions for these methods. Practically, devising an efficient block strategy to accelerate the reconstruction process is also critical.</p><p><strong>Objective: </strong>This paper aims to introduce the convergence conditions for the preconditioned Kaczmarz methods and design the block strategy with corresponding preconditioners for these methods in computed tomography (CT).</p><p><strong>Methods: </strong>We establish a kind of useful convergence conditions for the preconditioned block Kaczmarz methods and prove the dependence of the convergence limit on the initial guess. Tailored for the CT problem, we also propose a new method with a novel block strategy and specific preconditioners, which ensure accelerated convergence.</p><p><strong>Results: </strong>Numerical experiments with the Shepp-Logan phantom and a real chest CT image demonstrate that our proposed block strategy and preconditioners effectively accelerate the reconstruction process by the preconditioned block Kaczmarz methods while maintaining satisfactory image quality.</p><p><strong>Conclusions: </strong>Our proposed method, which incorporates the designed block strategy and specific preconditioners, has superior performance compared to the traditional Landweber iteration and the block Kaczmarz iteration without preconditioners.</p>","PeriodicalId":49948,"journal":{"name":"Journal of X-Ray Science and Technology","volume":" ","pages":"8953996251317421"},"PeriodicalIF":1.7000,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of X-Ray Science and Technology","FirstCategoryId":"3","ListUrlMain":"https://doi.org/10.1177/08953996251317421","RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"INSTRUMENTS & INSTRUMENTATION","Score":null,"Total":0}
引用次数: 0

Abstract

Background: Preconditioned Kaczmarz methods play a pivotal role in image reconstruction. A fundamental theoretical question lies in establishing the convergence conditions for these methods. Practically, devising an efficient block strategy to accelerate the reconstruction process is also critical.

Objective: This paper aims to introduce the convergence conditions for the preconditioned Kaczmarz methods and design the block strategy with corresponding preconditioners for these methods in computed tomography (CT).

Methods: We establish a kind of useful convergence conditions for the preconditioned block Kaczmarz methods and prove the dependence of the convergence limit on the initial guess. Tailored for the CT problem, we also propose a new method with a novel block strategy and specific preconditioners, which ensure accelerated convergence.

Results: Numerical experiments with the Shepp-Logan phantom and a real chest CT image demonstrate that our proposed block strategy and preconditioners effectively accelerate the reconstruction process by the preconditioned block Kaczmarz methods while maintaining satisfactory image quality.

Conclusions: Our proposed method, which incorporates the designed block strategy and specific preconditioners, has superior performance compared to the traditional Landweber iteration and the block Kaczmarz iteration without preconditioners.

求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
4.90
自引率
23.30%
发文量
150
审稿时长
3 months
期刊介绍: Research areas within the scope of the journal include: Interaction of x-rays with matter: x-ray phenomena, biological effects of radiation, radiation safety and optical constants X-ray sources: x-rays from synchrotrons, x-ray lasers, plasmas, and other sources, conventional or unconventional Optical elements: grazing incidence optics, multilayer mirrors, zone plates, gratings, other diffraction optics Optical instruments: interferometers, spectrometers, microscopes, telescopes, microprobes
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信