Convergent Data-Driven Regularizations for CT Reconstruction

扫码查看

原文链接

NETL
NSTL
万方数据

外文摘要：The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computer-ized tomography(CT).As the(naïve)solution does not depend on the measured data con-tinuously,regularization is needed to reestablish a continuous dependence.In this work,we investigate simple,but yet still provably convergent approaches to learning linear regu-larization methods from data.More specifically,we analyze two approaches:one generic linear regularization that learns how to manipulate the singular values of the linear opera-tor in an extension of our previous work,and one tailored approach in the Fourier domain that is specific to CT-reconstruction.We prove that such approaches become convergent regularization methods as well as the fact that the reconstructions they provide are typi-cally much smoother than the training data they were trained on.Finally,we compare the spectral as well as the Fourier-based approaches for CT-reconstruction numerically,discuss their advantages and disadvantages and investigate the effect of discretization errors at dif-ferent resolutions.

外文关键词：

Inverse problemsRegularizationComputerized tomography(CT)Machine learning

作者：

Samira Kabri、Alexander Auras、Danilo Riccio、Hartmut Bauermeister、Martin Benning、Michael Moeller、Martin Burger

展开 >

作者单位：

Helmholtz Imaging,Deutsches Elektronen-Synchrotron DESY,Notkestr.85,22607 Hamburg,Germany

Institute for Vision and Graphics,University of Siegen,Adolf-Reichwein-Straße 2a,57076 Siegen,Germany

School of Mathematical Sciences,Queen Mary University of London,Mile End Road,London E1 4NS,UK

The Alan Turing Institute,British Library,96 Euston Rd,London NW1 2DB,UK

Fachbereich Mathematik,Universität Hamburg,Bundesstrasse 55,20146 Hamburg,Germany

展开 >

基金：

German Research Foundation,projectsGerman Research Foundation,projectsEPSRC grantAlan Turing InstituteQMUL Research-ITOpen Access funding enabled and organized by Projekt DEAL

项目编号：

BU 2327/19-1MO 2962/7-1EP/R513106/1

出版年：

2024

DOI：

10.1007/s42967-023-00333-2

应用数学与计算数学学报

上海大学

应用数学与计算数学学报

影响因子：0.165

ISSN：1006-6330

年,卷(期)：2024.6(2)