Deflated Preconditioned Conjugate Gradients for Nonlinear Diffusion Image Enhancement

Xiujie Shan, Martin van Gijzen*

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

3 Citations (Scopus)
24 Downloads (Pure)

Abstract

Nonlinear diffusion equations have been successfully used for image enhancement by reducing the noise in the image while protecting the edges. In discretized form, the denoising requires the solution of a sequence of linear systems. The underlying system matrices stem from a discrete diffusion operator with large jumps in the diffusion coefficients. As a result these matrices can be very ill-conditioned, which leads to slow convergence for iterative methods such as the Conjugate Gradient method. To speed-up the convergence we use deflation and preconditioning. The deflation vectors are defined by a decomposition of the image. The resulting numerical method is easy to implement and matrix-free. We evaluate the performance of the method on a simulated image and on a measured low-field MR image for various types of deflation vectors.

Original languageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference
EditorsFred J. Vermolen, Cornelis Vuik
PublisherSpringer
Pages459-468
Number of pages10
ISBN (Print)978-3-0305-5873-4
DOIs
Publication statusPublished - 2021
EventEuropean Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019 - Egmond aan Zee, Netherlands
Duration: 30 Sept 20194 Oct 2019

Publication series

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

Conference

ConferenceEuropean Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019
Country/TerritoryNetherlands
CityEgmond aan Zee
Period30/09/194/10/19

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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