Using Lagrange principle for solving two-dimensional integral equation with a positive kernel

Y. Zhang; D. V. Lukyanenko; A. G. Yagola

doi:10.1080/17415977.2015.1077445

Using Lagrange principle for solving two-dimensional integral equation with a positive kernel

Y. Zhang^*
, D. V. Lukyanenko
, A. G. Yagola

^*Corresponding author for this work

Örebro University
Lomonosov Moscow State University

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

This article is devoted to a Lagrange principle application to an inverse problem of a two-dimensional integral equation of the first kind with a positive kernel. To tackle the ill-posedness of this problem, a new numerical method is developed. The optimal and regularization properties of this method are proved. Moreover, a pseudo-optimal error of the proposed method is considered. The efficiency and applicability of this method are demonstrated in a numerical example of an image deblurring problem with noisy data.

Original language	English
Pages (from-to)	811-831
Number of pages	21
Journal	Inverse Problems in Science and Engineering
Volume	24
Issue number	5
DOIs	https://doi.org/10.1080/17415977.2015.1077445
Publication status	Published - 12 Jun 2016
Externally published	Yes

Keywords

Fredholm integral equation of the first kind
Lagrange principle
error estimation
optimal recovery
regularization

Access to Document

10.1080/17415977.2015.1077445

Cite this

@article{977465db8c3d411090f9f5931f0cfece,

title = "Using Lagrange principle for solving two-dimensional integral equation with a positive kernel",

abstract = "This article is devoted to a Lagrange principle application to an inverse problem of a two-dimensional integral equation of the first kind with a positive kernel. To tackle the ill-posedness of this problem, a new numerical method is developed. The optimal and regularization properties of this method are proved. Moreover, a pseudo-optimal error of the proposed method is considered. The efficiency and applicability of this method are demonstrated in a numerical example of an image deblurring problem with noisy data.",

keywords = "Fredholm integral equation of the first kind, Lagrange principle, error estimation, optimal recovery, regularization",

author = "Y. Zhang and Lukyanenko, \{D. V.\} and Yagola, \{A. G.\}",

note = "Publisher Copyright: {\textcopyright} 2015 Taylor \& Francis.",

year = "2016",

month = jun,

day = "12",

doi = "10.1080/17415977.2015.1077445",

language = "English",

volume = "24",

pages = "811--831",

journal = "Inverse Problems in Science and Engineering",

issn = "1741-5977",

publisher = "Taylor and Francis Ltd.",

number = "5",

}

TY - JOUR

T1 - Using Lagrange principle for solving two-dimensional integral equation with a positive kernel

AU - Zhang, Y.

AU - Lukyanenko, D. V.

AU - Yagola, A. G.

PY - 2016/6/12

Y1 - 2016/6/12

N2 - This article is devoted to a Lagrange principle application to an inverse problem of a two-dimensional integral equation of the first kind with a positive kernel. To tackle the ill-posedness of this problem, a new numerical method is developed. The optimal and regularization properties of this method are proved. Moreover, a pseudo-optimal error of the proposed method is considered. The efficiency and applicability of this method are demonstrated in a numerical example of an image deblurring problem with noisy data.

AB - This article is devoted to a Lagrange principle application to an inverse problem of a two-dimensional integral equation of the first kind with a positive kernel. To tackle the ill-posedness of this problem, a new numerical method is developed. The optimal and regularization properties of this method are proved. Moreover, a pseudo-optimal error of the proposed method is considered. The efficiency and applicability of this method are demonstrated in a numerical example of an image deblurring problem with noisy data.

KW - Fredholm integral equation of the first kind

KW - Lagrange principle

KW - error estimation

KW - optimal recovery

KW - regularization

UR - https://www.scopus.com/pages/publications/84941792872

U2 - 10.1080/17415977.2015.1077445

DO - 10.1080/17415977.2015.1077445

M3 - Article

AN - SCOPUS:84941792872

SN - 1741-5977

VL - 24

SP - 811

EP - 831

JO - Inverse Problems in Science and Engineering

JF - Inverse Problems in Science and Engineering

IS - 5

ER -

Using Lagrange principle for solving two-dimensional integral equation with a positive kernel

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this