An optimal quasi solution for the Cauchy problem for Laplace equation in the framework of inverse ECG.
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| Title: | An optimal quasi solution for the Cauchy problem for Laplace equation in the framework of inverse ECG. |
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| Authors: | HERNANDEZ-MONTERO, EDUARDO1 eduardo.hdz.mto@gmail.com, FRAGUELA-COLLAR, ANDRES1, HENRY, JACQUES2 |
| Source: | Mathematical Modelling of Natural Phenomena. 2019, Vol. 14 Issue 2, pN.PAG-22. 22p. |
| Subjects: | Cauchy problem, Invariant imbedding, Factorization, Electrocardiography, Mathematical regularization |
| Abstract: | The inverse ECG problem is set as a boundary data completion for the Laplace equation: at each time the potential is measured on the torso and its normal derivative is null. One aims at reconstructing the potential on the heart. A new regularization scheme is applied to obtain an optimal regularization strategy for the boundary data completion problem. We consider the ℝn+1 domain Ω. The piecewise regular boundary of Ω is defined as the union ∂Ω = Γ1 ∪ Γ0 ∪ Σ, where Γ1 and Γ0 are disjoint, regular, and n-dimensional surfaces. Cauchy boundary data is given in Γ0, and null Dirichlet data in Σ, while no data is given in Γ1. This scheme is based on two concepts: admissible output data for an ill-posed inverse problem, and the conditionally well-posed approach of an inverse problem. An admissible data is the Cauchy data in Γ0 corresponding to an harmonic function in C2(Ω) ∩H1(Ω). The methodology roughly consists of first characterizing the admissible Cauchy data, then finding the minimum distance projection in the L2-norm from the measured Cauchy data to the subset of admissible data characterized by given a priori information, and finally solving the Cauchy problem with the aforementioned projection instead of the original measurement. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematical Modelling of Natural Phenomena is the property of EDP Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 134798625 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: An optimal quasi solution for the Cauchy problem for Laplace equation in the framework of inverse ECG. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22HERNANDEZ-MONTERO%2C+EDUARDO%22">HERNANDEZ-MONTERO, EDUARDO</searchLink><relatesTo>1</relatesTo><i> eduardo.hdz.mto@gmail.com</i><br /><searchLink fieldCode="AR" term="%22FRAGUELA-COLLAR%2C+ANDRES%22">FRAGUELA-COLLAR, ANDRES</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22HENRY%2C+JACQUES%22">HENRY, JACQUES</searchLink><relatesTo>2</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematical+Modelling+of+Natural+Phenomena%22">Mathematical Modelling of Natural Phenomena</searchLink>. 2019, Vol. 14 Issue 2, pN.PAG-22. 22p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Cauchy+problem%22">Cauchy problem</searchLink><br /><searchLink fieldCode="DE" term="%22Invariant+imbedding%22">Invariant imbedding</searchLink><br /><searchLink fieldCode="DE" term="%22Factorization%22">Factorization</searchLink><br /><searchLink fieldCode="DE" term="%22Electrocardiography%22">Electrocardiography</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+regularization%22">Mathematical regularization</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The inverse ECG problem is set as a boundary data completion for the Laplace equation: at each time the potential is measured on the torso and its normal derivative is null. One aims at reconstructing the potential on the heart. A new regularization scheme is applied to obtain an optimal regularization strategy for the boundary data completion problem. We consider the ℝn+1 domain Ω. The piecewise regular boundary of Ω is defined as the union ∂Ω = Γ1 ∪ Γ0 ∪ Σ, where Γ1 and Γ0 are disjoint, regular, and n-dimensional surfaces. Cauchy boundary data is given in Γ0, and null Dirichlet data in Σ, while no data is given in Γ1. This scheme is based on two concepts: admissible output data for an ill-posed inverse problem, and the conditionally well-posed approach of an inverse problem. An admissible data is the Cauchy data in Γ0 corresponding to an harmonic function in C2(Ω) ∩H1(Ω). The methodology roughly consists of first characterizing the admissible Cauchy data, then finding the minimum distance projection in the L2-norm from the measured Cauchy data to the subset of admissible data characterized by given a priori information, and finally solving the Cauchy problem with the aforementioned projection instead of the original measurement. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematical Modelling of Natural Phenomena is the property of EDP Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1051/mmnp/2018062 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 22 StartPage: N.PAG Subjects: – SubjectFull: Cauchy problem Type: general – SubjectFull: Invariant imbedding Type: general – SubjectFull: Factorization Type: general – SubjectFull: Electrocardiography Type: general – SubjectFull: Mathematical regularization Type: general Titles: – TitleFull: An optimal quasi solution for the Cauchy problem for Laplace equation in the framework of inverse ECG. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: HERNANDEZ-MONTERO, EDUARDO – PersonEntity: Name: NameFull: FRAGUELA-COLLAR, ANDRES – PersonEntity: Name: NameFull: HENRY, JACQUES IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: 2019 Type: published Y: 2019 Identifiers: – Type: issn-print Value: 09735348 Numbering: – Type: volume Value: 14 – Type: issue Value: 2 Titles: – TitleFull: Mathematical Modelling of Natural Phenomena Type: main |
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