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Hyperspectral and multispectral image fusion via graph Laplacian-guided coupled tensor decomposition / Yuanyang Bu in IEEE Transactions on geoscience and remote sensing, vol 59 n° 1 (January 2021)  

Public [article]  inIEEE Transactions on geoscience and remote sensing > vol 59 n° 1 (January 2021) . - pp 648 - 662 Titre : Hyperspectral and multispectral image fusion via graph Laplacian-guided coupled tensor decomposition Type de document : Article/Communication Auteurs : Yuanyang Bu, Auteur ; Yong-Qiang Zhao, Auteur ; Jize Xue, Auteur ; et al., Auteur Année de publication : 2021 Article en page(s) : pp 648 - 662 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Traitement d'image optique [Termes IGN] analyse spectrale [Termes IGN] calcul tensoriel [Termes IGN] équation de Laplace [Termes IGN] fusion d'images [Termes IGN] graphe [Termes IGN] image hyperspectrale [Termes IGN] image multibande [Termes IGN] optimisation (mathématiques) [Termes IGN] tenseur [Termes IGN] théorie des variétés Résumé : (auteur) We propose a novel graph Laplacian-guided coupled tensor decomposition (gLGCTD) model for fusion of hyperspectral image (HSI) and multispectral image (MSI) for spatial and spectral resolution enhancements. The coupled Tucker decomposition is employed to capture the global interdependencies across the different modes to fully exploit the intrinsic global spatial–spectral information. To preserve local characteristics, the complementary submanifold structures embedded in high-resolution (HR)-HSI are encoded by the graph Laplacian regularizations. The global spatial–spectral information captured by the coupled Tucker decomposition and the local submanifold structures are incorporated into a unified framework. The gLGCTD fusion framework is solved by a hybrid framework between the proximal alternating optimization (PAO) and the alternating direction method of multipliers (ADMM). Experimental results on both synthetic and real data sets demonstrate that the gLGCTD fusion method is superior to state-of-the-art fusion methods with a more accurate reconstruction of the HR-HSI. Numéro de notice : A2021-036 Affiliation des auteurs : non IGN Thématique : IMAGERIE/MATHEMATIQUE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1109/TGRS.2020.2992788 Date de publication en ligne : 18/05/2020 En ligne : https://doi.org/10.1109/TGRS.2020.2992788 Format de la ressource électronique : url article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=96738 [article]

Numerical solution to the oblique derivative boundary value problem on non-uniform grids above the Earth topography / Matej Medl’a in Journal of geodesy, vol 92 n° 1 (January 2018)  

Public [article]  inJournal of geodesy > vol 92 n° 1 (January 2018) . - pp 1 - 19 Titre : Numerical solution to the oblique derivative boundary value problem on non-uniform grids above the Earth topography Type de document : Article/Communication Auteurs : Matej Medl’a, Auteur ; Karol Mikula, Auteur ; Robert Cunderlik, Auteur ; Marek Macák, Auteur Année de publication : 2018 Article en page(s) : pp 1 - 19 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] champ de pesanteur local [Termes IGN] discrétisation [Termes IGN] équation de Laplace [Termes IGN] méthode des éléments finis [Termes IGN] problème des valeurs limites Résumé : (Auteur) The paper presents a numerical solution of the oblique derivative boundary value problem on and above the Earth’s topography using the finite volume method (FVM). It introduces a novel method for constructing non-uniform hexahedron 3D grids above the Earth’s surface. It is based on an evolution of a surface, which approximates the Earth’s topography, by mean curvature. To obtain optimal shapes of non-uniform 3D grid, the proposed evolution is accompanied by a tangential redistribution of grid nodes. Afterwards, the Laplace equation is discretized using FVM developed for such a non-uniform grid. The oblique derivative boundary condition is treated as a stationary advection equation, and we derive a new upwind type discretization suitable for non-uniform 3D grids. The discretization of the Laplace equation together with the discretization of the oblique derivative boundary condition leads to a linear system of equations. The solution of this system gives the disturbing potential in the whole computational domain including the Earth’s surface. Numerical experiments aim to show properties and demonstrate efficiency of the developed FVM approach. The first experiments study an experimental order of convergence of the method. Then, a reconstruction of the harmonic function on the Earth’s topography, which is generated from the EGM2008 or EIGEN-6C4 global geopotential model, is presented. The obtained FVM solutions show that refining of the computational grid leads to more precise results. The last experiment deals with local gravity field modelling in Slovakia using terrestrial gravity data. The GNSS-levelling test shows accuracy of the obtained local quasigeoid model. Numéro de notice : A2018-011 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-017-1040-z Date de publication en ligne : 30/05/2017 En ligne : https://doi.org/10.1007/s00190-017-1040-z Format de la ressource électronique : URL Article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=89054 [article]

Introduction to partial differential equations / David Borthwick (2016)  

Public Titre : Introduction to partial differential equations Type de document : Guide/Manuel Auteurs : David Borthwick, Auteur Editeur : Springer International Publishing Année de publication : 2016 Importance : 636 p. Format : 18 x 26 cm ISBN/ISSN/EAN : 978-3-319-48936-0 Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Mathématique [Termes IGN] équation de Laplace [Termes IGN] équation différentielle [Termes IGN] équation linéaire [Termes IGN] onde acoustique [Termes IGN] série de Fourier [Termes IGN] transformation de Fourier Résumé : (éditeur) This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solitons, Huygens'. Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements. Note de contenu : 1- Introduction 2- Preliminaries 3- Conservation Equations and Characteristics 4- The Wave Equation 5- Separation of Variables 6- The Heat Equation 7- Function Spaces 8- Fourier Series 9- Maximum Principles 10- Weak Solutions 11- Variational Methods 12- Distributions 13- The Fourier Transform Numéro de notice : 25868 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Manuel DOI : 10.1007/978-3-319-48936-0 En ligne : https://doi.org/10.1007/978-3-319-48936-0 Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=95528

Introduction to partial differential equations / Peter J. Olver (2014)  

Public Titre : Introduction to partial differential equations Type de document : Guide/Manuel Auteurs : Peter J. Olver, Auteur Editeur : Springer International Publishing Année de publication : 2014 Importance : 636 p. Format : 18 x 26 cm ISBN/ISSN/EAN : 978-3-319-02099-0 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Analyse mathématique [Termes IGN] équation de Laplace [Termes IGN] équation de Poisson [Termes IGN] équation différentielle [Termes IGN] équation linéaire [Termes IGN] équation non linéaire [Termes IGN] équation polynomiale [Termes IGN] fonction de Green [Termes IGN] principe de Huygens [Termes IGN] transformation de Fourier [Termes IGN] valeur limite Résumé : (auteur) This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solitons, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements. Note de contenu : 1- What Are Partial Differential Equations? 2- Linear and Nonlinear Waves 3- Fourier Series 4- Separation of Variables 5- Finite Differences 6- Generalized Functions and Green’s Functions 7- Fourier Transforms 8- Linear and Nonlinear Evolution Equations 9- A General Framework for Linear Partial Differential Equations 10- Finite Elements and Weak Solutions 11- Dynamics of Planar Media 12- Partial Differential Equations in Space Numéro de notice : 25874 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Manuel DOI : 10.1007/978-3-319-02099-0 En ligne : https://doi.org/10.1007/978-3-319-02099-0 Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=95568

Triangulated spherical splines for geopotential reconstruction / M.J. Lai in Journal of geodesy, vol 83 n° 8 (August 2009)  

Public [article]  inJournal of geodesy > vol 83 n° 8 (August 2009) . - pp 695 - 708 Titre : Triangulated spherical splines for geopotential reconstruction Type de document : Article/Communication Auteurs : M.J. Lai, Auteur ; C.K. Shum, Auteur ; V. Baramidze, Auteur ; P. Wenston, Auteur Année de publication : 2009 Article en page(s) : pp 695 - 708 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] champ de pesanteur local [Termes IGN] champ de pesanteur terrestre [Termes IGN] Earth Gravity Model 1996 [Termes IGN] équation de Laplace [Termes IGN] fonction spline [Termes IGN] fonction spline d'interpolation [Termes IGN] modèle de géopotentiel [Termes IGN] potentiel de pesanteur terrestre Résumé : (Auteur) We present an alternate mathematical technique than contemporary spherical harmonics to approximate the geopotential based on triangulated spherical spline functions, which are smooth piecewise spherical harmonic polynomials over spherical triangulations. The new method is capable of multi-spatial resolution modeling and could thus enhance spatial resolutions for regional gravity field inversion using data from space gravimetry missions such as CHAMP, GRACE or GOCE. First, we propose to use the minimal energy spherical spline interpolation to find a good approximation of the geopotential at the orbital altitude of the satellite. Then we explain how to solve Laplace’s equation on the Earth’s exterior to compute a spherical spline to approximate the geopotential at the Earth’s surface. We propose a domain decomposition technique, which can compute an approximation of the minimal energy spherical spline interpolation on the orbital altitude and a multiple star technique to compute the spherical spline approximation by the collocation method. We prove that the spherical spline constructed by means of the domain decomposition technique converges to the minimal energy spline interpolation. We also prove that the modeled spline geopotential is continuous from the satellite altitude down to the Earth’s surface. We have implemented the two computational algorithms and applied them in a numerical experiment using simulated CHAMP geopotential observations computed at satellite altitude (450 km) assuming EGM96 (n max = 90) is the truth model. We then validate our approach by comparing the computed geopotential values using the resulting spherical spline model down to the Earth’s surface, with the truth EGM96 values over several study regions. Our numerical evidence demonstrates that the algorithms produce a viable alternative of regional gravity field solution potentially exploiting the full accuracy of data from space gravimetry missions. The major advantage of our method is that it allows us to compute the geopotential over the regions of interest as well as enhancing the spatial resolution commensurable with the characteristics of satellite coverage, which could not be done using a global spherical harmonic representation. Copyright Springer Numéro de notice : A2009-323 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-008-0283-0 En ligne : https://doi.org/10.1007/s00190-008-0283-0 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=29953 [article]

Exemplaires(1)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
266-09071	SL	Revue	Centre de documentation	Revues en salle	Disponible

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La géodésie / P.L. Baetsle (1980)

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Erste Sitzung der Arbeitsgruppe Satellitengeodäsie der Bayerischen Kommission für die Internationale Erdmessung / Max Kneissl (1964)

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Résolution des systèmes linéaires, méthodes itératives, méthodes par élimination, essai d'une méthode synthétisant les 2 points de vue, cas de l'équation de Laplace / Henri Marcel Dufour (01/10/1961)

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Point de Laplace / Henri Marcel Dufour (1960)

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Cours d'analyse, 2. Tome 2 / P. Levy (1931)

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A treatise on attractions, Laplace's functions, and the figure of the Earth / J. Pratt (1871)

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