 |
|
|
|
| HAL : cea-00429914, version 1 |
| Fiche détaillée |  Récupérer au format |
|
|
| Optics Express 17, 21 (2009) 18433-18448 |
|
|
|
|
| Application of a wavelet-Galerkin method to the forward problem resolution in fluorescence Diffuse Optical Tomography |
|
|
Anne Landragin-Frassati 1Stéphane Bonnet 1 |
|
|
| (28/09/2009) |
|
|
|
| Fluorescence diffuse optical tomography is a powerful tool for the investigation of molecular events in studies for new therapeutic developments. Here, the emphasis is put on the mathematical problem of tomography, which can be formulated in terms of an estimation of physical parameters appearing as a set of Partial Differential Equations (PDEs). The standard polynomial Finite Element Method (FEM) is a method of choice to solve the diffusion equation because it has no restriction in terms of neither the geometry nor the homogeneity of the system, but it is time consuming. In order to speed up computation time, this paper proposes an alternative numerical model, describing the diffusion operator in orthonormal basis of compactly supported wavelets. The discretization of the PDEs yields to matrices which are easily computed from derivative wavelet product integrals. Due to the shape of the wavelet basis, the studied domain is included in a regular fictitious domain. A validation study and a comparison with the standard FEM are conducted on synthetic data. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Département Microtechnologies pour la Biologie et la Santé (DTBS) |
|
|
|
CEA : DRT/LETI |
|
|
| 2 : | Institut FRESNEL (IF) |
|
|
|
CNRS : UMR6133 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III – Ecole Centrale de Marseille |
|
|
| 3 : | Grenoble Images Parole Signal Automatique (GIPSA-lab) |
|
|
|
CNRS : UMR5216 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Université Stendhal - Grenoble III – Institut Polytechnique de Grenoble - Grenoble Institute of Technology |
|
|
|
|
|
|
|
|
|
| Domaine | : | Sciences du Vivant/Ingénierie biomédicale/Imagerie Mathématiques/Equations aux dérivées partielles Mathématiques/Analyse numérique |
| cea-00429914, version 1 | |
| http://hal-cea.archives-ouvertes.fr/cea-00429914 | |
| oai:hal-cea.archives-ouvertes.fr:cea-00429914 | |
| Contributeur : Alain Constans | |
| Soumis le : Jeudi 5 Novembre 2009, 10:41:44 | |
| Dernière modification le : Mardi 19 Janvier 2010, 16:48:21 | |
