학술논문
The direct Robin boundary value parabolic system of time-resolved diffuse optical tomography with fluorescence.
Document Type
Journal
Author
Belhachmi, Zakaria (F-HALS-MIA) AMS Author Profile; Dollé, Guillaume (F-URCA-LM) AMS Author Profile; Prud'homme, Christophe (F-STRAS-I) AMS Author Profile; Torregrossa, Murielle (F-STRAS-CUB) AMS Author Profile
Source
Subject
65 Numerical analysis -- 65J Numerical analysis in abstract spaces
65J22Inverse problems
78Optics, electromagnetic theory -- 78A General
78A46Inverse scattering problems
94Information and communication, circuits -- 94A Communication, information
94A12Signal theory
65J22
78
78A46
94
94A12
Language
English
Abstract
Summary: ``We consider a system of parabolic PDEs with measure data modelling a problem of the time resolved diffuse optical tomography with a fluorescence term and Robin boundary conditions. We focus on the direct problem where the quantity of interest is the density of photons in the diffusion equations and which constitutes a major step to solve the inverse problem of identifiability and reconstruction of diffusion, absorption and concentration of the fluorescent markers. We study the problem under a variational form and its discretization with finite element method and we give some numerical simulation results for verification purpose as well as simulations with real data from a tomograph.''