{"title":"具有荧光的时间分辨漫射光学层析成像的直接Robin边值抛物系统","authors":"Zakaria Belhachmi sci","doi":"10.4208/jms.v52n3.19.07","DOIUrl":null,"url":null,"abstract":"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. AMS subject classifications: 65N21, 65J22, 78A46","PeriodicalId":43526,"journal":{"name":"数学研究","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"The Direct Robin Boundary Value Parabolic System of Time-Resolved Diffuse Optical Tomography with Fluorescence\",\"authors\":\"Zakaria Belhachmi sci\",\"doi\":\"10.4208/jms.v52n3.19.07\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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. AMS subject classifications: 65N21, 65J22, 78A46\",\"PeriodicalId\":43526,\"journal\":{\"name\":\"数学研究\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2019-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"数学研究\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4208/jms.v52n3.19.07\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"数学研究","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/jms.v52n3.19.07","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Direct Robin Boundary Value Parabolic System of Time-Resolved Diffuse Optical Tomography with Fluorescence
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. AMS subject classifications: 65N21, 65J22, 78A46
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