{"title":"A high-order finite element method for forward problem in diffuse optical tomography","authors":"M. Hadinia, R. Jafari","doi":"10.1109/ISOT.2010.5687318","DOIUrl":null,"url":null,"abstract":"Diffuse optical tomography (DOT) is a non-invasive imaging modality for visualizing and continuously monitoring tissue and blood oxygenation levels in brain and breast. DOT includes an ill-posed inverse problem. The image reconstruction algorithm in the inverse problem involves generating images by means of forward modeling results and the boundary measurements. A for ward model describes the dependence of the photon intensity data on the distribution of absorbing and scattering coefficients. The ability of the forward model to generate the corresponding data efficiently plays an important issue in DOT image reconstruction. Small measurement or forward modeling errors can lead to unbounded fluctuations in the image reconstruction algorithm. Using a first-order finite element method for forward modeling, the discretization error is reduced by increasing the number of elements. However, increasing the number of elements may cause a critical issue in the ill-posed inverse problem. This paper focuses on applying the high-order finite element method for forward modeling. In this method, the polynomial degree of shape functions is increased and the mesh size is kept fixed. Numerical results are compared with an analytical solution.","PeriodicalId":91154,"journal":{"name":"Optomechatronic Technologies (ISOT), 2010 International Symposium on : 25-27 Oct. 2010 : [Toronto, ON]. International Symposium on Optomechatronic Technologies (2010 : Toronto, Ont.)","volume":"3 1","pages":"1-6"},"PeriodicalIF":0.0000,"publicationDate":"2010-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Optomechatronic Technologies (ISOT), 2010 International Symposium on : 25-27 Oct. 2010 : [Toronto, ON]. International Symposium on Optomechatronic Technologies (2010 : Toronto, Ont.)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISOT.2010.5687318","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2

Abstract

Diffuse optical tomography (DOT) is a non-invasive imaging modality for visualizing and continuously monitoring tissue and blood oxygenation levels in brain and breast. DOT includes an ill-posed inverse problem. The image reconstruction algorithm in the inverse problem involves generating images by means of forward modeling results and the boundary measurements. A for ward model describes the dependence of the photon intensity data on the distribution of absorbing and scattering coefficients. The ability of the forward model to generate the corresponding data efficiently plays an important issue in DOT image reconstruction. Small measurement or forward modeling errors can lead to unbounded fluctuations in the image reconstruction algorithm. Using a first-order finite element method for forward modeling, the discretization error is reduced by increasing the number of elements. However, increasing the number of elements may cause a critical issue in the ill-posed inverse problem. This paper focuses on applying the high-order finite element method for forward modeling. In this method, the polynomial degree of shape functions is increased and the mesh size is kept fixed. Numerical results are compared with an analytical solution.
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漫射光学层析成像正演问题的高阶有限元方法
漫射光学断层扫描(DOT)是一种非侵入性成像方式,用于可视化和连续监测脑和乳腺组织和血液氧合水平。DOT包含一个不适定逆问题。反问题中的图像重建算法是利用正演模拟结果和边界测量结果生成图像。ward模型描述了光子强度数据对吸收和散射系数分布的依赖性。在DOT图像重建中,前向模型能否有效地生成相应的数据是一个重要的问题。小的测量误差或正演建模误差会导致图像重建算法的无界波动。采用一阶有限元法进行正演,通过增加单元个数来减小离散化误差。然而,在病态逆问题中,元素数目的增加会引起一个关键问题。本文的重点是应用高阶有限元法进行正演模拟。该方法增加了形状函数的多项式次,并保持网格尺寸不变。数值结果与解析解进行了比较。
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