时域荧光漫反射光学断层扫描的提霍诺夫型正则化解决方案的收敛性估计

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-10-28 DOI:10.1016/j.aml.2024.109353

Chunlong Sun , Wenlong Zhang

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引用次数: 0

摘要

在这项工作中，我们研究了时域荧光漫反射光学层析成像的 Tikhonov 型正则化解决方案及其有限元解决方案。首先，我们分析了求解直接问题的有限元方法，并给出了其误差估计。在经典源条件下，我们进一步建立了正则化解及其有限元解的收敛估计。误差估计值与噪声水平、正则化参数、网格大小和时间步长等关键参数存在明确的依赖关系。

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Convergence estimates of the Tikhonov-type regularized solutions for the time-domain fluorescence diffuse optical tomography

In this work, we investigate the Tikhonov-type regularized solutions and their finite element solutions to the time-domain fluorescence diffuse optical tomography. Firstly, we analyze the finite element method for solving the direct problem and give its error estimates. With the classical source condition, we further establish the convergence estimates of the regularized solutions and their finite element solutions. The error estimates present explicit dependence on the critical parameters like noise level, regularization parameter, mesh size and time step size.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.