A globally accelerated numerical method for optical tomography with continuous wave source
A globally accelerated numerical method for optical tomography with continuous wave source
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DOI：
10.1515/jiip.2008.048
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发表时间：
2008-12-01
影响因子：
1.1
通讯作者：
Liu, H.
中科院分区：
文献类型：
--
作者：
Shan, H.;Klibanov, M. V.;Liu, H.
提出了一种求解具有未知位势的椭圆型方程反问题的新的数值方法。在这个问题中，点源是沿着直线运行和源相关的Dirichlet边界条件被测量作为反问题的数据。一个严格的收敛性分析表明，这种方法是全局收敛的，提供了所谓的尾函数是近似。数值实验验证了这种逼近的有效性，并证明了其全局收敛性.讨论了在医学成像、战场目标成像和电阻抗断层成像中的应用。
A new numerical method for an inverse problem for an elliptic equation with unknown potential is proposed. In this problem the point source is running along a straight line and the source-dependent Dirichlet boundary condition is measured as the data for the inverse problem. A rigorous convergence analysis shows that this method converges globally, provided that the so-called tail function is approximated well. This approximation is verified in numerical experiments, so as the global convergence. Applications to medical imaging, imaging of targets on battlefields and to electrical impedance tomography are discussed.