Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/36381
標題: New implementation of Elliptic Systems Method for time dependent diffusion tomography with back reflected and transmitted boundary data
作者: Shih, Y.
施因澤
Lucas, T.R.
關鍵字: inverse problem
optical mammography
elliptic systems method
Bogner-Fox-Schmit
optical tomography
期刊/報告no:: Applied Mathematics and Computation, Volume 188, Issue 1, Page(s) 64-74.
摘要: A problem of coefficient recovery from incomplete boundary data in inverse problems is considered. It uses a new implementation of the Elliptic Systems Method (ESM) in time dependent diffusion tomography. The basic formulation of the ESM involves solving a system of coupled fourth-order partial differential equations, with the time variable integrated out using Legendre polynomials. Here, we use C-1 Bogner-Fox-Schmit bi-cubic elements over rectangles, with a new treatment of boundary conditions in the common case of incomplete boundary data. This new method is fourth-order accurate for sufficiently smooth functions. The new boundary condition approach allows the use of homogeneous natural boundary conditions on parts of the boundary where no measured data is available. We will focus on a comparison with three previously published examples using back reflected or transmitted data with one or two inclusions. The new implementation gives markedly improved results for inclusion recovery, all of which are achieved without use of additional aids such as weight functions which previously have been thought to be essential, and is shown to be surprisingly robust with respect to noise. We conclude with two examples illustrating the effect of increasing levels of noise. (C) 2006 Elsevier Inc. All rights reserved.
URI: http://hdl.handle.net/11455/36381
ISSN: 0096-3003
文章連結: http://dx.doi.org/10.1016/j.amc.2006.09.083
Appears in Collections:應用數學系所

文件中的檔案:

取得全文請前往華藝線上圖書館



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.