@Article{CiCP-19-226,
author = {},
title = {A New Coupled Complex Boundary Method for Bioluminescence Tomography},
journal = {Communications in Computational Physics},
year = {2018},
volume = {19},
number = {1},
pages = {226--250},
abstract = {<p style="text-align: justify;">In this paper, we introduce and study a new method for solving inverse
source problems, through a working model that arises in bioluminescence tomography
(BLT). In the BLT problem, one constructs quantitatively the bioluminescence source
distribution inside a small animal from optical signals detected on the animal&#39;s body
surface. The BLT problem possesses strong ill-posedness and often the Tikhonov regularization
is used to obtain stable approximate solutions. In conventional Tikhonov
regularization, it is crucial to choose a proper regularization parameter for trade off
between the accuracy and stability of approximate solutions. The new method is
based on a combination of the boundary condition and the boundary measurement
in a parameter-dependent single complex Robin boundary condition, followed by the
Tikhonov regularization. By properly adjusting the parameter in the Robin boundary
condition, we achieve two important properties for our new method: first, the regularized
solutions are uniformly stable with respect to the regularization parameter
so that the regularization parameter can be chosen based solely on the consideration
of the solution accuracy; second, the convergence order of the regularized solutions
reaches one with respect to the noise level. Then, the finite element method is used to
compute numerical solutions and a new finite element error estimate is derived for discrete
solutions. These results improve related results found in the existing literature.
Several numerical examples are provided to illustrate the theoretical results.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.230115.150615a},
url = {http://global-sci.org/intro/article_detail/cicp/11087.html}
}