@inproceedings{fff84a2ca52048848e6b04a48ed5dfa1,
title = "Source localization of reaction-diffusion models for brain tumors",
abstract = "We propose a mathematically well-founded approach for locating the source (initial state) of density functions evolved within a nonlinear reaction-diffusion model. The reconstruction of the initial source is an ill-posed inverse problem since the solution is highly unstable with respect to measurement noise. To address this instability problem, we introduce a regularization procedure based on the nonlinear Landweber method for the stable determination of the source location. This amounts to solving a sequence of well-posed forward reaction-diffusion problems. The developed framework is general, and as a special instance we consider the problem of source localization of brain tumors. We show numerically that the source of the initial densities of tumor cells are reconstructed well on both imaging data consisting of simple and complex geometric structures.",
author = "Rym Jaroudi and George Baravdish and Freddie {\AA}str{\"o}m and Johansson, {B. Tomas}",
year = "2016",
month = aug,
day = "27",
doi = "10.1007/978-3-319-45886-1_34",
language = "English",
isbn = "978-3-319-45885-4",
series = "Lecture Notes in Computer Science",
publisher = "Springer",
pages = "414--425",
editor = "Bodo Rosenhahn and Bjoern Andres",
booktitle = "Pattern recognition",
address = "Germany",
note = "38th German Conference on Pattern Recognition, GCPR 2016 ; Conference date: 12-09-2016 Through 15-09-2016",
}