Source localization of reaction-diffusion models for brain tumors

Jaroudi, Rym, Baravdish, George, Åström, Freddie and Johansson, B. Tomas (2016). Source localization of reaction-diffusion models for brain tumors. IN: Pattern recognition. Rosenhahn, Bodo and Andres, Bjoern (eds) Lecture Notes in Computer Science . Cham (CH): Springer.

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.

Publication DOI: https://doi.org/10.1007/978-3-319-45886-1_34
Divisions: Engineering & Applied Sciences > Mathematics
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Event Title: 38th German Conference on Pattern Recognition
Event Type: Other
Event Dates: 2016-09-12 - 2016-09-15
Uncontrolled Keywords: Theoretical Computer Science,Computer Science(all)
Full Text Link: http://link.spr ... -319-45886-1_34
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
Published Date: 2016-08-27
Authors: Jaroudi, Rym
Baravdish, George
Åström, Freddie
Johansson, B. Tomas ( 0000-0001-9066-7922)

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Version: Accepted Version


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