### 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.

Original language | English |
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Title of host publication | Pattern recognition |

Subtitle of host publication | 38th German Conference, GCPR 2016, Hannover, Germany, September 12-15, 2016, Proceedings |

Editors | Bodo Rosenhahn, Bjoern Andres |

Place of Publication | Cham (CH) |

Publisher | Springer |

Pages | 414-425 |

Number of pages | 12 |

ISBN (Electronic) | 978-3-319-45886-1 |

ISBN (Print) | 978-3-319-45885-4 |

DOIs | |

Publication status | Published - 27 Aug 2016 |

Event | 38th German Conference on Pattern Recognition - Hannover, Germany Duration: 12 Sep 2016 → 15 Sep 2016 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

Volume | 9796 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 38th German Conference on Pattern Recognition |
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Abbreviated title | GCPR 2016 |

Country | Germany |

City | Hannover |

Period | 12/09/16 → 15/09/16 |

### Fingerprint

### Cite this

*Pattern recognition: 38th German Conference, GCPR 2016, Hannover, Germany, September 12-15, 2016, Proceedings*(pp. 414-425). (Lecture Notes in Computer Science; Vol. 9796). Cham (CH): Springer. https://doi.org/10.1007/978-3-319-45886-1_34

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*Pattern recognition: 38th German Conference, GCPR 2016, Hannover, Germany, September 12-15, 2016, Proceedings.*Lecture Notes in Computer Science, vol. 9796, Springer, Cham (CH), pp. 414-425, 38th German Conference on Pattern Recognition, Hannover, Germany, 12/09/16. https://doi.org/10.1007/978-3-319-45886-1_34

**Source localization of reaction-diffusion models for brain tumors.** / Jaroudi, Rym; Baravdish, George; Åström, Freddie; Johansson, B. Tomas.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Source localization of reaction-diffusion models for brain tumors

AU - Jaroudi, Rym

AU - Baravdish, George

AU - Åström, Freddie

AU - Johansson, B. Tomas

PY - 2016/8/27

Y1 - 2016/8/27

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84988432734&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-45886-1_34

DO - 10.1007/978-3-319-45886-1_34

M3 - Conference contribution

AN - SCOPUS:84988432734

SN - 978-3-319-45885-4

T3 - Lecture Notes in Computer Science

SP - 414

EP - 425

BT - Pattern recognition

A2 - Rosenhahn, Bodo

A2 - Andres, Bjoern

PB - Springer

CY - Cham (CH)

ER -