## Abstract

This paper introduces a mathematical formulation of the problem

of detection and characterization of shallowly buried landmines (more gener-

ally, buried objects) using passive thermal infrared technique. The problem

consists of two steps. In the first step, referred to as thermal modeling which

aims at predicting the soil temperature provided by the thermal properties of

the soil and the buried objects, a parabolic partial differential equation based

model is formulated. The proposed model is validated using experimental

data. For solving the model, a splitting finite difference scheme is used. In

the second step, referred to as inverse problem setting for landmine detection,

the forward thermal model and acquired infrared images are used to detect

the presence of buried objects and characterize them based on the estima-

tion of their thermal and geometrical properties. Mathematically, this inverse

problem is stated as the estimation of a piecewise constant coefficient of the

heat transfer equation. To reduce the ill-posedness of this problem, which is

due to the lack of spatial information in the measured data, we make use of

a parametrization of the coefficient which needs only a small number of un-

knowns. The problem is then solved by gradient-based optimization methods.

Numerical results both validate the proposed thermal model and illustrate the

performance of the suggested algorithm for the inverse problem.

of detection and characterization of shallowly buried landmines (more gener-

ally, buried objects) using passive thermal infrared technique. The problem

consists of two steps. In the first step, referred to as thermal modeling which

aims at predicting the soil temperature provided by the thermal properties of

the soil and the buried objects, a parabolic partial differential equation based

model is formulated. The proposed model is validated using experimental

data. For solving the model, a splitting finite difference scheme is used. In

the second step, referred to as inverse problem setting for landmine detection,

the forward thermal model and acquired infrared images are used to detect

the presence of buried objects and characterize them based on the estima-

tion of their thermal and geometrical properties. Mathematically, this inverse

problem is stated as the estimation of a piecewise constant coefficient of the

heat transfer equation. To reduce the ill-posedness of this problem, which is

due to the lack of spatial information in the measured data, we make use of

a parametrization of the coefficient which needs only a small number of un-

knowns. The problem is then solved by gradient-based optimization methods.

Numerical results both validate the proposed thermal model and illustrate the

performance of the suggested algorithm for the inverse problem.

Original language | English |
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Pages (from-to) | 469-504 |

Number of pages | 36 |

Journal | Acta Mathematica Vietnamica |

Volume | 36 |

Publication status | Published - 2011 |

## Keywords

- IR
- inverse problems