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THERMAL INFRARED TECHNIQUE FOR LANDMINE DETECTION: MATHEMATICAL FORMULATION AND METHODS This publication appears in: Acta Mathematica Vietnamica Authors: T. Thanh Nguyen, H. Dinh Nho and H. Sahli Volume: 36 Pages: 469-504 Publication Year: 2011
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.
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