Thermal tomography is a nondestructive method for detecting inhomogeneities in a material by localizing variations in its thermal conductivity. Based on a finite element discretization of the heat conduction equation, we obtain a set of equations that relate the conductivity of a medium to temperature measurements on the surface of the medium. We investigate the use of both a linearization and regularization technique and a randomized search procedure based on a genetic algorithm to invert this set of equations. We found a tradeoff exists between the accuracy of the conductivity mapping and the resolution of the conductivity mapping. To increase the resolution of the mapping, we propose a zooming method in which the finite elements are grouped into blocks and a low-resolution mapping of the conductivity is obtained. Improved mappings are then obtained by increasing the number of blocks in regions where inhomogeneities appear to be present and repeating the inversion process.

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