Thermal tomography with unknown boundary
For practitioners of thermal tomography, this method relaxes the requirement of known boundary shape, but results are only demonstrated on simulated data without quantitative comparison to existing methods.
This work addresses thermal tomography with unknown boundary shape, using an adaptive sparse pseudospectral method to create a polynomial surrogate for temperature measurements, enabling reconstruction of thermal properties and shape via regularized least squares. Numerical experiments in 2D demonstrate the algorithm's functionality.
Thermal tomography is an imaging technique for deducing information about the internal structure of a physical body from temperature measurements on its boundary. This work considers time-dependent thermal tomography modeled by a parabolic initial/boundary value problem without accurate information on the exterior shape of the examined object. The adaptive sparse pseudospectral approximation method is used to form a polynomial surrogate for the dependence of the temperature measurements on the thermal conductivity, the heat capacity, the boundary heat transfer coefficient and the body shape. These quantities can then be efficiently reconstructed via nonlinear, regularized least squares minimization employing the surrogate and its derivatives. The functionality of the resulting reconstruction algorithm is demonstrated by numerical experiments based on simulated data in two spatial dimensions.