Thermal tomography with unknown boundary

Nuutti Hyvönen, Lauri Mustonen

Research output: Contribution to journalArticleScientificpeer-review

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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.

Original languageEnglish
Pages (from-to)B662-B683
JournalSIAM Journal on Scientific Computing
Issue number3
Publication statusPublished - 1 Jan 2018
MoE publication typeA1 Journal article-refereed


  • Inaccurate measurement model
  • Inverse boundary value problems
  • Sparse pseudospectral approximation
  • Thermal tomography

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