Dimensionality reduction in thermal tomography

Abstract Estimation of material parameters plays an important role in many scientific fields ranging from geophysics, medical imaging, archaeology, material science to the preservation of historical structures. This paper focuses on the civil engineering problem of heat transfer in cases where an intervention into a structure might not be allowed and where estimation of the material parameter can be conducted using only boundary measurements. For two decades, thermal tomography has addressed such scenarios. This study introduces a novel approach for recovering spatially distributed thermal properties based on the random field theory, which efficiently parametrizes the unknown parameter fields. The proposed approach is verified computationally and the results achieved correspond well to those provided by standard thermal tomography procedures.