Thermal tomography with unknown boundary

TY - JOUR

T1 - Thermal tomography with unknown boundary

AU - Hyvönen, Nuutti

AU - Mustonen, Lauri

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Inaccurate measurement model

KW - Inverse boundary value problems

KW - Sparse pseudospectral approximation

KW - Thermal tomography

UR - http://www.scopus.com/inward/record.url?scp=85049486939&partnerID=8YFLogxK

U2 - 10.1137/16M1104573

DO - 10.1137/16M1104573

M3 - Article

VL - 40

SP - B662-B683

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

SN - 1064-8275

IS - 3

ER -