Determination of the space-dependent source in the thermal-wave model of bio-heat transfer

We consider linear but ill-posed inverse problems consisting of finding the unknown space-dependent source in the thermal-wave model of bio-heat transfer from final-time or time-average temperature measurements. In contrast to the previous research on parabolic bio-heat transfer models, this work concerns a more involved and practical hyperbolic model used in biomedical engineering. First, the unique solvability of the linear inverse source problems is established. Then, the inverse problems are recast as variational problems, allowing the gradients of the least-squares objective functionals to be derived. These latter problems are solved iteratively using the conjugate gradient method combined with the discrepancy principle. Finally, the inversion algorithm is tested on identifying one- and two-dimensional space-dependent sources.