Implementation of total variation regularization-based approaches in the solution of linear inverse heat conduction problems concerning the estimation of surface heat fluxes

In this work, we propose the extension of total variation regularization strategies in principle formulated to be implemented in image processing and signal analysis research fields, to the solution of one-dimensional linear inverse heat conduction problems concerning the estimation of surface heat fluxes. Three solution procedures are considered in the current study, and these include the lagged diffusivity fixed point iteration, the iteratively reweighted least-squares, and the split Bregman iteration methods. The performance of such procedures is tested using four cases, and the regularization parameter is selected via the L-curve criterion. The results are compared to the reconstruction obtained via a classical Tikhonov-like strategy. The main outcome is that the staircase effect dominated all the reconstructions. Despite it deteriorated the quality of the solutions in some specific cases, it did not prevent the appropriate fulfillment of the reconstruction task. The results achieved in this communication have been useful to demonstrate the suitability and reliability of extending total variation approaches to the solution of linear inverse heat conduction problems concerning the estimation of surface heat fluxes, as an appropriate and novel alternative to standard procedures.

Automated summary

This work proposes the extension of total variation regularization strategies to solve one-dimensional linear inverse heat conduction problems. Three solution procedures are tested and compared in terms of their performance, showing that the staircase effect dominates the reconstructions. Despite deteriorating the quality in some cases, it does not prevent the appropriate fulfillment of the reconstruction task. This study demonstrates the suitability and reliability of extending total variation approaches as a novel alternative to standard procedures in solving linear inverse heat conduction problems involving the estimation of surface heat fluxes.