Mercer's spectral decomposition for the characterization of thermal parameters

We investigate a tractable Singular Value Decomposition (SVD) method used in thermography for the characterization of thermal parameters. The inverse problem to solve is based on the model of transient heat transfer. The most significant advantage is the transformation of the dynamic identification problem into a steady identification equation. The time dependence is accounted for by the SVD in a performing way. We lay down a mathematical foundation well fitted to this approach, which relies on the spectral expansion of Mercer kernels. This enables us to shed more light on most of its important features. Given its potentialities, the analysis we propose here might help users understanding the way the SVD algorithm, or the TSVD, its truncated version, operate in the thermal parameters estimation and why it is relevant and attractive. When useful, the study is complemented by some analytical and numerical illustrations realized within matlab's code.