Solving inverse heat conduction problem with discrete wavelet transform

We consider as a test case the linear one-dimensional inverse heat conduction problem. Usual regularization methods are equivalent to filtering out high-frequency components, in a uniform way on the whole stretch of data. This sets a limit to the trade-off that can be obtained between good resolution and efficient noise reduction. To overcome this limit, we propose the use of wavelet decomposition, which enables us to perform time–frequency analysis of the data content. A simple thresholding algorithm is used to eliminate noise components. The method is compared with the usual singular-value decomposition. Preliminary results on simple test cases show that wavelet decomposition permits us to enhance the results of the inversion procedure, by giving smoother estimates of slow-varying parts of the solution while maintaining a sharp estimation of fast transients.