A linear inverse problem algorithm based on the wavelet-Galerkin method has been constructed to solve the single-component basic x-ray absorption spectrum fine structure (XAFS) equation. Daubechies wavelet and Landweber-Friedman-Bialy iteration are utilized in this formulation. Solutions for exact and noise-contaminated model K-edge Cu XAFS spectra are estimated to illustrate our method. It is possible to obtain a sufficiently exact solution for the radial distribution function with expansion by using rather a small number of wavelet bases. For the experimental K-edge Cu XAFS spectrum, our method predicts almost the exact locations of the peaks up to the third shell.
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Yamaguchi et al. (1999) studied this question.
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