Separation of Overlapping Spectral Lines Using the Tikhonov Regularization Method

An algorithm for separating overlapping spectral components using the Tikhonov weighted regularization method is proposed. Use of the weighting function allows one to significantly reduce the regularization parameters and separate closely spaced spectral lines. The problem of the appearance of spurious oscillations in a sparse solution is solved by an iterative algorithm for correcting the main matrix. An a posteriori minimum threshold algorithm is used to determine the regularization parameter that provides the maximum resolution of the method. Use of the algorithm fundamentally improves the quality of spectra processing and increases the information content of the spectroscopic methods. The efficiency of the proposed algorithm is shown using processing of model and experimental Mossbauer spectra as examples.