Deterministic regularization method for the problem of background line identification in experimental data analysis

Tikhonov’s regularization method is applied to develop an efficient algorithm and the corresponding programs for identifying a smooth background line. The algorithm can also be used to construct the filtering function. Some applications are examined. The problem of background line identification often arises in primary analysis of physical experimental data, when the background component has to be extracted from the raw observations. This is primarily associated with the analysis of diffraction spectra in neutronography, Auger spectroscopy, gas electronography, and with the analysis of Debye powder diagrams. Random factors are generally responsible for the creation of the background line, and it is not always known what physical factors are actually responsible for its appearance. The key issue in background line identification is therefore how to choose the modeling functions. The main properties of these functions are smoothness and boundedness of the curvature function. The curvature function is defined as