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 Mössbauer spectra as examples.
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D. Hong, J. J. A. van Asten, S. R. Rankouhi, J.-W. Thielen, and D. G. Norris, J. Magn. Reson., 304, 53–61 (2019); https://doi.org/https://doi.org/10.1016/j.jmr.2019.05.002.
V. Fernandez, D. Kiani, N. Fairley, F.-X. Felpin, and J. Baltrusaitis, Appl. Surf. Sci., 505, 143841 (2020), https://doi.org/https://doi.org/10.1016/j.apsusc.2019.143841.
F. Ambrosino, Appl. Radiat. Isot., 159, 109090 (2020), https://doi.org/https://doi.org/10.1016/j.apradiso.2020.109090.
J. M. Borrego, A. Conde, V. A. Pena-Rodriguez, and J. M. Greneche, Hyperfine Interact., 131, 67–82 (2000), https://doi.org/https://doi.org/10.1023/A:1010858927701.
N. V. Baidakova, N. I. Chernykh, V. M. Koloskov, and Y. N. Subbotin, Ural Math. J., 3, No. 2, 33–39 (2017), http://dx.doi.org//https://doi.org/10.15826/umj.2017.2.005.
F. Yue, Cheng Chen, Z. Yan, Chen Chen, Z. Guo, Z. Zhang, Z. Chen, F. Zhang, and X. Lv, Photodiagn. Photodyn. Ther., 32, 101923 (2020), https://doi.org/https://doi.org/10.1016/j.pdpdt.2020.101923.
E. Juszynska-Galazka, N. Osiecka, and A. Budziak, Vib. Spectrosc., 92, 62–69 (2017), https://doi.org/https://doi.org/10.1016/j.vibspec.2017.05.004.
P. Jutaporn, M. D. Armstrong, and O. Coronell, Water Res., 172, 115460 (2020), https://doi.org/https://doi.org/10.1016/j.watres.2019.115460.
L. Liu, Y. Cheng, X. Sun, and F. Pi, Spectrochim. Acta, Part A, 197, 153–158 (2018), https://doi.org/https://doi.org/10.1016/j.saa.2018.01.022.
J. Yang, X. Wang, R. Wang, and H. Wang, Geoderma, 380, 114616 (2020), https://doi.org/https://doi.org/10.1016/j.geoderma.2020.114616.
N. Hakimi, A. Jodeiri, M. Mirbagheri, and S.K. Setarehdan, Comput. Biol. Med., 121, 103810 (2020), https://doi.org/https://doi.org/10.1016/j.compbiomed.2020.103810.
Z. Shafahi, S. Sina, and R. Faghihi, Radiat. Phys. Chem., 166, 108437 (2020), https://doi.org/https://doi.org/10.1016/j.radphyschem.2019.108437.
A. L. Gavrilyuk, D. A. Osinkin, and D. I. Bronin, Electrochim. Acta, 354, 136683 (2020), https://doi.org/https://doi.org/10.1016/j.electacta.2020.136683.
L. F. Ibanez and G. Jeschke, J. Magn. Reson., 300, 28–40 (2019), https://doi.org/https://doi.org/10.1016/j.jmr.2019.01.008.
T. H. Edwards and S. Stoll, J. Magn. Reson., 288, 58–68 (2018), http://doi.org/https://doi.org/10.1016/j.jmr.2018.01.021.
A. L. Ageev, M. E. Korshunov, T. Ye. Reich, T. Reich, and H. Moll, J. Inverse Ill-Posed Probl., 15, 767–783 (2007), https://doi.org/https://doi.org/10.1515/jiip.2007.041.
S. Morigi, L. Reichel, and F. Sgallari, Numer. Algorithms, 43, 197–213 (2006), http://doi.org/https://doi.org/10.1007/s11075-006-9053-3.
Zh. Zh. Bai, A. Buccini, K. Hayamic, and L. Reichel, J. Comput. Appl. Math., 319, 1–13 (2017), http://dx.doi.org/https://doi.org/10.1016/j.cam.2016.12.023.
A. Buccini, Appl. Numer. Math., 116, 64–81 (2017), http://dx.doi.org/https://doi.org/10.1016/j.apnum.2016.07.009.
D. Bianchi, A. Buccini, M. Donatelli, and S. Serra-Capizzano, Inverse Probl., 31, 055005 (2015), https://doi.org/https://doi.org/10.1088/0266-5611/31/5/055005.
G. K. Wertheim, Mössbauer Effect: Principles and Applications, Academic Press (2013).
B. K. Teo, EXAFS: Basic Principles and Data Analysis, Springer (1986).
J. F. Moulder, Handbook of X-ray Photoelectron Spectroscopy, Physical Electronics Division Perkin-Elmer Corporation (1992).
T. Carlson, Photoelectron and Auger Spectroscopy, Springer US (1975), https://www.springer.com/gp/book/9781475701203.
V. Sizikov and D. Sidorov, Appl. Spectrosc., 71, No. 7, 1640–1651 (2017), https://doi.org/https://doi.org/10.1177/0003702817694181.
V. P. Gladkov, V. A. Kashcheev, A. Kh. Kuskov, and V. I. Petrov, J. Appl. Spectrosc., 71, No. 5, 731–735 (2004), https://doi.org/https://doi.org/10.1023/B:JAPS.0000049636.15453.0c.
Yu. A. Babanov, O. M. Nemtsova, I. Yu. Kamensky, and S. S. Mikhailova, J. Electron. Spectrosc. Relat. Phenom., 182, No. 3, 90–96 (2010), https://doi.org/https://doi.org/10.1016/j.elspec.2010.07.008.
G. D. Reddy, Appl. Math. Computation, 347, 464–476 (2019), https://doi.org/https://doi.org/10.1016/j.amc.2018.11.015.
O. M. Nemtsova and G. N. Konygin, J. Appl. Spectrosc., 85, 931–935 (2018), https://doi.org/https://doi.org/10.1007/s10812-018-0741-2.
V. E. Porsev, O. M. Nemtsova, and G. N. Konygin, Khim. Fiz. Mezoskopiya, 21, No. 4, 514–524 (2019), https://doi.org/https://doi.org/10.15350/17270529.2019.4.54.
A. N. Tikhonov and V. Y. Arsenin, Solution of Ill-posed Problems, Winston & Sons, Washington (1977).
K. Pearson, London, Edinburgh Dublin Philos. Mag. J. Sci., 50, No. 5, 157–175 (1900).
J. Prakash, D. Sanny, S. K. Kalva, M. Pramanik, and Ph. K. Yalavarthy, IEEE Trans. Med. Imaging, 38, No. 8, 1935–1947 (2019), http://doi.org/https://doi.org/10.1109/TMI.2018.2889314.
B. Qiao, Junjiang Liu, Jinxin Liu, Zh. Yang, and X. Chen, Mech. Syst. Signal Process., 126, 341–367 (2019), https://doi.org/https://doi.org/10.1016/j.ymssp.2019.02.039.
B. W. Rust and D. P. O'Leary, Inverse Probl., 24, 034005 (2008), http://doi:https://doi.org/10.1088/0266-5611/24/3/034005.
L. Reichel, Numer. Algorithms, 63, 65–87 (2013), http://doi.org/https://doi.org/10.1007/s11075-012-9612-8.
G. N. Konygin, E. P. Elsukov, and V. E. Porsev, Phys. Met. Metallogr., 96, No. 3, 298–304 (2003).
A. K. Arzhnikov, L. V. Dobysheva, G. N. Konygin, and E. P. Elsukov, Phys. Solid State, 47, No. 11, 2063–2071 (2005), https://doi.org/https://doi.org/10.1134/1.2131146.
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Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 88, No. 2, pp. 315–324, March–April, 2021.
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Nemtsova, O.M., Konygin, G.N. & Porsev, V.E. Separation of Overlapping Spectral Lines Using the Tikhonov Regularization Method. J Appl Spectrosc 88, 373–381 (2021). https://doi.org/10.1007/s10812-021-01185-5
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DOI: https://doi.org/10.1007/s10812-021-01185-5