SEPARATION OF SPECTRAL LINES FROM A BROADBAND BACKGROUND AND NOISE FILTRATION BY THE MODIFIED TIKHONOV REGULARIZATION
I.A. Larkin1, A.V. Vagov2, V.I. Korepanov1
1Institute of Microelectronics Technology and High Purity Materials, Russian Academy of Sciences (IMT RAS), Chernogolovka, Russia
2HSE Tikhonov Moscow Institute of Electronics and Mathematics, National Research University Higher School of Economics, Moscow, Russia
Keywords: Raman scattering, Tikhonov regularization, data processing
Abstract
In this paper, we propose a technique for processing noisy spectral data, which allows implementing a mathematically sound selection of sharp signal peaks above an unknown smooth background, for which there is no reliable theoretical model. The main idea of the method is to construct an optimizing functional that predicts the most probable parameters of spectral lines. Unlike the Tikhonov regularization method, in which a smooth unknown function is extracted from the noisy signal, here we consider the problem of regularization of the superposition of a smooth background function with sharp peaks. The proposed approach provides an algorithm for processing experimental data that allows us to filter out random noise and determine both the parameters of the peaks and the background function with good accuracy. Finding the optimal regularization parameters is based on a priori assumptions about the smoothness of the background function and statistical properties of the random noise.
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