Separation of Spectral Lines from a Broadband Background and Noise Filtering by Modified Tikhonov Regularization

We propose a technique for processing noisy spectral data that implements a mathematically based selection of sharp signal peaks on an unknown smooth background, for which there is no reliable theoretical model. The fundamental concept of the technique is to construct an optimizing functional that gives the most probable parameters of spectral lines. Unlike the Tikhonov regularization method, where a smooth unknown function is extracted from a noisy signal, we consider the problem of regularizing the superposition of a smooth background function with sharp peaks. The proposed approach provides an algorithm for processing experimental data that makes it possible to filter out random noise and determine both the peak parameters 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 the statistical properties of random noise.