Baseline Search in Raman Spectroscopy by Modified Tikhonov Regularization with Automatic Choice of Both Parameters

Baseline estimation in vibrational spectroscopy can be done efficiently with Tikhonov regularization. The state-of-the-art approaches, based on asymmetric weighting, require an additional parameter. Besides λ, the penalty for the second derivative, they introduce the asymmetry parameter p that sets different weights for the points above and below the baseline. To choose the parameters "once and for all" is not possible, because they always depend on the noise level and baseline flexibility. Currently, the common practice is to choose these two parameters visually, without any well-defined criteria. The present work shows how such criteria can be constructed in a form of a specific functional. This formulation makes it possible to optimize the regularization parameters for the given spectrum. The Python code is provided for the derivative-and-peak-screened ALS algorithm.