Spectrum deconvolution: the indicator for the balance region and regularization parameter choice by the +S-curve method

When solving the problem of spectrum deconvolution, i.e., the problem of eliminating the distorting influence of equipment during the registration of experimental spectrometric data, the choice of the regularization parameter (RP) in the commonly used regularization method is important. In the article, a tool (indicator) for determining the region of favorable values of the RP is proposed. The indicator shows the range of values of the RP for which a balance is observed between the size of a regularized solution and its fit to the given data. The graphical form of the balance range indicator (+S-curve) is convenient for comparing different RP choice methods. In the article own version of RP choice based on the +S-curve is proposed. The new approach is compared with popular RP choice methods such as the discrepancy principle and the L-curve method.