The problem of reconstructing gas concentrations in laser photoacoustic gas analysis is considered. Signal processing procedures based on the search for quasi-solutions of the ill-posed problems are described for the differential absorption method. The results of mathematical modeling and processing of experimental data are presented. It is shown that using the search for quasi-solutions based on neural network algorithms it is possible to solve efficiently the problem of gas concentration reconstruction for both few- and many-component gas mixtures without involving additional information about the noise level in the measurement channels.