Spline-based LMS method with constraints for spectrophotometric data correction

The results of spectrophotometric measurements are subject to systematic errors of instrumental type which may be partially corrected provided a mathematical model of the instrumental imperfections is identified. It is assumed that this model has the form of an integral, convolution-type equation of the first kind. The correction of the results of measurements subject to random measurement errors consists in the numerical solution of this equation on the basis of these results. An algorithm of correction is proposed. It is based on the approximation of the solution with a spline function whose parameters are determined using the least-mean square (LMS) method with two constraints of the set of feasible solutions. The efficiency of the incorporation of these constraints into the algorithm of correction is demonstrated using synthetic data. The possibility of improving resolution of spectrometric measurements is shown using specially acquired sets of spectrometric data