Approximation of spectrogrammes by cubic splines using the Kalman filter

The raw spectrogrammes are subject to systematic errors of an instrumental type that may be reduced provided a mathematical model of the instrumental imperfections is identified. It is assumed in the paper that this model has the form of an integral, convolution-type equation of the first kind. The correction of the spectrogrammes consists in numerically solving this equation on the basis of the noisy data acquired by a spectrometer. An algorithm of correction is proposed which is based on the approximation of the solution with a spline function whose parameters are determined by means of a recursive Kalman-filter-based algorithm with a non-negativity constraint imposed on the set of feasible solutions. It is shown, using synthetic and real spectrophotometric data, that an improvement in the quality of correction is attained