Cauchy-filter-based algorithms for reconstruction of absorption spectra

The computer-based interpretation of spectrometric data {y_n ^Tr} is aimed at identification of the main components of an analyte. The first step of interpretation consists in estimation of its spectrum using an operator of (generalized) deconvolution {xˆ_n^Tr}=R[{y_n^~Tr}, p _R], where p_R is a vector of parameters to be estimated during calibration of the spectrometer. A new structure of this operator based on a nonlinear transformation of the Cauchy filter, is proposed and studied in this paper using both synthetic and real-world spectrophotometric data. Its superiority over existing algorithms for spectrum reconstruction is demonstrated both with respect to accuracy of spectrum reconstruction and numerical complexity