Cauchy-filter-based algorithms for reconstruction of absorption spectra

The computer-based interpretation of spectrometric data {y/spl tilde//sub n//sup Tr/} is aimed at identification of the main components of an analyte. The first step of interpretation consists of estimation of its spectrum using an operator R of (generalized) deconvolution {x/spl circ//sub n//sup Tr/}=R[{y/spl tilde//sub n//sup Tr/}; p/sub R/], where p/sub 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.