A frequency deconvolution procedure using a conjugate-gradient minimization method with suitable constraints

In a variety of spectroscopic techniques the fundamental problem exists of determination of the individual spectral components, intrinsically overlapped in the measured spectrum. This is a typical deconvolution problem and several methods and techniques have been proposed for its solution in the technical literature, but suggestions of new approaches are still of interest. A new deconvolution procedure is presented here based on the use of the conjugate gradient minimization algorithm with the addition of suitable constraints directly obtained by the application to the measured spectrum of the second-derivative operator or more sophisticated resolution enhancement procedures. Since in the examined case deconvolution essentially requires the minimization of a non-convex function, the use of such constraints is extremely important to supply suitable input parameters to the conjugate gradient algorithm to avoid obtaining minimum points which have no physical meaning. In our case each spectral component used for deconvolution has been assumed to have a Gaussian analytical definition fully identified by three parameters (amplitude, central frequency, spectral bandwidth), so that the input values required to start the deconvolution process are the number M of Gaussian components and 3M suitable initial approximations of the parameters above. It is shown that all this information can be obtained from the measured data. The deconvolution procedure was implemented by a FORTRAN Microsoft Version 5.1 program and experimental results relative to spectroscopic data obtained by FT-IR analysis of human serum albumin are reported. The results are discussed and compared with data obtained by the use of other techniques.