Maximum Entropy Deconvolution of Infrared Spectra: Use of a Novel Entropy Expression without Sign Restriction

Abstract

Absorbance and difference infrared spectra are often acquired aiming to characterize protein structure and structural changes of proteins upon ligand binding, as well as for many other chemical and biochemical studies. Their analysis requires as a first step the identification of the component bands (number, position, and area) and as a second step their assignment. The first step of the analysis is challenged by the habitually strong band overlap in infrared spectra. Therefore, it is useful to make use of a mathematical method able to narrow the component bands to the extent to eliminate, or at least reduce, the band overlap. Additionally, to be of general applicability this method should permit negative values for the solution. We present a maximum entropy deconvolution approach for the band-narrowing of absorbance and difference spectra showing the required characteristics, which uses the generalized negative Burg-entropy (Itakura-Saito discrepancy) generalized for difference spectra. We present results on synthetic noisy absorbance and difference spectra, as well as on experimental infrared spectra from the membrane protein bacteriorhodopsin.

Blind Spectral Signal Deconvolution with Sparsity Regularization: An Iteratively Reweighted Least-Squares Solution

“…Different approaches to spectral deconvolution have been proposed over the recent past [1,6,13,14,16,17,19,22,26,27,29]. The existing algorithms can be classified into two major categories: curve-fitting [1,16] and spectral deconvolution [6,22,27,29]. With the curve-fitting [16] method, the measured spectral signal can be fitted by a Gaussian, Lorentzian, or Voigt function or a combination of these functions.…”

Peak separation by derivative spectroscopy applied to ftir analysis of hydrolized silica

“…While the former can be solved by increasing instrumental resolution, the later can be reversed only by mathematical methods. 1 Overlapping due to intrinsic factors is more likely to be observed in spectra of materials with random structures like glass or water, characterized by fewer bands and peak broadening. [2][3][4] The first step to investigate the spectrum for hidden and overlapped peaks is to gather all information available on the system under investigation.…”

“…5,6 In the first method, the measured spectrum is divided by the instrumental function to reverse signal distortion 5 and this can be conveniently done in the Fourier domain. 6,7 Several methods have been developed for deconvolution recently, 1,[8][9][10][11][12] spurred mainly by the advance of personal computers. 13 Deconvolution is performed numerically.…”

“…It is an unstable process and different strategies have been proposed for stabilization. 1 The second method involves the analysis of the second 6,14 or the fourth derivative 15 of the spectrum.…”

“…5,6 First and higher order spectrum derivatives can be obtained by successive numerical differentiation of the digitized data according to the following algorithm: (1) where (Y i+1 /X i+1 ) and (Y i-1 /X i-1 ) are, respectively, the subsequent and preceding data points of the (Y i /X i ) data point. Since differentiation introduces noise amplification, if necessary, differentiation should be followed by data smoothing.…”