The Role and Selection of the Filter Function in Fourier Self-Deconvolution Revisited

Abstract

Overlapped bands often appear in applications of infrared spectroscopy, for instance in the analysis of the amide I band of proteins. Fourier self-deconvolution (FSD) is a popular band-narrowing mathematical method, allowing for the resolution of overlapped bands. The filter function used in FSD plays a significant role in the factor by which the deconvolved bands are actually narrowed (the effective narrowing), as well as in the final signal-to-noise degradation induced by FSD. Moreover, the filter function determines, to a good extent, the band-shape of the deconvolved bands. For instance, the intensity of the harmful side-lobule oscillations that appear in over-deconvolution depends importantly on the filter function used. In the present paper we characterized the resulting band shape, effective narrowing, and signal-to-noise degradation in infra-, self-, and over-deconvolution conditions for several filter functions: Triangle, Bessel, Hanning, Gaussian, Sinc2, and Triangle2. We also introduced and characterized new filters based on the modification of the Blackmann filter. Our conclusion is that the Bessel filter (in infra-, self-, and mild over-deconvolution), the newly introduced BL3 filter (in self- and mild/moderate over-deconvolution), and the Gaussian filter (in moderate/strong over-deconvolution) are the most suitable filter functions to be used in FSD.

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

“…To demonstrate the effectiveness of the proposed method, we compared two nonblind deconvolution methods, FSD [7] and SDTR (spectral deconvolution with Tikhonov regularization) [20], both of which need an accurate IRF, with the proposed method.…”

Blind infrared spectroscopic data restoration with the similarity of multi-scales regularization

“…All the test spectra were normalized to [0, 1]. Three spectral deconvolution methods, the Fourier-self deconvolution method (FSD) [11], semi-blind deconvolution method (SBD) [13] and blind deconvolution with adaptive total variation method (BD-ATV) [18] were compared. In order to give an overall evaluation, five quantitative indexes are employed.…”

“…It is seen that all the deconvolution methods raise the indexes, but the proposed method obtains the highest values for the six spectra. [11]. (c) BD-ATV method [18].…”

“…In sum, all the deconvolution methods for spectroscopic data can be divided into three types: the nonblind deconvolution (NBD) method [11,12] with the known instrument function, semi-blind deconvolution (SBD) [13,14] method with the parametrically modeled instrument function, and the blind deconvolution (BD) [15] method with unknown instrument function. Because the instrument function is hardly known when the degraded spectrum captured using an infrared spectrometer, we only concern the blind case in this paper.…”

Spectral pre-processing for biomedical vibrational spectroscopy and microspectroscopic imaging

“…When applying FSD to real data one should be aware of the fact that the actual shape of the FSD filter function defines the factor by which the deconvolved bands are narrowed. Furthermore, FSD filter functions determine the shape of deconvolved bands and the SNR degradation in the FSD spectra [38]. Inadequate FSD filter parameters may result in under-or over-deconvolution, with the latter one characterized by noise amplification and the appearance of large negative side-lobes (see [31,38,39] for details].…”