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Raman spectroscopy grows into an essential tool for biomedical applications. Nevertheless, the weak Raman signal associated mainly with biological samples is often obscured by a broad background signal due to the intrinsic fluorescence of the organic molecules present, making further analysis unfeasible. A computational geometry method based on the definition of convex hull is described to estimate the background from Raman spectra of samples with biological interest. The method is semiautomated requiring sample-dependent user intervention. It does not depend, however, on curve fitting, requires no information about background distribution or source, and keeps the original spectral data intact.

Raman spectroscopy has been extensively applied in recent years in a variety of biological research ranging from the in situ tissue diagnosis to the analysis of subcellular components. Being a vibrational spectroscopic technique based on inelastic scattering, Raman spectroscopy provides rich molecular information about the chemical composition of samples and exhibits high sensitivity to minute biochemical changes. Furthermore, it is attractive for biomedical studies since it is intrinsically nonintrusive and does not require external labels. The positions and relative intensities of the Raman bands are the basic spectral characteristics for exploring the structure and the function of several biological molecules. This interpretation, however, is often hindered by the broad background signal mostly due to fluorescence from organic molecules and contaminants. The intensity of fluorescent is usually much higher than the weak Raman signal in biological samples, and therefore the subtraction of background is an essential process to extract reliable analytical information from biomedical Raman data.

Apart from instrumental specific design approaches, a number of computational methods have been proposed for background removal from Raman spectra. These methods include polynomial fitting [

In the present study, we describe a novel semiautomated background removal method which is based on the geometric definition of convex hull [

The signal,

The algorithm was implemented in Mathematica software package (Wolfram Research). For signals sampled at discrete intervals, as in our case, Mathematica uses the discrete Fourier transform [

Simulated spectrum consisting of three Gaussian peaks with curved background and random noise is shown in Figure

Simulated spectrum with curved background and random noise. (a) Fourier filtering, (b) convex optimization, (c) background estimation.

As previously discussed, the first step, (a), is the low-pass filtering, the second step, (b), is finding and optimizing the convex sets, and the last one, (c), is joining the convex sets in a continuous manner. In the case of simulated data, the performance of the algorithm is flawless. Figures

Raman spectrum of paracetamol. (a) Fourier filtering, (b) convex optimization, (c) background estimation.

Raman spectrum of PAT. (a) Fourier filtering, (b) convex optimization, (c) background estimation.

Raman spectrum of chondrocytes in cartilage. (a) Fourier filtering, (b) convex optimization, (c) background estimation.

It is evident that the more complicated the signal is, the more Fourier components are needed to approximate the experimental baseline curve. A rough approximation, however, is adequate even for complicated spectra with several bands (Figure

A computational geometry method for the estimation of the Raman background signal of highly fluorescent samples has been described in this study. Background subtraction was achieved in all cases while the peaks were preserved. The proposed algorithm is semiautomated and requires user input for two variables which define the degree of the Fourier series approximation and the connection of the convex sets. The method is valid for all signals which are convex, that is, one-directional, and, as such, it can be possibly applied to other spectroscopic techniques as well as X-ray powder diffractograms. Preliminary results confirm its wide applicability across diverse spectroscopic data.

The authors thank Dr. Zhi-Min Zhang and Dr. Claudia Beleites for providing the raw data considered in this paper.