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All signals obtained as instrumental response of analytical apparatus areaffected by noise, as in Raman spectroscopy. Whereas Raman scattering is aninherently weak process, the noise background can lead to misinterpretations.Although surface amplification of the Raman signal using metallic nanoparticleshas been a strategy employed to partially solve the signal-to-noise problem,the pre-processing of Raman spectral data through the use of mathematicalfilters has become an integral part of Raman spectroscopy analysis. In thispaper, a Tikhonov modified method to remove random noise in experimental datais presented. In order to refine and improve the Tikhonov method as filter, theproposed method includes Euclidean norm of the fractional-order derivative ofthe solution as an additional criterion in Tikhonov function. In the strategyused here, the solution depends on the regularization parameter, $\lambda$, andon the fractional derivative order, $\alpha$. As will be demonstrated, with thealgorithm presented here, it is possible to obtain a noise free spectrumwithout affecting the fidelity of the molecular signal. In this alternative,the fractional derivative works as a fine control parameter for the usualTikhonov method. The proposed method was applied to simulated data and tosurface-enhanced Raman scattering (SERS) spectra of crystal violet dye in Agnanoparticles colloidal dispersion.

Smoothing and differentiation of data by Tikhonov and fractional  derivative tools, applied to surface-enhanced Raman scattering (SERS) spectra  of crystal violet dye