High-order cumulant-based blind deconvolution of Raman spectra

The spectra recorded by a dispersion spectrophotometer are usually distorted by the response function of the instrument. To improve the resolving power, double or triple cascade spectrophotometers with narrow slits have been employed, but the total flux of the radiation available decreases accordingly, resulting in a low signal-to-noise ratio and a longer measuring time. The actual spectra can be restored approximately by mathematically removing the effects of the measuring instruments. Based on the Shalvi-Weinstein criterion, a (6, 2)-order normalized cumulant-based blind deconvolution algorithm for Raman spectral data is proposed. The actual spectral data and the unit-impulse response of the measuring instruments can be estimated simultaneously. By conducting experiments on real Raman spectra of some organic compounds, it is shown that this algorithm has a robust performance and fast convergence behavior and can improve the resolving power and correct the relative intensity distortion considerably.