Discrete wedgelet transform regularization-based spectral deconvolution for infrared spectroscopy

Infrared spectral data often exhibit band overlap and random noise when it is applied to recognize the unknown chemical materials. To address these issues, a novel regularization-based spectral deconvolution method for unknown chemical material detection (DWTSD) was proposed in this paper. The discrete wedgelet transform is introduced to analyze the difference between the latent infrared spectrum and the noisy infrared spectrum. The instrument response function is also needed to estimate simultaneously with the latent infrared spectrum. Therefore, the improved total variation regularization is introduced to constrain the smoothness of the spectral lines. Then the split Bregman iteration algorithm is also introduced to optimize the cost function. The proposed DWTSD method is simple and offers good performance with low computational load. Experimental results on simulated and real infrared spectrums show that the proposed DWTSD method has good performance in noise reduction and spectral detail generation. With the proposed methodology, the problem of instrument aging can be largely eliminated, making the reconstruction of infrared spectra a more convenient tool for the extraction of features of an unknown material and their interpretation. The applicability of the method transcends infrared spectroscopy, offering utility in a spectrum of spectroscopic analyses.