Adaptive total variation-based spectral deconvolution with the split Bregman method

Spectral bandwidth correction with optimal parameters based on deep learning

Spectral bandwidth correction is an effective way to obtain the original spectrum. However, the correct selection of optimal parameters used to recover the distortion spectrum in bandwidth correction algorithms has always been an important problem. To overcome the shortcomings of traditional parameter selection methods and obtain the optimal parameter, we propose a new optimal parameter selection method based on deep learning (DL). First, the database and neural network were constructed, and then the optimal parameters of corresponding algorithms were obtained through the training of the neural network. In order to verify the superiority of the optimal parameter selection method based on DL, the Levenberg-Marquardt (L-M) and Richardson-Lucy (R-L) algorithms with corresponding optimal parameters were compared with the traditional L-M and R-L algorithms to recover the distortion white light-emitting diode, Raman spectrum, and compact fluorescent lamp spectrum. The type A uncertainty and root mean square error values of the different cases were calculated. The results proved that, compared with the traditional methods for obtaining the optimal parameters, the neural network was capable of obtaining parameters that can make the bandwidth correction algorithm more efficient at recovering the distorted spectrum.

Automated decomposition algorithm for Raman spectra based on a Voigt line profile model

Raman spectra measured by spectrometers usually suffer from band overlap and random noise. In this paper, an automated decomposition algorithm based on a Voigt line profile model for Raman spectra is proposed to solve this problem. To decompose a measured Raman spectrum, a Voigt line profile model is introduced to parameterize the measured spectrum, and a Gaussian function is used as the instrumental broadening function. Hence, the issue of spectral decomposition is transformed into a multiparameter optimization problem of the Voigt line profile model parameters. The algorithm can eliminate instrumental broadening, obtain a recovered Raman spectrum, resolve overlapping bands, and suppress random noise simultaneously. Moreover, the recovered spectrum can be decomposed to a group of Lorentzian functions. Experimental results on simulated Raman spectra show that the performance of this algorithm is much better than a commonly used blind deconvolution method. The algorithm has also been tested on the industrial Raman spectra of ortho-xylene and proved to be effective.

Infrared spectrum blind deconvolution algorithm via learned dictionaries and sparse representation

Band overlap and random noise are a serious problem in infrared spectra, especially for aging spectrometers. In this paper, we have presented a simple method for spectrum restoration. The proposed method is based on local operations, and involves sparse decompositions of each spectrum piece under an evolving overcomplete dictionary, and a simple averaging calculation. The content of the dictionary is of prime importance for the deconvolution process. Quantitative assessments of this technique on simulated and real spectra show significant improvements over the state-of-the-art methods. The proposed method can almost eliminate the effects of instrument aging. The features of these deconvoluted infrared spectra are more easily extracted, aiding the interpretation of unknown chemical mixtures.

Joint baseline-correction and denoising for Raman spectra

Laser instruments often suffer from the problem of baseline drift and random noise, which greatly degrade spectral quality. In this article, we propose a variation model that combines baseline correction and denoising. First, to guide the baseline estimation, morphological operations are adopted to extract the characteristics of the degraded spectrum. Second, to suppress noise in both the spectrum and baseline, Tikhonov regularization is introduced. Moreover, we describe an efficient optimization scheme that alternates between the latent spectrum estimation and the baseline correction until convergence. The major novel aspect of the proposed algorithms is the estimation of a smooth spectrum and removal of the baseline simultaneously. Results of a comparison with state-of-the-art methods demonstrate that the proposed method outperforms them in both qualitative and quantitative assessments.