MAP-based blind infrared spectral deconvolution via modified total variation regularization for mixture identification

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Infrared (IR) spectral signals have problems with random noise and overlapping of adjacent peaks. To address these issues, we proposed a novel infrared spectral reconstruction model with improved total variation. The maximum a posteriori theory (MAP) is introduced to build the signal reconstruction model for the latent infrared spectrum. The proposed model can remove the random spectral noise and generate new peaks. In the MAP architecture, the prior probability is modeled as an improved total variation constraint, the spectral noise based on the Gaussian distribution is constructed for the likelihood probability distribution. Then, the proposed infrared spectral signal model is optimized by the famous split Bregman iteration approach. The high-quality infrared spectrum and instrument function can be estimated from the simulated and real spectral signals using the proposed model. The compared experiments show the good performance in suppressing spectral noise and splitting overlap peaks.