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Spectral signals often suffer from the common problems of band overlap and random Gaussian noise. To address these problems, we propose a sparsity regularization-based model that deconvolutes the degraded spectral signals. Sparsity regularization is achieved by fitting the probability density function of the gradient of the signal, and then, the iteratively reweighted least-squares method is used to solve the minimization problem. Results from experiments using real spectral signals showed that this algorithm separates the overlapping peaks and effectively suppresses the noise. The deconvoluted spectral signals will promote the practical application of infrared spectral analysis in the fields of target recognition, material identification, and chemometrics analysis. [ABSTRACT FROM AUTHOR]

• A novelty infrared imaging technology for facial express recognition with convolution neural network. • Discrete beamlet transform regularization is designed to retain infrared spectral structures. • The split Bregman iteration algorithm is introduced to optimize the proposed DBTR-BR model. • The proposed model is applied for infrared facial expression recognition problem in Oulu-CASIA dataset. Facial expression recognition is an important research topic in the field of human-machine interaction. Infrared imaging technology has illustrated good potential in the applications of facial expression recognition and computer vision. But the low-resolution spectral data has limited its applications, such as band overlap and random noises. To address the problems, a rapid blind restoration model with discrete beamlet transforms regularization is presented to reconstruct the infrared spectrum. To compare the sparsity between the observed infrared spectrum and ground-truth one in frequency domain, the discrete beamlet transforms is applied to analyze the different of their coefficients distributions. We propose an IR spectral deconvolution model with the sparsity coefficients regularization by L 0 -norm. We execute the proposed algorithm on the simulated and actual IR spectrum data, and the results demonstrate that can effectively suppress the Poisson noises and retain infrared spectral structure. The high-resolution IR spectrum can raise the recognition rate of facial expression classification task. [ABSTRACT FROM AUTHOR]