Sanya Liu

Richardson–Lucy blind deconvolution of spectroscopic data with wavelet regularization

In this work, we introduce a blind deconvolution approach with wavelet regularization for the Raman spectrum and total variation regularization for instrument function. The proposed algorithm can effectively suppress the Poisson noise as well as preserve the spectral structure information. Moreover, the split Bregman method is adopted to solve the proposed model. The comparative results on the simulated and measured Raman spectra show that the wavelet-based method outperforms the conventional methods. The deconvolution Raman spectrum is more convenient for extracting the spectral feature and interpreting the unknown chemical mixtures.

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

Spectroscopic data often suffer from common problems of band overlap and noise. This paper presents a maximum a posteriori (MAP)-based algorithm for the band overlap problem. In the MAP framework, the likelihood probability density function (PDF) is constructed with Gaussian noise assumed, and the prior PDF is constructed with adaptive total variation (ATV) regularization. The split Bregman iteration algorithm is employed to optimize the ATV spectral deconvolution model and accelerate the speed of the spectral deconvolution. The main advantage of this algorithm is that it can obtain peak structure information as well as suppress noise simultaneity. Simulated and real spectra experiments manifest that this algorithm can satisfactorily recover the overlap peaks as well as suppress noise and are robust to the regularization parameter.

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.

Blind spectral deconvolution algorithm for Raman spectrum with Poisson noise

A blind deconvolution algorithm with modified Tikhonov regularization is introduced. To improve the spectral resolution, spectral structure information is incorporated into regularization by using the adaptive term to distinguish the spectral structure from other regions. The proposed algorithm can effectively suppress Poisson noise as well as preserve the spectral structure and detailed information. Moreover, it becomes more robust with the change of the regularization parameter. Comparative results on simulated and real degraded Raman spectra are reported. The recovered Raman spectra can easily extract the spectral features and interpret the unknown chemical mixture.

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.

Blind Spectral Signal Deconvolution with Sparsity Regularization: An Iteratively Reweighted Least-Squares Solution

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.

Blind Poissonian reconstruction algorithm via curvelet regularization for an FTIR spectrometer

An FTIR spectrometer often suffers from common problems of band overlap and Poisson noises. In this paper, we show that the issue of infrared (IR) spectrum degradation can be considered as a maximum a posterior (MAP) problem and solved by minimized a cost function that includes a likelihood term and two prior terms. In the MAP framework, the likelihood probability density function (PDF) is constructed based on the observed Poisson noise model. A fitted distribution of curvelet transform coefficient is used as spectral prior PDF, and the instrument response function (IRF) prior is described based on a Gauss-Markov function. Moreover, the split Bregman iteration method is employed to solve the resulting minimization problem, which highly reduces the computational load. As a result, the Poisson noises are perfectly removed, while the spectral structure information is well preserved. The novelty of the proposed method lies in its ability to estimate the IRF and latent spectrum in a joint framework, thus eliminating the degradation effects to a large extent. The reconstructed IR spectrum is more convenient for extracting the spectral feature and interpreting the unknown chemical or biological materials.

Nonlocal low-rank-based blind deconvolution of Raman spectroscopy for automatic target recognition

Raman spectroscopy often suffers from the problems of band overlap and random noise. In this work, we develop a nonlocal low-rank regularization (NLR) approach toward exploiting structured sparsity and explore its applications in Raman spectral deconvolution. Motivated by the observation that the rank of a ground-truth spectrum matrix is lower than that of the observed spectrum, a Raman spectral deconvolution model is formulated in our method to regularize the rank of the observed spectrum by total variation regularization. Then, an effective optimization algorithm is described to solve this model, which alternates between the instrument broadening function and latent spectrum until convergence. In addition to conceptual simplicity, the proposed method has achieved highly competent objective performance compared to several state-of-the-art methods in Raman spectrum deconvolution tasks. The restored Raman spectra are more suitable for extracting spectral features and recognizing the unknown materials or targets.

Band narrowing with sparsity regularization for spectroscopic data

Spectroscopic data often suffers from common problems of bands overlap and random Gaussian noise. Spectral resolution can be improved by mathematically removing the effect of the instrument response function (IRF). In this paper, a novelty model is proposed to deconvolute the measured spectrum with the sparsity regularization. The proposed model is solved by iteratively reweighted least square method. The major novelty of the proposed method is that it can estimate the IRF and latent spectrum simultaneously. Experimental results with actual Raman spectra manifest that this algorithm can recover the overlap peaks as well as suppress the noise effectively.

Parametric spectral signal restoration via maximum entropy constraint and its application

In this paper, we will propose a new framework which can estimate the desired signal and the instrument response function (IRF) simultaneously from the degraded spectral signal. Firstly, the spectral signal is considered as a distribution, thus, new entropy (called differential-entropy, DE) is defined to measure the distribution with a uniform distribution, which allows negative value existing. Moreover, the IRF is parametrically modeled as a Lorentzian function. Comparative results manifest that the proposed method outperforms the conventional methods on peak narrowing and noise suppression. The deconvolution IR spectrum is more convenient for extracting the spectral feature and interpreting the unknown chemical mixtures.