Constrained nonlinear method for estimating component spectra from multicomponent mixtures

Sasaki, Keiji; Kawata, Satoshi; Minami, Shigeo

doi:10.1364/ao.22.003599

Cited by 78 publications

(43 citation statements)

References 10 publications

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“…Since only accounting for non-negativity does not ensure the uniqueness of the solution, this approach leads to a set of admissible solutions [1,[9][10][11][12]. In order to reduce this set [13,14] suggest to add further constraints, in addition to the non-negativity, and propose to search a linear transformation by minimizing a compound criterion, in which a first part penalizes negative estimates of the pure spectra and mixing coefficients, and the second part uses an entropic cost function to make the estimated spectra smoother and mutually independent.…”

Section: Algebraic Methodsmentioning

confidence: 99%

“…Permitted regions of the rotational parameters. These regions has been obtained using the method of [10]. The algorithm has been run with 1000 random initializations.…”

Section: Illustration Of the Methodsmentioning

confidence: 99%

“…A challenging task is to state the admissible solutions and to define further information or assumptions allowing to get a solution where the estimated pure spectra and mixing coefficients are as close as possible to the actual ones. To give an idea about the range of admissible solutions of the synthetic mixture data presented in 4.1, the algorithm of [10] is used to obtain a set of feasible linear transformations of the actual pure spectra and mixing coefficients yielding transformed pure spectra and mixing coefficients which also are non-negative. Assume pure spectra summing to unity and consider the transformation matrix given as…”

Section: Admissible Solutionsmentioning

confidence: 99%

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Bayesian analysis of spectral mixture data using Markov Chain Monte Carlo Methods

Moussaoui

Carteret

Brie

et al. 2006

Chemometrics and Intelligent Laboratory Systems

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This paper presents an original method for the analysis of multicomponent spectral data sets. The proposed algorithm is based on Bayesian estimation theory and Markov Chain Monte Carlo (MCMC) methods. Resolving spectral mixture analysis aims at recovering the unknown component spectra and at assessing the concentrations of the underlying species in the mixtures. In addition to non-negativity constraint, further assumptions are generally needed to get a unique resolution. The proposed statistical approach assumes mutually independent spectra and accounts for the non-negativity and the sparsity of both the pure component spectra and the concentration profiles. Gamma distribution priors are used to translate all these information in a probabilistic framework. The estimation is performed using MCMC methods which lead to an unsupervised algorithm, whose performances are assessed in a simulation study with a synthetic data set.

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Section: Algebraic Methodsmentioning

confidence: 99%

“…Permitted regions of the rotational parameters. These regions has been obtained using the method of [10]. The algorithm has been run with 1000 random initializations.…”

Section: Illustration Of the Methodsmentioning

confidence: 99%

Section: Admissible Solutionsmentioning

confidence: 99%

See 1 more Smart Citation

Bayesian analysis of spectral mixture data using Markov Chain Monte Carlo Methods

Moussaoui

Carteret

Brie

et al. 2006

Chemometrics and Intelligent Laboratory Systems

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show abstract

“…Minimum-entropy spectral reconstruction was initiated by Sasaki et al, 15,16 followed by Neal et al, 17 Brown and Harper 18 and Volkov. 19 Recently, we re-examined the entropy minimization approach for large-scale pure component spectral reconstruction.…”

Section: Computational Aspectsmentioning

confidence: 99%

Application of FT‐Raman and FTIR measurements using a novel spectral reconstruction algorithm

Sin

Widjaja

et al. 2003

J Raman Spectroscopy

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Recently, an advanced spectral reconstruction algorithm based on information entropy was developed to identify individual compounds contained in mixture spectra without recourse to any library or any a priori knowledge. In this study, standard mixtures containing various polycyclic aromatic hydrocarbons (PAHs) and a,!-dicarboxylic acids were measured by solid-state FT-Raman and FTIR spectroscopy, and this was followed by the application of the aforementioned algorithm to recover all pure component spectra contained therein. The results demonstrate that the developed algorithm successfully recovered the spectra of individual species even though only a very limited number of mixture spectral measurements were made. FT-Raman measurements coupled with chemometric analysis provides satisfactory pure spectral results for both PAHs and a,!-dicarboxylic acids. Additionally, FT-Raman measurements together with FTIR measurements provided even better spectral recovery for some of the a,!-dicarboxylic acids when using band-target entropy minimization (BTEM). This study demonstrates that chemometric analysis without a priori information provides a promising solution and simplified approach to identify individual components from samples containing a complex composition. In particular, this is desired for a better understanding of environmental samples.

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“…One of the more interesting and different approaches, proposed by Sasaki et al [7], involves entropy minimization. Indeed, entropy minimization is known to be a powerful pattern recognition tool [8] and is associated with the principle of simplicity [9].…”

mentioning

confidence: 99%

Weighted two-band target entropy minimization for the reconstruction of pure component mass spectra: Simulation studies and the application to real systems

Zhang

Garland

Zeng

et al. 2003

J. Am. Soc. Mass Spectrom.

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A method is proposed, on the basis of a recently developed algorithm-Band Target Entropy Minimization (BTEM)-to reconstruct mass spectra of pure components from mixture spectra. This method is particular useful in dealing with spectral data with discrete features (like mass spectra). Compared to the original BTEM, which has been applied to differentiable spectroscopies such as Fourier-transfer infrared spectroscopy (FTIR), ultraviolet (UV), Raman, and nuclear magnetic resonance (NMR), the latest modifications were obtained through: (1) Reformulating the objective function using the peak heights instead of their derivatives; (2) weighting the abstract vector V T to reduce the effect of noise; (3) using a two-peak targeting strategy (tBTEM) to deal with strongly overlapping peaks; and (4) using exhaustive search to locate all the component spectra. A set of 50 multi-component mass spectra was generated from ten reference experimental pure component spectra. Many of the compounds chosen have common MS fragments and therefore, many of the pure component spectra have considerable intensity in same data channels. In addition, a set of MS spectra from a real system with four components was used to examine the newly developed algorithm. Successful reconstruction of the ten component spectra of the simulated system and the four component spectra of the real system was rapidly achieved using the new tBTEM algorithm. The advantages of the new algorithm and its implication for rapid system identification of unknown mixtures are readily apparent. (J

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Constrained nonlinear method for estimating component spectra from multicomponent mixtures

Cited by 78 publications

References 10 publications

Bayesian analysis of spectral mixture data using Markov Chain Monte Carlo Methods

Bayesian analysis of spectral mixture data using Markov Chain Monte Carlo Methods

Application of FT‐Raman and FTIR measurements using a novel spectral reconstruction algorithm

Weighted two-band target entropy minimization for the reconstruction of pure component mass spectra: Simulation studies and the application to real systems

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