Band-target entropy minimization. A robust algorithm for pure component spectral recovery. Application to complex randomized mixtures of six components

A newly developed self-modeling curve resolution method, band-target entropy minimization (BTEM), is described. This method starts with the data decomposition of a set of spectroscopic mixture data using singular value decomposition. It is followed by the transformation of the orthonormal basis vectors/loading vectors into individual pure component spectra one at a time. The transformation is based in part on some seminal ideas borrowed from information entropy theory with the desire to maximize the simplicity of the recovered pure component spectrum. Thus, the proper estimate is obtained via minimization of the proposed information entropy function or via minimization of derivative and area of the spectral estimate. Nonnegativity constraints are also imposed on the recovered pure component spectral estimate and its corresponding concentrations. As its name suggests, in this method, one targets a spectral feature readily observed in loading vectors to retain, and then combinations of the loading vectors are searched to achieve the global minimum value of an appropriate objective function. The major advantage of this method is its one spectrum at a time approach and its capability of recovering minor components having low spectroscopic signals. To illustrate the application of BTEM, spectral resolution was performed on FT-IR measurements of very highly overlapping mixture spectra containing six organic species with a two-component background interference (air). BTEM estimates were also compared with the estimates obtained using other self-modeling curve resolution techniques, i.e., SIMPLISMA, IPCA, OPA-ALS, and SIMPLISMA-ALS.     

An information-theoretic methodology for the resolution of pure component spectra without prior information using spectroscopic measurements

The resolution of pure component spectra based on spectroscopic measurements from a reaction system is a challenging task for chemometric systems in the absence of a priori knowledge about the reaction components involved. A popular approach in the literature is based on constrained entropy minimization of the second-order derivative of the resolved pure component spectra. Using an analytical information theoretic framework, it can however be shown that minimization of this cost function is not sufficient to completely separate the underlying components from a set of mixture spectra. Instead, an augmented objective function derived from this analysis is proposed for complete minimization of the mutual information between separated components. The final optimization approach is further shown to be analog to independent component analysis (ICA), a signal processing technique successfully applied to biomedical and speech data to separate linear source mixtures in the absence of a priori information. The developed theoretical insights and proposed methodologies in this paper are illustrated in a simulation study on the separation of three component spectra based on absorbance data acquired from a first-order kinetic reaction system.     

Use of Raman microscopy and band-target entropy minimization analysis to identify dyes in a commercial stamp. Implications for authentication and counterfeit detection

Raman microscopy was used in mapping mode to collect more than 1000 spectra in a 100 microm x 100 microm area from a commercial stamp. Band-target entropy minimization (BTEM) was then employed to unmix the mixture spectra in order to extract the pure component spectra of the samples. Three pure component spectral patterns with good signal-to-noise ratios were recovered, and their spatial distributions were determined. The three pure component spectral patterns were then identified as copper phthalocyanine blue, calcite-like material, and yellow organic dye material by comparison to known spectral libraries. The present investigation, consisting of (1) advanced curve resolution (blind-source separation) followed by (2) spectral data base matching, readily suggests extensions to authenticity and counterfeit studies of other types of commercial objects. The presence or absence of specific observable components form the basis for assessment. The present spectral analysis (BTEM) is applicable to highly overlapping spectral information. Since a priori information such as the number of components present and spectral libraries are not needed in BTEM, and since minor signals arising from trace components can be reconstructed, this analysis offers a robust approach to a wide variety of material problems involving authenticity and counterfeit issues.     

Second-derivative variance minimization method for automated spectral subtraction

A new second-derivative variance minimization (SDVM) procedure is used to automatically extract spectra of a dilute component (solute) from a mixture whose spectrum is dominated by a major component (solvent). This procedure involves the subtraction of Savitzky-Golay second-derivative preprocessed pure solvent and mixture spectra by minimizing the variance of the difference spectrum. The resulting undifferentiated output spectra contain primarily features associated with the solute and/or solute-induced perturbations of the solvent. The SDVM method is found to outperform several related methods, including a previously proposed derivative minimization method, as demonstrated using 1000 randomly generated solute/solvent synthetic spectral pairs and experimental Raman spectra of dilute solutions of benzene in n-hexane and water in acetone. The former experimental solution produced SDVM difference spectra containing benzene bands with virtually no n-hexane interference, while the latter revealed water-induced shifts in acetone spectral features. Several other types of SDVM applications, such as the spectroscopic analysis of layered composites, are discussed.     

The multi-reconstruction entropy minimization method: unsupervised spectral reconstruction of pure components from mixture spectra, without the use of a priori information

The band-target entropy minimization method (BTEM) and its variant methods excel at reconstructing known/unknown pure spectra from mixtures without prior information. These mixtures may represent either non-reactive or even reactive systems. In this work, an unsupervised form of the entropy minimization curve resolution, namely, the multi-reconstruction entropy minimization method (MREM), is presented. MREM differs from BTEM by removing the need for band-targets and by introducing a multiple search routine to find multiple local entropy minima. This multiple search routine, which provides a rapid survey of spectral estimates, utilizes a localized form of Corona's simulated annealing method in the optimization. The objective functions and penalty functions of the BTEM type methods are essentially retained. Compared to BTEM type methods, MREM (1) searches for multiple local minima instead of a single global minimum and hence reconstructs many pure component spectra at once instead of one pure spectrum; and (2) utilizes a user-defined broad spectral range [v1, v2] for all searches instead of multiple user-defined narrow "targets" as in BTEM. The new MREM has been tested on four sets of real spectra using Fourier transform infrared spectroscopy (FT-IR), mass spectroscopy (MS), and ultraviolet-visible (UV-Vis) spectroscopy. The results show that MREM is computationally much faster than BTEM for finding the major components present. Also, because MREM does not rely on band targeting, it is very useful for spectra that have no localized features and are highly overlapping, such as UV-Vis.     

Remote monitoring of a multi-component liquid-phase organic synthesis by infrared emission spectroscopy: the recovery of pure component emissivities by band-target entropy minimization

A liquid-phase cycloaddition reaction near ambient temperature involving dimethyl acetylenedicarboxylate (DMAD) and cyclopentadiene (CP) as reactants was measured using a conventional Fourier transform infrared (FT-IR) spectrometer with an emission accessory. Two semi-batch experiments were performed and a total of 55 spectra were collected using a DTGS detector. Band-target entropy minimization (BTEM), a pure component spectral reconstruction technique, was applied to analyze the data set to retrieve the pure component emission spectrum from the reaction system. The estimated emission spectra of the solvent chloroform, DMAD, CP, and product, namely dimethyl bicyclo[2.2.1]-2,5-heptadiene-2,3-dicarboxylate, were all reconstructed with rather good quality. The estimated emission spectra are similar to independent FT-IR spectra of the same cycloaddition reaction. Using a least squares fit, the relative concentration profiles of the species are obtained. Because this appears to be the first time that a liquid-phase reaction has been monitored by infrared emission spectroscopy, further improvements and opportunities for general multi-phase liquid reaction monitoring are discussed.     

On the use of band-target entropy minimization to simplify the interpretation of two-dimensional correlation spectroscopy

Two-dimensional (2D) correlation spectroscopy has been extensively applied to analyze various vibrational spectroscopic data, especially infrared and Raman. However, when it is applied to real-world experimental data, which often contains various imperfections (such as noise interference, baseline fluctuations, and band-shifting) and highly overlapping bands, many artifacts and misleading features in synchronous and asynchronous maps will emerge, and this will lead to difficulties with interpretation. Therefore, an approach that counters many artifacts and therefore leads to simplified interpretation of 2D correlation analysis is certainly useful. In the present contribution, band-target entropy minimization (BTEM) is employed as a spectral pretreatment to handle many of the artifact problems before the application of 2D correlation analysis. BTEM is employed to elucidate the pure component spectra of mixtures and their corresponding concentration profiles. Two alternate forms of analysis result. In the first, the normally vxv problem is converted to an equivalent nvxnv problem, where n represents the number of species present. In the second, the pure component spectra are transformed into simple distributions, and an equivalent and less computationally intensive nv'xnv' problem results (v'相似文献   

Kinetic hard-modelling and spectral validation of rank-deficient spectroscopic data: A case study

In this case study, we apply a recently developed method to systematically predict the linear dependencies in concentration profiles and identify minimum requirements to enable optimisation of rate constants and pure component spectra via direct multivariate kinetic hard-modelling of spectroscopic data. This systematic method was applied to the rank-deficient acid catalysed reaction of benzophenone with phenylhydrazine in THF. Various experimental conditions (different dosing and initial concentrations) and data treatments (defining uncoloured species, including known component spectra into the analysis) were considered. For all these conditions, the kinetic mechanism of this condensation reaction was successfully validated by the agreement between fitted and independently measured mid-IR and UV–vis pure component spectra and by the highly reproducible fitted rate constants. This case study particularly demonstrated the value of the direct spectral fitting as a tool for the validation of rank-deficient kinetic mechanisms, as inherent contributions within the fitted component spectra, due to the definition of uncoloured species, can be systematically addressed.     

Development of 2D band-target entropy minimization and application to the deconvolution of multicomponent 2D nuclear magnetic resonance spectra

Spectral reconstruction from multicomponent spectroscopic data is the frequent primary goal in chemical system identification and exploratory chemometric studies. Various methods and techniques have been reported in the literature. However, few algorithms/methods have been devised for spectral recovery without the use of any a priori information. In the present studies, a higher dimensional entropy minimization method based on the BTEM algorithm (Widjaja, E.; Li, C.; Garland, M. Organometallics 2002, 21, 1991-1997.) and related techniques were extended to large-scale arrays, namely, 2D NMR spectroscopy. The performance of this novel method had been successfully verified on various real experimental mixture spectra from a series of randomized 2D NMR mixtures (COSY NMR and HSQC NMR). With the new algorithm and raw multicomponent NMR alone, it was possible to reconstruct the pure spectroscopic patterns and calculate the relative concentration of each species without recourse to any libraries or any other a priori information. The potential advantages of this novel algorithm and its implications for general chemical system identification of unknown mixtures are discussed.     

Combined use of conventional and second-derivative data in the SIMPLISMA self-modeling mixture analysis approach

Simple-to-use interactive self-modeling mixture analysis (SIMPLISMA) is a successful pure variable approach to resolve spectral mixture data. A pure variable (e.g., wavenumber, frequency number, etc.) is defined as a variable that has significant contributions from only one of the pure components in the mixture data set. For spectral data with highly overlapping pure components or significant baselines, the pure variable approach has limitations; however, in this case, second-derivative spectra can be used. In some spectroscopies, very wide peaks of components of interest are overlapping with narrow peaks of interest. In these cases, the use of conventional data in SIMPLISMA will not result in proper pure variables. The use of second-derivative data will not be successful, since the wide peaks are lost. This paper describes a new SIMPLISMA approach in which both the conventional spectra (for pure variables of wide peaks) and second-derivative spectra (for pure variables of narrow peaks, overlapping with the wide peaks) are used. This new approach is able to properly resolve spectra with wide and narrow peaks and minimizes baseline problems by resolving them as separate components. Examples will be given of NMR spectra of surfactants and Raman imaging data of dust particle samples taken from a lead and zinc factory's ore stocks that were stored outdoors.     

Band-target entropy minimization (BTEM) applied to hyperspectral Raman image data

Band-target entropy minimization (BTEM) has been applied to extraction of component spectra from hyperspectral Raman images. In this method singular value decomposition is used to calculate the eigenvectors of the spectroscopic image data set. Bands in non-noise eigenvectors that would normally be used for recovery of spectra are examined for localized spectral features. For a targeted (identified) band, information entropy minimization or a closely related algorithm is used to recover the spectrum containing this feature from the non-noise eigenvectors, plus the next 5-30 eigenvectors, in which noise predominates. Tests for which eigenvectors to include are described. The method is demonstrated on one synthesized Raman image data set and two bone tissue specimens. By inclusion of small amounts of signal that would be unused in other methods, BTEM enables the extraction of a larger number of component spectra than are otherwise obtainable. An improvement in signal/noise ratio of the recovered spectra is also obtained.     

Highlight detection and removal from spectral image

We present a constrained spectral unmixing method to remove highlight from a single spectral image. In the constrained spectral unmixing method, the constraints have been imposed so that all the fractions of diffuse and highlight reflection sum up to 1 and are positive. As a result, the spectra of the diffuse image are always positive. The spectral power distribution (SPD) of the light source has been used as the pure highlight spectrum. The pure diffuse spectrum of the measured spectrum has been chosen from the set of diffuse spectra. The pure diffuse spectrum has a minimum angle among the angles calculated between spectra from a set of diffuse spectra and the measured spectrum projected onto the subspace orthogonal to the SPD of the light source. The set of diffuse spectra has been collected by an automated target generation program from the diffuse part in the image. Constrained energy minimization in a finite impulse response linear filter has been used to detect the highlight and diffuse parts in the image. Results by constrained spectral unmixing have been compared with results by the orthogonal subspace projection (OSP) method [Proceedings of International Conference on Pattern Recognition (2006), pp. 812-815] and probabilistic principal component analysis (PPCA) [Proceedings of the 4th WSEAS International Conference on Signal Processing, Robotics and Automation (2005), paper 15]. Constrained spectral unmixing outperforms OSP and PPCA in the visual assessment of the diffuse results. The highlight removal method by constrained spectral unmixing is suitable for spectral images.     

Application of two-dimensional correlation spectroscopy to chemometrics: self-modeling curve resolution analysis of spectral data sets

This paper demonstrates the use of two-dimensional (2D) correlation spectroscopy in conjunction with alternating least squares (ALS) based self-modeling curve resolution (SMCR) analysis of spectral data sets. This iterative regression technique utilizes the non-negativity constraints for spectral intensity and concentration. ALS-based SMCR analysis assisted with 2D correlation was applied to Fourier transform infrared (FT-IR) spectra of a polystyrene/methyl ethyl ketone/deuterated toluene (PS/MEK/d-toluene) solution mixture during the solvent evaporation process to obtain the pure component spectra and then the time-dependent concentration profiles of these three components during the evaporation process. We focus the use of asynchronous 2D correlation peaks for the identification of pure variables needed for the initial estimates of the ALS process. Choosing the most distinct bands via the positions of asynchronous 2D peaks is a viable starting point for ALS iteration. Once the pure variables are selected, ALS regression can be used to obtain the concentration profiles and pure component spectra. The obtained pure component spectra of MEK, d-toluene, and PS matched well with known spectra. The concentration profiles for components looked reasonable.     

Attenuated total reflection infrared difference spectroscopy (ATR-IRDS) for quantitative reaction monitoring

Monitoring of chemical reactors is key to optimizing yield and efficiency of chemical transformation processes. Aside from tracking pressure and temperature, the measurement of the chemical composition is essential in this context. We present an infrared difference spectroscopy approach for determining the reactant (cyclooctene) and product (cyclooctane) concentrations during a catalytic hydrogenation reaction in the solvent cyclohexane, which is present in large excess. Subtracting the spectrum of the pure solvent from the reactor mixture spectra yields infrared (IR) spectra, which can ultimately be evaluated using a curve-fitting procedure based on spectral soft modeling. An important feature of our evaluation approach is that the calibration only requires recording the pure component spectra of the reactants, products, and solvent. Hence, no time-consuming preparation of mixtures for calibration is necessary. The IR concentration results are in good agreement with gas chromatography measurements.     

Method of spectral subtraction of gas-phase Fourier transform infrared (FT-IR) spectra by minimizing the spectrum length

A new method of spectral subtraction for gas-phase Fourier transform infrared (FT-IR) spectra was developed for long-path gas measurements. The method is based on minimization of the length of the spectrum that results from subtracting the spectrum of an individual component of a gas mixture (water, CO(2), etc.) from the experimental spectrum of the mixture. For this purpose a subtraction coefficient (k(min)) is found for which the length of the resulting spectrum is minimized. A mathematical simulation with two Lorentzian absorption bands was conducted and the limits of application for the proposed method were determined. Two experimental examples demonstrate that a successful result could be achieved in the case when the subtrahend spectrum contains a number of narrow absorption bands (such as the spectrum of water vapor).     

Prediction of source rock origin by chemometric analysis of fourier transform infrared-attenuated total reflectance spectra of oil petroleum: evaluation of aliphatic and aromatic fractions by self-modeling mixture analysis

This study describes a new methodology for the interpretation of Fourier transform infrared (FT-IR) attenuated total reflectance (ATR) spectra of Algerian, Brazilian, and Venezuelan crude oils. It is based on a comparative study between a chemometric treatment and the classical one, which refers to indices calculation. In fact, the combined use of FT-IR indices and principal component analysis (PCA) has led to the classification of the studied samples in terms of geographic distribution. Quantitative analysis has been successfully realized by the supervised method partial least squares (PLS), which has permitted the prediction of the locations of oils. We have also applied another mathematical processing method, simple-to-use interactive self-modeling mixture analysis (SIMPLISMA), to evaluate the aromatic and aliphatic composition of the oils by extracting pure spectra representative of the different fractions.     

Application of band-target entropy minimization to infrared emission spectroscopy and the reconstruction of pure component emissivities from thin films and liquid samples

Thermal emission spectral data sets were collected for a thin solid film (parafilm) and a thin liquid film (isopropanol) on the interval of 298-348 K. The measurements were performed using a conventional Fourier transform infrared (FT-IR) spectrometer with external optical bench and in-house-designed emission cell. Both DTGS and MCT detectors were used. The data sets were analyzed with band-target entropy minimization (BTEM), which is a pure component spectral reconstruction program. Pure component emissivities of the parafilm, isopropanol, and thermal background were all recovered without any a priori information. Furthermore, the emissivities were obtained with increased signal-to-noise ratios, and the signals due to absorbance of thermal radiation by gas-phase moisture and CO2 were significantly reduced. As expected, the MCT results displayed better signal-to-noise ratios than the DTGS results, but the latter results were still rather impressive given the low temperatures used in this study. Comparison is made with spectral reconstruction using the orthogonal projection approach-alternating least squares (OPA-ALS) technique. This contribution introduces the primary equation for emission spectral reconstruction using BTEM and discusses some of the unusual characteristics of thermal emission and their impact on the analysis.     

Extraction of mass spectra and chromatographic profiles from overlapping GC/MS signal with background

An adaptive immune algorithm (AIA) was proposed for resolution of the overlapping GC/MS signal with background. By using AIA, the chromatographic profiles corresponding to the independent components (ICs) in the overlapping signal are calculated with the mass spectra extracted by means of independent component analysis (ICA). The number of the ICs in the overlapping signal is determined by the difference between the reconstructed and the original data. Both simulated and experimental data are investigated with the proposed AIA approach. It was found that the mass spectra and chromatographic profiles of the components in an overlapping multicomponent GC/MS signal can be accurately resolved with the existence of background, and the results are better than that by using an interactive self-modeling mixture analysis (SIMPLISMA) method. The AIA approach may be a promising tool for the resolution of overlapping GC/MS signal.     

Resolution of intermediate adsorbate structures in the potential-dependent self-assembly of n-hexanethiolate on Silver by in situ surface-enhanced Raman spectroscopy

Resolution of the reaction steps and the associated component Raman spectra during the formation or desorption of self-assembled monolayers is challenging because intermediate adsorbate populations are present at low concentrations and their spectral bands overlap. By collecting Raman spectra versus applied potential into a two-dimensional data set, one can utilize multivariate statistical techniques to resolve the component concentration profiles along with their corresponding Raman spectra. In situ surface-enhanced Raman spectroscopy (SERS) spectra were collected during the potential-dependent formation and desorption (-1.50 to -0.70V versus Ag/AgCl) of n-hexanethiolate monolayer at a polycrystalline Ag electrode. Resolution of the pure component spectra from these components was accomplished by using self-modeling curve resolution (SMCR), which does not require a physical model. For monolayer adsorption, the potential-dependent Raman spectra could be described by three significant eigenvectors; the eigenvectors could be rotated into a set of pure component spectra and concentration profiles using a linear least-squares step to find a common plane in the space of the eigenvectors representing the linear combination of the real-component responses. The convex hull surrounding the data in the plane and positive amplitude criteria were utilized to identify the coordinates of the pure component responses. The C-S stretching vibrations of the resolved spectra show that the initial adsorbate is a gauche conformer, which allows the hydrocarbon chain to lie on the metal surface; a second phase arises at higher coverage with trans C-S conformation, where the hydrocarbon chains are oriented off the surface plane, and a final complete monolayer is formed with a well-ordered, all-trans C-S configuration. In contrast, desorption studies showed only two surface phases, the initial well-ordered monolayer and the low-density phase dominated by gauche conformations. The results illustrate the utility of self-modeling curve resolution to unravel interfacial reaction mechanisms and intermediate structures from two-dimensional SERS data, without requiring prior knowledge of a physical model for the process.     

Theory of evolutionary factor analysis for resolution of quaternary-plus mixtures

A self-modeling approach for the resolution of quaternary mixtures is developed from explicit theoretical principles. The SEPARATOR, an algorithm for separation of ternary mixtures under evolutionary conditions, is extended to quaternary-plus mixtures. The SEPARATOR is applied to simulated and experimental data composed of four components yielding upper and lower boundaries for the pure component spectra and concentration profiles. Resolution of flow injection analysis data of a mixture containing six overlapping components is described.