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WO2010058230A2 - Procédé et système d'extraction aveugle de plus de deux composantes pures à partir de mesures spectroscopiques ou spectrométriques de seulement deux mélanges par une analyse en composantes parcimonieuses - Google Patents

Procédé et système d'extraction aveugle de plus de deux composantes pures à partir de mesures spectroscopiques ou spectrométriques de seulement deux mélanges par une analyse en composantes parcimonieuses Download PDF

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WO2010058230A2
WO2010058230A2 PCT/HR2008/000037 HR2008000037W WO2010058230A2 WO 2010058230 A2 WO2010058230 A2 WO 2010058230A2 HR 2008000037 W HR2008000037 W HR 2008000037W WO 2010058230 A2 WO2010058230 A2 WO 2010058230A2
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pure components
mixtures
domain
equation
new representation
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WO2010058230A3 (fr
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Kopriva Ivica
Jeric Ivanka
Smrecki Vilko
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INSTITUT RUDJER BOSKOVIC
INST RUDJER BOSKOVIC
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INSTITUT RUDJER BOSKOVIC
INST RUDJER BOSKOVIC
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Priority to PCT/HR2008/000037 priority patent/WO2010058230A2/fr
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Priority to US13/090,629 priority patent/US20110213566A1/en
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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/213—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods
    • G06F18/2134—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods based on separation criteria, e.g. independent component analysis

Definitions

  • the present invention generally relates to a computer-implemented system for processing data for the purpose of blind extraction of pure components from the mixtures recorded in the fields of spectroscopy and spectrometry.
  • the invention relates to the application of the method of sparse component analysis (SCA), also known as underdetermined blind source separation (uBSS), to blind decomposition of two spectroscopic data (also called mixtures) into more than two pure components.
  • SCA sparse component analysis
  • uBSS underdetermined blind source separation
  • Spectroscopic data refers to data gathered by nuclear magnetic resonance (NMR) spectroscopy, electron paramagnetic resonance (EPR) spectroscopy, infrared (IR) spectroscopy, ultraviolet (UV) spectroscopy, Raman spectroscopy or mass spectrometry.
  • NMR nuclear magnetic resonance
  • EPR electron paramagnetic resonance
  • IR infrared
  • UV ultraviolet
  • Raman spectroscopy Raman spectroscopy or mass spectrometry.
  • ICA independent component analysis
  • NMF nonnegative matrix factorization
  • BSS methods mostly ICA, are used to extract pure components from the plurality of the spectroscopic or spectrometric signals.
  • ICA a number of times it is emphasized that statistical independence among the pure components is not a correct assumption in spectroscopy and spectrometry.
  • number of linearly independent mixtures is required to be greater than or equal to the unknown number of pure components.
  • Magnetic resonance spectroscopy with sparse spectral sampling and interleaved dynamic shimming is related to 4D (three spatial and one spectral dimension) magnetic resonance spectroscopy and is characterized by sparse sampling across spectral dimension.
  • sparseness of the components is a consequence of the multidimensionality of the data, i.e. sensing device.
  • the US Patent 7,280,943 Systems and methods for separating multiple sources using directional filtering
  • the method is semi-blind because it assumes that each source signals can be represented by a set of known basis functions and directional filters that incorporate prior knowledge on the type of the sources and their directions of arrival.
  • the last assumption surely does not hold when spectroscopy and spectrometry are considered as application domains. This is because the signals arising in spectroscopy and spectrometry do not have spatial structure, i.e. there are no distinct spatial locations to which the pure component signals can be associated and there are no distinct spatial locations of the receiving sensors (the multiple mixtures are acquired over different time slots or different wavelengths).
  • the US Patent 6,944,579 “Online blind source separation,” aims to extract multiple source signals from two mixtures only.
  • the method transforms mixtures into time-frequency domain and employs the strategy of the algorithm published in: Blind Separation of Disjoint Orthogonal Signals: Demixing n sources from 2 mixtures, by A. Jourjine, S. Rickard, and O. Yilmaz, in Proc. Int. Conf. on Acoust, Speech, Signal Processing, 2000, vol. 5, pp. 2985- 2988.
  • the specific request of patented algorithm is that source signals are disjointly orthogonal in time-frequency plane. It is empirically known that this assumption is fulfilled for the voice signals.
  • the US Patent Application 20070257840 “Enhancement Techniques for Blind Source Separation,” is related to improving performance of the BSS algorithms for separation of audio signals from two microphone recordings.
  • Decorrelation based pre- and post-filtering (least means square filtering) is applied to the first and second microphone signals for the enhancement purpose.
  • the method assumes that a first microphone is in the proximity of a first source signal and a second microphone is in the proximity of a second source signal.
  • the known method is very limited and can not be applied to the field of spectroscopy and spectrometry where mixtures are obtained over time or wavelength (there is no plurality of the physical sensors) and more than two sources (pure components) exist.
  • the US patent application 20060064299 “Device and method for analyzing an information signal,” is related to extraction of multiple audio signals from single mixture.
  • the method splits the mixture into plurality of component signals and finds information content of each component .signal based on calculation of their features; wherein feature is defined so that it is correlated with two source signals in two different subspaces.
  • the features are audio signal specific and that is what limits this patent application to separate audio signals only.
  • the algorithm presented in cited patent application is not applicable to the type of signals that arise in the fields of spectroscopy and spectrometry.
  • the algorithm in cited patent applications has the following deficiencies: (i) the number of sensors must be greater than two if more than two sources are active at the same frequency; (ii) in relation to comment (i) Fourier basis (frequency domain), that is used by the cited application, is not optimal for the type of signals that arise in spectroscopy.
  • This aim is achieved by a method of blind extraction of more than two pure components out of spectroscopic or spectrometric measurements of only two mixtures by means of sparse component analysis, characterised in that said blind extraction comprises the following steps:
  • the results presentation domain is the recording domain of the two mixtures data
  • estimating the mixing or concentration matrix A and the number of the pure components Ti(S) in the first new representation domain by means of linear programming, constrained convex programming or constrained quadratic programming, inverse transforming the estimated pure components Ti (S) from the first new representation domain defined by equation [II] to the recording domain defined by equation [I] by applying the inverse of the transform Ti according to equation [IV]:
  • the results presentation domain is the second new representation domain defined by equation [III]
  • a system for blind extraction of more than two pure components out of spectroscopic or spectrometric measurements of only two mixtures by means of sparse component analysis comprising: a mixtures sensing device (1) for recording mixtures data X, " an input storing device or medium (2) for storing the mixture data X recorded by the mixtures sensing device (1), a processor (3), wherein code is implemented or carried out for executing a method, according to any one of the claims 1 to 9 based on the mixtures data X stored in/on the input storing device or medium (2), an output storing device or medium (4) for storing the result of the method carried out by the processor.
  • the linear transform 7 / is a wavelet transform with either Morlet or Mexican hat wavelet.
  • the linear transform T 2 can be a Fourier transform.
  • the data clustering algorithm is of the type capable to simultaneously estimate the mixing matrix and the number of pure components in the first new representation domain.
  • a numerical method is used to estimate the pure components in the second new representation domain that is a linear programming method, a convex programming method with quadratic constraint ( 2 -norm based constraint) or a quadratic programming method with • -norm based constraint.
  • a linear transform Tj is a wavelet transform with the second to eight order Daubechies wavelets or symlets or coiflets of the order one to five.
  • the data clustering algorithm is of the type capable to simultaneously estimate the mixing matrix and the number of pure components in the first new representation domain.
  • a numerical method can be used to estimate the pure components in the first new representation domain that is a linear programming methods, a convex programming method with quadratic constraint ( 2 -norm based constraint) or a quadratic programming method with ' -norm based constraint.
  • a computer-readable medium having computer-executable instructions stored thereon which, when executed by a computer, will cause the computer to carry out a method of the present invention.
  • said method is applied to the identification of the chemical compounds in chemical synthesis, food quality inspection or pollution inspection i. e. environment protection.
  • the output storing device can be a printer or plotter and the output storing medium can be a memory base device that is computer- readable.
  • the mixtures sensing device is a nuclear magnetic resonance (NMR) spectrometer, ultraviolet spectrometer, IR spectrometer, electron paramagnetic resonance spectrometer, Raman spectrometer or mass spectrometer.
  • NMR nuclear magnetic resonance
  • figure 1 schematically illustrates a block diagram of a device for blind decomposition of spectroscopic or spectrometric data into more than two pure components using two mixtures only and employing methodology of sparse component analysis and underdetermined blind source separation according to an embodiment of the present invention
  • figures 2A to 2F demonstrate a concept of sparse component analysis by blind extraction of four sinusoid signals with different frequencies from two mixtures
  • figure 3 shows positions of the three unit length mixing vectors in the coordinate system defined by mixtures xi and X 2
  • figures 4A and 4B show the real part of a time domain 1 H NMR signal (pure component) and Morlet wavelet at the corresponding scale
  • figure 5 shows a normalized absolute value of wavelet coefficients vs.
  • FIG. 1 A schematic block diagram of a device for blind decomposition of spectroscopic or spectrometric data into more than two pure components using two mixtures only defined by equation [I] and employing methodology of sparse component analysis and underdetermined blind source separation according to an embodiment of the present invention is shown in figure 1.
  • the device consists of: mixtures sensing device 1 used to gather spectroscopic or spectrometric data; storing device 2 used to store gathered spectroscopic or spectrometric data; CPU 3 or computer where algorithms for sparse component analysis and underdetermined blind source separation are implemented for blind extraction of pure components from gathered spectroscopic or spectrometric data; and output device 4 used to store and present extracted pure components.
  • the procedure for processing gathered and stored spectroscopic or spectrometric mixture data with the aim to blindly extract pure components is implemented in the software or firmware in the CPU 3 and according to an embodiment of the present invention consists of the following steps: two recorded mixtures defined by equation [I] are transformed by linear transform Ti into the first new representation domain defined by equation [II] with the aim to increase sparseness of the pure components; the transformed mixtures equation [II] are used for estimation of the number of pure components and estimation of the mixing matrix (also called concentration matrix); based on the estimated mixing matrix pure components are estimated by either linear programming, convex programming with constraints or quadratic programming with constrains using two mixtures in the first new representation domain defined by equation [II] or the second new representation domain defined by equation [III] that are obtained by transforming two mixtures from recording domain defined by equation
  • procedure for extraction of the pure components using sparse component analysis for blind decomposition of the recorded two mixtures of spectroscopic or spectrometric data consists of the following steps:
  • mixtures sensing device 1 for e.g. nuclear magnetic resonance spectroscopy, infrared spectroscopy, ultraviolet spectroscopy, electron paramagnetic resonance spectroscopy, Raman spectroscopy or mass spectrometry, wherein mixtures are defined as a product of an unknown mixing matrix A. (also called concentration matrix) and matrix of the unknown pure components S,
  • the first new representation domain defined by equation [II] is not the domain where final results are presented estimated pure components are transformed into the results presentation domain that coincides with the recording domain defined by equation [I] by applying inverse of the transform T 1 on estimated pure components Ti(S) (see equation [IV]), selecting estimated pure components of interest in accordance with negentropy-based ranking criteria, and
  • Figures 2A to 2F demonstrate the concept of sparse component analysis by blind extraction of four sinusoid signals with different frequencies from two mixtures.
  • the four sinusoid signals that play the role of pure components, have frequencies of 200 Hz, 400 Hz, 800 Hz and 1600 Hz.
  • Figure 2A shows four sinusoid signals in time domain on large time scale, while figure 2B shows the same four signals in zoomed time interval. The overlap between the time domain pure component signals is evident, especially in figure 2A on large time scale. There, instead of being mutually sparse signals are very dense.
  • Figure 2C shows the same four sinusoid signals in frequency domain.
  • FIG. 2D shows the amplitude spectrum of the two mixtures obtained by mixing four pure components shown in figure 2C with the mixing matrix consisting of the four 2D mixing vectors.
  • the mixing angles see discussion associated with figure 3 in paragraph [0067], in degrees were: [63.44 25.57 14.04 71.57].
  • Figure 2E shows clustering function in the mixing angle domain. Four peaks at the approximate locations of the mixing angles are distinguished. The estimates of the mixing angles in degrees were: [63.54 26.55 14.05 71.57].
  • Figure 2F shows the amplitude spectrum of the estimated four pure components. Similarity with the true pure components, the amplitude spectrum of which is shown in figure 2C, is evident. Note that in this case the first new representation domain defined by equation [II] and the second new representation domain defined by equation [III] were the same, i.e. there was only one transform Tj used and that was the Fourier transform. The reason was that the Fourier transform yields perfectly sparse representation for the sinusoid signals.
  • Figures 6 A to 6K demonstrate experimentally blind extraction of three pure components and two outliers from two 1 H NMR mixtures by means of sparse component analysis according to an embodiment of the present invention.
  • Compounds used in this analysis were derivatives of amino acids tyrosine and phenylalanine with large structural similarities and significant overlapping in NMR spectra.
  • Figures 6 A to 6C show 1 H NMR amplitude spectra (in the Fourier basis) of the three pure components. Negentropy measures calculated on the amplitude spectra of the three pure components were: 1.955x1017, 2.793x1016 and 2.627x1016.
  • Figures 6D and 6E show IH NMR amplitude spectra of the two mixtures.
  • Figure 6F shows clustering function in the mixing angle domain wherein for Tj continuous wavelet transform with the Morlet wavelet has been used to transform two mixtures from recording domain defined by equation [I] to the first new representation domain defined by equation [H].
  • the clustering function shown in figure 6F illustrates this later case.
  • the amplitude spectra of the estimated pure components that correspond to the three true pure components are shown in figures 6G to 61.
  • Figures 7 A to 71 demonstrate experimentally the concept of sparse component analysis by blind extraction of three pure components from two 13 C NMR mixtures according to an embodiment of the present invention.
  • the compounds used to illustrate the SCA concept on 13 C NMR data were the same as in the previous paragraph [0051], where the SCA concept was illustrated on IH NMR data.
  • Figures 7A to 7C show 13 C NMR amplitude spectra (in Fourier basis) of the three pure components.
  • Figures 7D and 7E show 13 C NMR amplitude spectra of the two mixtures.
  • Figure 7F shows the clustering function in the mixing angle domain, wherein for Ti continuous wavelet transform with the Morlet wavelet has been used to transform mixtures from recording domain defined by equation [I] to the first new representation domain defined by equation [II].
  • the clustering function shown in figure 7F illustrates this case.
  • the dispersion factor could be varied as in the previous case of 1 H NMR data and negentropy measure could be used to discriminate estimates of the true pure components from those that are classified as outliers.
  • the amplitude spectra of the estimated pure components that correspond to the true tree pure components are shown in figures 7G to 71. Note also the relatively large discrepancy between the true third pure component, figure 7C, and its estimate, figure 71. This is the consequence of the great spectral similarity between the second and third pure components and the small amount of concentration of the third pure component in the mixtures.
  • Figures 8A to 8H demonstrate experimentally the concept of sparse component analysis by blind extraction of two pure components from two UV mixtures according to an embodiment of the present invention.
  • the compounds used to illustrate the SCA concept on UV data were the same as in the previous paragraphs [0051] and [0052], where the SCA concept was illustrated on 1 H and 13 C NMR data.
  • Figures 8 A to 8C show UV spectra of the three pure components. Note that the second and third pure components have the same UV spectra, because they have the same chromophore responsible for the UV absorption (aromatic ring). Consequently, only two true pure components will show up in the mixtures.
  • Figures 8D and 8E show UV spectra of the two mixtures defined by equation [I].
  • Figure 8F shows the clustering function in the mixing angle domain, wherein for Ti continuous wavelet transform with the second order Daubechies wavelet has been used to transform two mixtures from recording domain defined by equation [I] to the first new representation domain defined by equation [H].
  • the clustering function shown in figure 8F illustrates this case.
  • the dispersion factor could be varied as in the previous cases of 1 H and 13 C NMR data and the negentropy or smoothness measures could be used to discriminate estimates of the true pure components from those that are classified as outliers.
  • the spectra of the estimated pure components that correspond to the true two pure components are shown in figures 8G and 8H. Note the good agreement between the true pure components shown in figures 8A and 8B and their estimates shown in figures 8G and 8H.
  • Figures 9A to 91 demonstrate experimentally the concept of sparse component analysis by blind extraction of two pure components from two IR mixtures according to an embodiment to the present invention.
  • the compounds used to illustrate the SCA concept on IR data were the same as in the previous paragraphs [0051], [0052] and [0053] where the SCA concept was illustrated on 1 H and 13 C NMR data and UV data.
  • Figures 9 A to 9C show IR spectra of the three pure components.
  • Figures 9D and 9E show IR spectra of the two mixtures defined by equation [I].
  • Figure 9F shows the clustering function in the mixing angle domain, wherein for Ti continuous wavelet transform with the fourth order symmlet wavelet has been used to transform two mixtures from recording domain define by equation [I] to the first new representation domain defined by equation [H].
  • the clustering function shown in figure 9F illustrates this case.
  • negentropy measure has been used to discriminate estimates of the true pure components from the outlier.
  • the IR spectra of the three estimated pure components that correspond to the three true pure components, are shown in drawings 9G to 91.
  • the present invention relates to the field of spectroscopy and spectrometry. More specific, the invention relates to the application of the method of SCA and uBSS for blind extraction of more than two pure chemical compounds from two spectroscopic or spectrometric mixtures, wherein mixtures are gathered by NMR spectroscopy, EPR spectroscopy, IR spectroscopy, UV spectroscopy, Raman spectroscopy or mass spectrometry.
  • Proposed blind mixture decomposition approach estimates the unknown number of pure components from the mixtures. Identified pure components can be used for identification of the compounds in chemical synthesis, food quality control, environment protection, etc.
  • the unknown number of pure components during the mixing matrix estimation phase in the new representation domain is estimated by means of the clustering method recently proposed in: F.M. Naini et al., "Estimating the mixing matrix in Sparse Component Analysis (SCA) based on partial k-dimensional subspace clustering," Neurocomputing 71, 2330-2343, 2008.
  • SCA Sparse Component Analysis
  • the pure components are recovered by solving an underdetermined system of linear equations in the new representation domain. If the pure components are in average m-1 sparse, the solution can be obtained by several methods that are based on constrained convex optimization: J.A. Tropp, A.C. Gilbert, “Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit,” IEEE Transactions on Information Theory, vol. 53,No. 12, 4655-4666, 2007; SJ. Kim et al., "An Interior-Point Method for Large-Scale ' -Regularized Least Squares," IEEE Journal of Selected Topics in Signal Processing, vol. 1, No. 4, 606-617, 2007. Moreover, it has been proven (I.
  • X AS [I]
  • a term "the two mixtures recording domain” is defined by equation [I].
  • a domain which was obtained by applying linear transform Ti on the mixtures in recording domain defined by equation [I], and which is called in the present invention is defined by equation [H].
  • domain which was obtained by applying linear transform T 2 on the mixtures in recording domain defined by equation [I], and which is called in the present invention is defined by equation [III].
  • a term "results presentation domain” relates to the domain where results obtained by blind decomposition algorithm ought to be presented. Depending on the mixtures sensing device that relates to the chosen spectroscopic technology the results presentation domain can be mixtures recording domain defined by equation [I], the first new representation domain defined by equation [II] or the second new representation domain defined by equation [III].
  • m-1 sparse representations means that at each coordinate in the first new representation domain defined by equation [II] at most one pure component is non-zero i.e. it is assumed that pure component do not overlap in the first new representation domain defined by equation [H].
  • Candidates for the linear transform Ti are the Fourier transform or wavelet transform. The Fourier transform can be a good choice for 13 C NMR data, where a small degree of overlap between pure components is expected. However the m-1 sparseness requirement is not very likely to be met, when Fourier transform is applied on 1 H NMR data or some other spectroscopic or spectrometric data.
  • the wavelet transform has greater chance to yield sparse pure components T](S) due to possibility to choose a wavelet basis function that matches the structure of the spectroscopic or spectrometric signals defined by equation [I].
  • Morlet and Mexican hat wavelets match the structure of the NMR signals very well.
  • the Morlet or Mexican hat based wavelet transform yields very sparse representation of the NMR signals.
  • figures 4A and 4B respectively show the real part of the time domain 1 H NMR signal (pure component) and Morlet wavelet at the corresponding scale. The similarity of the waveforms is evident.
  • Figure 2E shows the clustering function for the example when four sinusoid signals with different frequencies were mixed into two mixtures and then transformed into Fourier domain, i.e. T ⁇ is implemented by Fourier transform.
  • T ⁇ is implemented by Fourier transform.
  • FIGS 6F and 7F Two more examples are shown in figures 6F and 7F for the case of experimental 1 H and 13 C NMR data comprised of three pure components with one component contained in small concentration and two components contained in similar concentrations. [00069] After the number of pure components and the mixing matrix are estimated, the pure components themselves ought to be estimated. This can be achieved either in the first new representation domain defined by equation [II] and implemented by transform Ti, or in the second new representation domain defined by equation [III] and obtained by applying linear transform T 2 on the two mixtures defined by equation [I]. This yields
  • Transform T 2 is useful when the domain in which results are presented differs from the two mixtures recording domain defined by equation [I] and from the first new representation domain defined by equation [II] obtained by means of transform Ti.
  • transformed pure components 7 ⁇ S) are comparably sparse as the transformed components Ti(S)
  • the second new representation domain defined by equation [III] enables the estimation of the pure components.
  • the mixing matrix is most accuratley estimated in the new representation domain one defined by equation [II], wherein transform Ti represents wavelet basis with either Morlet or Mexican hat wavelets. This is because such basis provides the sparsest representation of the NMR signals.
  • inverse transform • are wavelet and inverse wavelet transforms with suitable chosen wavelet function.
  • the number of pure components is estimated simultaneously with the mixing matrix employing a data clustering algorithm in the first new representation domain defined by equation [H].
  • the sensitivity of the clustering function is regulated through the dispersion factor ⁇ . Since the experimental data can contain errors due the presence of chemical noise or outliers, as discussed in the US patent application 20040111220 in paragraph [0014], it is necessary to derive a robust estimator of the number of pure components. For this purpose we propose to slightly variate the dispersion factor ⁇ and estimate the mixing matrix, related number of pure components m and pure components themselves for each value of ⁇ .
  • RMSE root-mean-squared-error
  • negentropy is entropy defined relatively in relation to the entropy of the Gaussian random process. Since the Gaussian random process has the largest entropy its negentropy will be zero. The more informative (non-Gaussian) the random process is, the largest negentropy it has. Since we intuitively expect the pure components to be informative we also expect their negentropies to be large. As opposed to that we expect the negentropies of the possible outliers to be small.
  • the present invention is related to blind extraction of more than two pure components from the two mixtures of the chemical compounds by means of sparse component analysis and underdetermined blind source separation.
  • the invention is insensitive to statistical dependence among the pure components and is capable of automatically determining their number from the two available mixtures.
  • the present invention solves blind decomposition problem using two mixtures only and estimates the unknown number of pure components using data clustering algorithm commented in paragraphs [0058], [0067] and [0068]. It is related to spectroscopy where sparseness is generally not ensured but is achieved by transforming recorded data into either Fourier or wavelet basis with properly chosen wavelet function that matches the structure of the related spectroscopic or spectrometric signals.
  • the present invention estimates mixing matrix using purely geometric approach known as data clustering. In particular an algorithm is used (F.M. Naini, et. al, "Estimating the mixing matrix in Sparse Component Analysis (SCA) based on partial k-dimensional subspace clustering," Neurocomputing, vol.
  • SCA Sparse Component Analysis
  • the invention can be applied to identification of the compounds in the pharmaceutical industry in the chemical synthesis of new compounds with different properties. It can also be applied in the food quality inspection and environment protection through pollution inspection. Another application of the proposed invention is in software packages, as the built in computer code, that are used for the analysis and identification of the chemical compounds.

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Abstract

La présente invention concerne de façon générale un système informatisé de traitement de données destiné à l’extraction aveugle de plus de deux composantes pures à partir de deux mélanges ayant fait l'objet d’enregistrements dans les domaines de la spectroscopie et de la spectrométrie. Plus précisément, l'invention concerne l’application de la méthode d’analyse en composantes parcimonieuses, également appelée séparation aveugle sous-déterminée de sources, à la décomposition aveugle de données spectroscopiques consistant en deux mélanges X en plus de deux composantes pures S et une matrice de concentration A. On entend par données spectroscopiques des données recueillies par spectroscopie à résonance magnétique nucléaire (RMN), spectroscopie à résonance paramagnétique électronique (RPE), spectroscopie à infrarouges (IR), spectroscopie à ultraviolets (UV), spectroscopie Raman ou spectrométrie de masse. Deux mélanges sont analysés soit dans un domaine d’enregistrement, soit dans un premier domaine nouveau de représentation en utilisant une transformation linéaire T1, les composantes pures dans le premier domaine nouveau de représentation étant plus éparses que dans le domaine d’enregistrement. Le nombre de composantes pures et la matrice de mélange sont estimés soit dans le domaine d’enregistrement, soit dans le premier domaine nouveau de représentation au moyen d’un algorithme de regroupement de données. Les composantes pures sont estimées par une méthode de programmation linéaire, de programmation convexe avec contrainte quadratique (contrainte basée sur une norme L2) ou de programmation quadratique avec une contrainte basée sur une norme L1 soit dans le domaine d’enregistrement, soit dans le premier domaine nouveau de représentation ou un deuxième domaine nouveau de représentation, le deuxième domaine nouveau de représentation étant obtenu  par une autre transformation linéaire T2 et le deuxième domaine nouveau de représentation devant être le domaine où les résultats seront présentés. Les composantes pures estimées sont classées à l’aide d’un critère de néguentropie. Les composantes dont la mesure de néguentropie diffère d’au moins 10 ordres de grandeur de la néguentropie de la majorité des composantes sont classifiées comme points aberrants et éliminées. Si des composantes pures sont estimées dans le premier domaine nouveau de représentation, la transformation inverse T1 -1 est appliquée pour estimer les composantes pures afin de les retransformer vers le domaine d’enregistrement des deux mélanges.
PCT/HR2008/000037 2008-11-24 2008-11-24 Procédé et système d'extraction aveugle de plus de deux composantes pures à partir de mesures spectroscopiques ou spectrométriques de seulement deux mélanges par une analyse en composantes parcimonieuses Ceased WO2010058230A2 (fr)

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EP08875693A EP2350926A2 (fr) 2008-11-24 2008-11-24 Procédé et système d extraction aveugle de plus de deux composantes pures à partir de mesures spectroscopiques ou spectrométriques de seulement deux mélanges par une analyse en composantes parcimonieuses
PCT/HR2008/000037 WO2010058230A2 (fr) 2008-11-24 2008-11-24 Procédé et système d'extraction aveugle de plus de deux composantes pures à partir de mesures spectroscopiques ou spectrométriques de seulement deux mélanges par une analyse en composantes parcimonieuses
US13/090,629 US20110213566A1 (en) 2008-11-24 2011-04-20 Method Of And System For Blind Extraction Of More Than Two Pure Components Out Of Spectroscopic Or Spectrometric Measurements Of Only Two Mixtures By Means Of Sparse Component Analysis

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