Multiplicative signal correction method and apparatus
First Claim
1. A method for correcting signals representing input spectral data (Xki) derived from a sensor during a measurement, at least as to multiplicative errors, said method comprising the steps of:
- providing a first and primary reference spectrum signal (Pko) representing a predetermined standard for such data;
providing at least one second reference spectrum signal (Pka or Pkj);
estimating coefficients for a selected appropriate model to be applied to said input data based on said first and second reference spectra signals; and
correcting said signals representing said spectral data based on said estimated coefficients at least as to multiplicative errors for producing signals representing a linear additive structure for use in calibration, validation and determination by linear multivariate analysis.
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Abstract
An improved method and apparatus are disclosed for processing spectral data to remove undesired variations in such data and to remove interfering information present in the data. The method land apparatus corrects multiplicative effects present in the spectral data. Additive and interferent contributions can be corrected as well. In one aspect of the method, coefficients for a selected appropriate model are applied to the input spectral data based on first and second reference spectra. The spectral data are then corrected based on the estimated coefficients at least as to multiplicative errors for producing a linear additive structure for use in calibration, validation and determination by linear multivariate analysis. The method and apparatus will improve the accuracy of spectral data structures derived from measurements Using spectroscopy, chromatography, thermal analysis, mechanical vibration and acoustic analysis, rheology, electrophoresis, image analysis and other analytical technologies producing data of similar multivariate nature.
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Citations
49 Claims
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1. A method for correcting signals representing input spectral data (Xki) derived from a sensor during a measurement, at least as to multiplicative errors, said method comprising the steps of:
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providing a first and primary reference spectrum signal (Pko) representing a predetermined standard for such data; providing at least one second reference spectrum signal (Pka or Pkj); estimating coefficients for a selected appropriate model to be applied to said input data based on said first and second reference spectra signals; and correcting said signals representing said spectral data based on said estimated coefficients at least as to multiplicative errors for producing signals representing a linear additive structure for use in calibration, validation and determination by linear multivariate analysis. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27)
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28. Apparatus for correcting input spectral data (Xki) derived from a sensor during a measurement, at least as to multiplicative errors, said apparatus comprising:
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input means for supplying a signal representing spectral data subject to correction for at least multiplicative errors; means for supplying a signal representing a first and primary reference spectrum (Pko) as a predetermined standard for such data; means for supplying a signal representing at least one second reference spectrum (Pka or Pkj); means for estimating coefficients for a selected model for application to said input spectral data, said input spectral data signal and first and second reference spectrum signals being supplied to said estimating means; and means responsive to said estimating means for correcting said spectral data based on estimated coefficients at least as to multiplicative errors for producing a signal representing a linear additive structure for use in calibration, validation and determination by linear multivariate analysis. - View Dependent Claims (29, 30, 31, 32, 33, 34)
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35. In a system for analyzing a medium, said system having a spectrophotometric sensor for providing a signal representing input spectral data (Xki), the improvement comprising:
apparatus for correcting said spectral data for at least multiplicative errors, said apparatus including; means for supplying a signal representing a first and primary reference spectrum (Pko) as a predetermined standard for said spectral data; means for supplying a signal representing at least one second reference spectrum (Pka or Pkj); means for estimating coefficients for a selected model for application to said input spectral data, said input spectral signals and first and second reference spectral signals being supplied to said estimating means; and means responsive to said estimating means for correcting said spectral data based on estimated coefficients at least as to multiplicative errors for producing a signal representing a linear additive structure for use in calibration, validation and determination based on linear multivariate analysis.
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36. The method for correcting input spectral data (Xki) derived from a measurement, by applying an additive model and multiplicative model for the data in a sequential fashion, comprising the steps of:
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1) obtaining a set of spectral data Z from original input spectral data corrected for multiplicative effects by using a standard multiplicative scatter correction technique; 2) estimating an additive model which takes into account spectral variations of analytes and interferences; 3) reconstructing spectral data Y without the estimated additive effects; 4) estimating the multiplicative effects on Y; 5) constructing a new matrix of corrected spectra Z from X; and repeating steps 2, 3 and 4 until convergence occurs. - View Dependent Claims (37, 38, 39, 44, 45, 46)
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40. The method for correcting input spectral data (Xki) derived from a measurement or for correcting the scores obtained by bilinear modeling of such data, said method comprising the steps of:
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examining the measured spectral data as a combined additive and multiplicative structure such that
space="preserve" listing-type="equation">X=T*P'"'"'+Ewhere X=(xik) is the matrix of spectral ordinates for i=1,2 . . . N objects, k=1,2 . . . , K wavelengths, T=(til) is the matrix of scores for objects i, l=1,2 . . . L representing bilinear factors Obtained from a bilinear model, P=(Pki) are the loadings for objects i on bilinear factors l, and E=(eik) are the residuals between data X and model T*P'"'"'; decomposing the loadings into a function of a reference spectral and, optionally, a matrix of spectral components for analyte and interference phenomena; obtaining the additive and multiplicative effects for the input spectra from the coefficients from the loading decomposition and scores; and correcting said input spectra based on said obtained additive and multiplicative effects. - View Dependent Claims (41)
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42. The method for correcting input spectral data (Xki) derived from a measurement or for correcting the scores obtained by bilinear modeling of such data, said method comprising the steps of:
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examining the measured spectral data as a combined additive and multiplicative structure such that
space="preserve" listing-type="equation">X=T*P'"'"'+Ewhere X=(xik) is the matrix of spectral ordinates for i=1,2 . . . N objects, k=1,2 . . . , K wavelengths, T=(til) is the matrix of scores for objects i, l=1,2 . . . L representing bilinear factors obtained from a bilinear model, P=(Pki) are the loadings for objects i on bilinear factors l, and E=(eik) are the residuals between data X and model T*P'"'"'; decomposing the loadings into a function of a reference spectrum and, optionally, a matrix of spectral components for analyte and interference phenomena; obtaining the additive effects for the scores T from the offset corrected loadings and the scores T; and applying the obtained additive effects to the scores; obtaining the multiplicative effect from the coefficient d from the reference spectrum; and obtaining scores corrected for additive and multiplicative effects using the multiplicative effect, or scores T and, optionally, the additive effect. - View Dependent Claims (43)
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47. Apparatus for correcting an input spectral data (Xki) signal derived from a measurement, particularly as to multiplicative errors, by the fitting of an additive model and multiplicative model in sequential fashion, comprising:
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first means for obtaining a signal representing a set of spectral data Z from the original input spectral data signal corrected for multiplicative effect by using a standard multiplicative scatter correction technique; second means for providing a signal representing estimate of an additive model which takes into account spectral variations of analytes and interferences; third means for providing a signal representing the reconstructing of spectral data Y without the estimated additive effects; fourth means for providing a signal representing an estimate of the multiplicative effects on Y; fifth means for providing a signal representing the construction of a new matrix of corrected spectra Z from X; means for respectively providing said signal from said fifth means to said second, third and fourth means; and means responsive to the output signals of said second, third and fourth means for determining when convergence occurs.
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48. Apparatus for correcting an input spectral data (Xki) signal derived from a measurement or for correcting a signal representing the scores obtained by bilinear modeling of such data, comprising:
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means for providing a signal responsive to said input signal representing the measured spectral data as a combined additive and multiplicative structure such that
space="preserve" listing-type="equation">X=T*P'"'"'+Ewhere X=(xik) is the matrix of spectral ordinates for i=1,z . . . N objects, k=1,2 . . . , k wavelengths, T=(til) is the matrix of scores for objects i, l=1,2 . . . L representing bilinear factors obtained from a bilinear model, P=(Pki) are the loadings for objects i on bilinear factors l and E=(eik) are the residuals between data X and model T*P'"'"'; means for providing a signal representing decomposed loadings which have been decomposed into a function of a reference spectra and, optionally, a matrix of spectral components for analyte and interference phenomena; means for providing a signal representing the additive and multiplicative effects for the input spectra obtained from the coefficients from the loading decomposition and scores; and means for providing a signal representing the correction of said input spectra from said signal representing the additive and multiplicative effects.
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49. Apparatus for correcting an input spectral data (Xki) signal derived from a measurement or for correcting a signal representing the scores obtained by linear modeling of such data, comprising:
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means for providing a signal responsive to said input signal representing the measured spectral data as a combined additive and multiplicative structure such that
space="preserve" listing-type="equation">X=T*P'"'"'+Ewhere X=(xik) is the matrix of spectral ordinates for i=1,z . . . N objects, k=1,2 . . . , k wavelengths, T=(til) is the matrix of scores for objects i, l=1,2 . . . L representing bilinear factors obtained from a bilinear model, P=(Pki) are the loadings for objects i on bilinear factors l and E=(eik) are the residuals between data X and model T*P'"'"'; means for providing a signal representing decomposed loadings which have been decomposed into a function of a reference spectra and, optionally, a matrix of spectral components for analyte and interference phenomena; means for providing a signal representing the additive effects for the scores T obtained from the offset corrected loadings and the scores T; means responsive to said signal representing the additive effects for providing a signal representing the application of the additive effects to the multivariate scores; means for providing a signal representing the multiplicative effect from the coefficient d from the reference spectrum; and means for providing a signal representing scores corrected for additive and multiplicative effects using the multiplicative effect, or scores T and, optionally the additive effect.
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Specification