Multiplicative signal correction method and apparatus

Apparatus for correcting input spectral data (X.sub.ki) derived from a sensor during a measurement, at least as to multiplicative errors, said apparatus comprising:

• 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 (P.sub.ko) as a predetermined standard for such data;
• means for supplying a signal representing at least one second reference spectrum (P.sub.ka or P.sub.kj);
• 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.

In a system for analyzing a medium, said system having a spectrophotometric sensor for providing a signal representing input spectral data (X.sub.ki), 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 (P.sub.ko) as a predetermined standard for said spectral data;
• means for supplying a signal representing at least one second reference spectrum (P.sub.ka or P.sub.kj);
• 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.

The method for correcting input spectral data (X.sub.ki) derived from a measurement, by applying an additive model and multiplicative model for the data in a sequential fashion, comprising the steps of:

• 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.

The method for correcting input spectral data (X.sub.ki) derived from a measurement or for correcting the scores obtained by bilinear modeling of such data, said method comprising the steps of:

• examining the measured spectral data as a combined additive and multiplicative structure such that
• X=T*P'+E
• where X=(x.sub.ik) is the matrix of spectral ordinates for i=1,2 . . . N objects, k=1,2 . . . , K wavelengths, T=(t.sub.il) is the matrix of scores for objects i, l=1,2 . . . L representing bilinear factors Obtained from a bilinear model, P=(P.sub.ki) are the loadings for objects i on bilinear factors l, and E=(e.sub.ik) 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.

The method for correcting input spectral data (X.sub.ki) derived from a measurement or for correcting the scores obtained by bilinear modeling of such data, said method comprising the steps of:

• examining the measured spectral data as a combined additive and multiplicative structure such that
• X=T*P'+E
• where X=(x.sub.ik) is the matrix of spectral ordinates for i=1,2 . . . N objects, k=1,2 . . . , K wavelengths, T=(t.sub.il) is the matrix of scores for objects i, l=1,2 . . . L representing bilinear factors obtained from a bilinear model, P=(P.sub.ki) are the loadings for objects i on bilinear factors l, and E=(e.sub.ik) 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.

Apparatus for correcting an input spectral data (X.sub.ki) signal derived from a measurement, particularly as to multiplicative errors, by the fitting of an additive model and multiplicative model in sequential fashion, comprising:

• 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.

Apparatus for correcting an input spectral data (X.sub.ki) signal derived from a measurement or for correcting a signal representing the scores obtained by bilinear modeling of such data, comprising:

• means for providing a signal responsive to said input signal representing the measured spectral data as a combined additive and multiplicative structure such that
• X=T*P'+E
• where X=(x.sub.ik) is the matrix of spectral ordinates for i=1,z . . . N objects, k=1,2 . . . , k wavelengths, T=(t.sub.il) is the matrix of scores for objects i, l=1,2 . . . L representing bilinear factors obtained from a bilinear model, P=(P.sub.ki) are the loadings for objects i on bilinear factors l and E=(e.sub.ik) 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.

Apparatus for correcting an input spectral data (X.sub.ki) signal derived from a measurement or for correcting a signal representing the scores obtained by linear modeling of such data, comprising:

• means for providing a signal responsive to said input signal representing the measured spectral data as a combined additive and multiplicative structure such that
• X=T*P'+E
• where X=(x.sub.ik) is the matrix of spectral ordinates for i=1,z . . . N objects, k=1,2 . . . , k wavelengths, T=(t.sub.il) is the matrix of scores for objects i, l=1,2 . . . L representing bilinear factors obtained from a bilinear model, P=(P.sub.ki) are the loadings for objects i on bilinear factors l and E=(e.sub.ik) 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.