SYSTEMS AND METHODS FOR IDENTIFYING A MIXTURE

1 . A spectrometer for identifying a mixture, said spectrometer comprising:

a detector configured to generate a signal based on an interaction of light with a sample of the mixture;

a memory device having a library and a correlation matrix stored therein, wherein the library includes a plurality of spectra, each spectrum associated with a respective compound, and wherein the correlation matrix includes a correlation between each possible pair of spectra in the library; and

a processor coupled to said memory device and configured to:

determine a spectrum of the mixture based on the signal generated by said detector;

calculate a correlation vector that includes a correlation between the mixture spectrum and each spectrum in the library; and

identify the mixture based on the correlation matrix and the correlation vector.

2 . A spectrometer in accordance with claim 1 , wherein the correlation matrix is computed by a remote computing device and loaded onto said memory device.

3 . A spectrometer in accordance with claim 1 , wherein said processor is configured to identify the mixture using at least one of a covariance matrix and standard deviations of spectra in the library, wherein at least one of the covariance matrix and the standard deviations are stored in said memory device.

4 . A spectrometer in accordance with claim 1 , wherein to identify the mixture, said processor is configured to:

rank elements of the correlation vector to generate a top hit set that includes a number of compounds that are most closely correlated with the mixture;

generate a residual spectrum for each compound in the top hit set;

calculate a correlation between each residual spectrum and each spectrum in the library using the correlation matrix and the correlation vector;

generate a residual top hit set for each residual spectrum;

produce a plurality of two-compound models from the top hit set and each residual top hit set;

rank the two-compound models according to a predetermined criteria; and

identify the mixture as one of the two-compound models based on the ranking.

5 . A spectrometer in accordance with claim 4 , wherein said processor is configured to rank the two-compound models according to a mean absolute error of each two-compound model, and wherein said processor is configured to identify the mixture as the two-compound model with the lowest mean absolute error.

6 . A spectrometer in accordance with claim 1 , wherein to identify the mixture, said processor is configured to:

fit the mixture spectrum to a plurality of spectra each associated with a multi-compound model;

calculate the mean squared error for each fit using the correlation matrix and the correlation vector; and

identify the mixture as the multi-compound model associated with the lowest mean squared error.

7 . A spectrometer in accordance with claim 6 , wherein said processor is configured to fit the mixture spectrum to spectra associated with two-compound models, and wherein said processor is configured to calculated the mean squared error as

MSE

=

sd

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where MSE is the mean squared error, sd is the standard deviation of the mixture spectrum, r u is the correlation between the mixture spectrum and the spectrum of compound u, r y is the correlation between the mixture spectrum and the spectrum of compound v, and R uv is the correlation between the spectrum of compound u and the spectrum of compound v from the correlation matrix.

8 . A processing device configured to:

acquire a spectrum of a mixture;

calculate a correlation vector that includes a correlation between the mixture spectrum and each of a plurality of spectra stored in a library; and

identify the mixture based on the correlation vector and a correlation matrix that includes a correlation between each possible pair of spectra in the library.

9 . A processing device in accordance with claim 8 , wherein said processing device is further configured to calculate the correlation matrix.

10 . A processing device in accordance with claim 8 , wherein said processing device is configured to update the correlation matrix when at least one new spectrum is added to the library.

11 . A processing device in accordance with claim 8 , wherein to identify the mixture, said processing device is configured to:

rank elements of the correlation vector to generate a top hit set that includes a number of compounds that are most closely correlated with the mixture;

generate a residual spectrum for each compound in the top hit set;

calculate a correlation between each residual spectrum and each spectrum in the library using the correlation matrix and the correlation vector;

generate a residual top hit set for each residual spectrum;

produce a plurality of two-compound models from the top hit set and each residual top hit set;

rank the two-compound models according to a predetermined criteria; and

identify the mixture as one of the two-compound models based on the ranking.

12 . A processing device in accordance with claim 11 , wherein said processing device is configured to rank the two-compound models according to a mean absolute error of each two-compound model, and wherein said processing device is configured to identify the mixture as the two-compound model with the lowest mean absolute error.

13 . A processing device in accordance with claim 8 , wherein to identify the mixture, said processing device is configured to:

fit the mixture spectrum to a plurality of spectra each associated with a multi-compound model;

calculate the mean squared error for each fit using the correlation matrix and the correlation vector; and

identify the mixture as the multi-compound model associated with the lowest mean squared error.

14 . A method for identifying a mixture, said method comprising:

acquiring, using a spectrometer, a spectrum of the mixture;

calculating, using a processing device, a correlation vector that includes a correlation between the mixture spectrum and each of a plurality of spectra stored in a library, each library spectrum associated with a respective compound; and

identifying, using the processing device, the mixture based on the correlation vector and a correlation matrix that includes a correlation between each possible pair of spectra in the library.

15 . A method in accordance with claim 14 , further comprising calculating the correlation matrix.

16 . A method in accordance with claim 14 , further comprising updating the correlation matrix when at least one new spectrum is added to the library.

17 . A method in accordance with claim 14 , wherein identifying the mixture comprises:

ranking elements of the correlation vector to generate a top hit set that includes a number of compounds that are most closely correlated with the mixture;

generating a residual spectrum for each compound in the top hit set;

calculating a correlation between each residual spectrum and each spectrum in the library using the correlation matrix and the correlation vector;

generating a residual top hit set for each residual spectrum;

producing a plurality of two-compound models from the top hit set and each residual top hit set;

ranking the two-compound models according to a predetermined criteria; and

identifying the mixture as one of the two-compound models based on the ranking.

18 . A method in accordance with claim 17 , wherein ranking the two-compound models comprises ranking the two-compound models according to a mean absolute error of each two-compound model, and wherein identifying the mixture comprises identifying the mixture as the two-compound model with the lowest mean absolute error.

19 . A method in accordance with claim 14 , wherein identifying the mixture comprises:

fitting the mixture spectrum to a plurality of spectra each associated with a multi-compound model;

calculating the mean squared error for each fit using the correlation matrix and the correlation vector; and

identifying the mixture as the multi-compound model associated with the lowest mean squared error.

20 . A method in accordance with claim 19 , wherein fitting the mixture spectrum comprises fitting the mixture spectrum to spectra associated with two-compound models, and wherein calculating the mean squared error comprises calculating the mean squared error using

MSE

=

sd

×

(

1

-

r

u

2

+

r

v

2

-

2



r

u



r

v



R

uv

1

-

R

uv

2

)

,

where MSE is the mean squared error, sd is the standard deviation of the mixture spectrum, r u is the correlation between the mixture spectrum and the spectrum of compound u, r v is the correlation between the mixture spectrum and the spectrum of compound v, and R uv is the correlation between the spectrum of compound u and the spectrum of compound v from the correlation matrix.