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

• US 20110213566A1
• Filed: 04/20/2011
• Published: 09/01/2011
• Est. Priority Date: 11/24/2008
• Status: Abandoned Application

• Current Assignee: Ruđjer Bošković Institute
• Original Assignee: Ruđjer Bošković Institute
• Inventors: Kopriva, Ivica, Smrecki, Vilko, Jeric, Ivanka
• Application Number:
  US13/090,629
• Publication Number:
  US 20110213566A1
• Time in Patent Office: Days
• US Class Current: 702/28
• CPC Class Codes: G06F 18/2134 based on separation criteria, e.g. independent component analysis

Abstract

A method, system, and computer program product for identification of more than two pure components from two mixtures using sparse component analysis. Spectroscopic data for two mixtures X are analyzed in a recording domain or in a first new representation domain by using linear transform T₁, wherein pure components in the first new representation domain are sparser than in the recording domain. The number of pure components and mixing matrix are estimated by means of a data clustering algorithm. The pure components are estimated by means of linear programming, convex programming with quadratic constraint (l₂-norm based constraint) or quadratic programming method with l₁-norm based constraint. The estimated pure components are ranked using negentropy based criterion.

Claims

1. A method of blind extraction of more than two pure components out of spectroscopic or spectrometric measurements of only two mixtures using sparse component analysis, comprising the steps of:

recording two mixtures data X using a mixtures sensing device wherein a recording domain of the two mixture data is defined by equation [I];

X=AS 

 

[I]

where S is an unknown matrix of pure components and A is an unknown mixing or concentration matrix,

storing the recorded two mixtures data in a data storing device,

executing instructions on a processor of an instruction executing computer for;

transforming the two mixtures data X into a first new representation domain by using linear transform wherein the transformed mixtures T₁(X) are represented by equation [II];

T₁(X)=AT₁(S) 

 

[II]

and pure components in the first new representation domain defined by equation [II] are sparser than in recording domain defined by equation [I],

estimating the number of pure components S and the mixing or concentration matrix A in the first new representation domain defined by equation [II] by means of a data clustering algorithm,

provided that 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 T₁(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 T₁(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 T₁ according to equation [IV];

S=T₁<sup>−

1</sup>(T₁(S)) 

 

[IV]

provided that the results presentation domain is the second new representation domain defined by equation [III], transforming the mixtures data from the recording domain defined by equation [I] to a second new representation domain by using linear transform T₂, wherein the transformed mixtures T₂(X) are represented by equation [III];

T₂(X)=AT₂(S) 

 

[III]

and pure components in the second new representation domain defined by equation [III] are sparser than in recording domain defined by equation [I],

estimating the pure components in the second new representation domain defined by equation [III] by means of linear programming, constrained convex programming or constrained quadratic programming,

selecting the estimated pure components in accordance with the negentropy-based raking criteria, and

outputting output data including an identification of the estimated selected pure components to an output device for displaying or storing output data.

2. The method of claim 1, wherein the linear transform T₁ is a wavelet transform with either Morlet or Mexican hat wavelet.

3. The method of claim 1, wherein the linear transform T₂ is a Fourier transform.

4. The method of claim 3, wherein 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.

5. The method of claim 4, wherein 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 (l₂-norm based constraint) or a quadratic programming method with l₁-norm based constraint.

6. The method of claim 2, wherein the linear transform T₁ is a wavelet transform with the second to eight order Daubechies wavelets or symlets or coiflets of the order one to five.

7. The method of claim 6, wherein 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.

8. The method of claim 7, wherein a numerical method is 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 (l₂-norm based constraint) or a quadratic programming method with l₁-norm based constraint.

9. The method of claim 1, wherein said method is applied to the identification of the compounds in chemical synthesis, food quality inspection or pollution inspection.

10. Computer-readable medium having computer-executable instructions stored thereon which, when executed by a computer, will cause the computer to carry out the method of claim 1.

11. 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:

an instruction executing computer having a data storing device, a processor, and an output device;

a mixtures sensing device for recording mixtures data X, wherein a recording domain of the two mixture data is defined by equation [I];

X=AS 

 

[I]

where S is an unknown matrix of pure components and A is an unknown mixing or concentration matrix,

said data storing device receiving and storing the mixture data X recorded by the mixtures sensing device,

instructions executed on said processor for processing the mixtures data X stored in the input data storing device, for;

transforming the two mixtures data X into a first new representation domain by using linear transform T₁ wherein the transformed mixtures T₁(X) are represented by equation [II];

T₁(X)=AT₁(S) 

 

[II]

and pure components in the first new representation domain defined by equation [II] are sparser than in recording domain defined by equation [II],

estimating the number of pure components S and the mixing or concentration matrix A in the first new representation domain defined by equation [II] by means of a data clustering algorithm,

provided that 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 T₁(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 T₁(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 T₁ according to equation [IV];

S=T₁<sup>−

1</sup>(T₁(S)) 

 

[IV]

provided that the results presentation domain is the second new representation domain defined by equation [III], transforming the mixtures data from the recording domain defined by equation [I] to a second new representation domain by using linear transform T₂, wherein the transformed mixtures T₂(X) are represented by equation [III];

T₂(X)=AT₂(S) 

 

[III]

and pure components in the second new representation domain defined by equation [III] are sparser than in recording domain defined by equation [I],

estimating the pure components in the second new representation domain defined by equation [III] by means of linear programming, constrained convex programming or constrained quadratic programming,

selecting the estimated pure components in accordance with the negentropy-based raking criteria, and

outputting output data including an identification of the estimated selected pure components; and

said output device for displaying or storing output data.

13. The system of claim 11, wherein the mixtures sensing device is a nuclear magnetic resonance (NMR) spectrometer, ultraviolet spectrometer, IR spectrometer, electron paramagnetic resonance spectrometer, Raman spectrometer or mass spectrometer.

14. The system of claim 13, wherein the linear transform T₁ is a wavelet transform with either Morlet or Mexican hat wavelet.

15. The system of claim 14, wherein the linear transform T₂ is a Fourier transform.

16. The system of claim 15, wherein 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.

17. The system of claim 16, wherein 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 (l₂-norm based constraint) or a quadratic programming method with l₁-norm based constraint.

18. The system of claim 14, wherein the linear transform T₁ is a wavelet transform with the second to eight order Daubechies wavelets or symlets or coiflets of the order one to five.

12. (canceled)

19. A computer readable medium having computer executable instructions stored thereon for

receiving mixtures data X from a mixtures sensing device, wherein a recording domain of the two mixture data is defined by equation [I]:

X=AS 

 

[I]

where S is an unknown matrix of pure components and A is an unknown mixing or concentration matrix,

storing the mixture data X recorded by the mixtures sensing device,

transforming the two mixtures data X into a first new representation domain by using linear transform T₁ wherein the transformed mixtures T₁(X) are represented by equation [II];

T₁(X)=AT₁(S) 

 

[II]

and pure components in the first new representation domain defined by equation [II] are sparser than in recording domain defined by equation [I],

estimating the number of pure components S and the mixing or concentration matrix A in the first new representation domain defined by equation [II] by means of a data clustering algorithm,

provided that 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 T₁(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 T₁(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 T₁ according to equation [IV];

S=T₁<sup>−

1</sup>(T₁(S)) 

 

[IV]

provided that the results presentation domain is the second new representation domain defined by equation [III], transforming the mixtures data from the recording domain defined by equation [I] to a second new representation domain by using linear transform T₂, wherein the transformed mixtures T₂(X) are represented by equation [III];

T₂(X)=AT₂(S) 

 

[III]

and pure components in the second new representation domain defined by equation [III] are sparser than in recording domain defined by equation [I],

estimating the pure components in the second new representation domain defined by equation [III] by means of linear programming, constrained convex programming or constrained quadratic programming,

selecting the estimated pure components in accordance with the negentropy-based raking criteria, and

outputting output data including an identification of the estimated selected pure components.