US 2011/0213566 A1Published application

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

OwnerIvica Kopriva, Ivanka Jeric +1inventors

InventorsIvica Kopriva, Ivanka Jeric, Vilko Smrecki

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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.

Claims19

Dependent claims

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=T1−1(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.

15 more elements

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=T1−1(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.

18 more elements

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=T1−1(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.

14 more elements

Dependencies are inferred from the claim text.