Process for finding endmembers in a data set
AssigneeSpectral Sciences, Inc.
InventorsJohn Gruninger, Steven Adler-Golden
Life of this patent
Estimating the term…
Abstract
A method of representing spectral data, such as hyperspectral imaging data (HSI) and multispectral imaging data (MSI), as a set of simplex models. The method finds end-images or end-spectra in the data (termed “endmembers”) as extreme points, and simultaneously determines the abundance of the endmembers.
Claims22
A process for determining a subset of members of a group of N data vectors, the subset denoted as endmembers, which may be taken in positive linear combinations to approximate the other members of the group, comprising:
- a. providing a data set comprised of a plurality of spectra;
- b. defining an error metric dependent on a difference between two spectra;
- c. selecting a first spectrum as the first endmember;
- d. for the member spectra in the group, determining a non-negative weighting factor such that, when the first spectrum is multiplied by the weighting factor and subtracted from the spectrum, the resulting difference generates a smallest error metric;
- e. selecting as a next endmember the member spectrum whose calculated difference from step d generates the largest error metric;
- f. for the N member spectra in the group, determining a weighting factor, determining an updated difference by subtracting from the prior difference the difference for the endmember in step e multiplied by the weighting factor, and determining an updated set of member weighting factors by subtracting from the prior set of weighting factors the set of weighting factors for the endmember in step d multiplied by the weighting factor, such that all updated weighting factors are non-negative and the updated member difference generates a smallest error metric;
- and
- g. repeating steps e and f for all or a subset of member spectra one or more times.
A process for approximating each member of a group of N data vectors by means of a positive linear combination of a prior selected subset of members, the subset denoted as endmembers, each endmember being multiplied by a corresponding positive weighting factor, in which the process for determining the weighting factors comprises:
- a. providing a data set comprised of a plurality of spectra;
- b. defining an error metric dependent on a spectrum difference;
- c. selecting a first endmember as a starting spectrum;
- d. for each of the N member spectra in the group that is not the starting spectrum, determining a non-negative member weighting factor such that, when the starting spectrum is multiplied by the member weighting factor and subtracted from the member spectrum, the resulting member difference generates a smallest error metric;
- e. selecting a next endmember;
- f. for each of the N member spectra in the group that is not the starting spectrum or any selected endmember, determining a weighting factor, determining an updated member difference by subtracting from the prior member difference the difference for the endmember in step e multiplied by the weighting factor, and determining an updated set of member weighting factors by subtracting from the prior set of member weighting factors the set of weighting factors for the endmember in step e multiplied by the weighting factor, such that all updated member and endmember weighting factors are non-negative and the updated member difference generates a smallest error metric;
- and
- g. repeating steps e and f until all endmembers have been selected.
Dependencies are inferred from the claim text.