Spectral compression algorithms for the analysis of very large multivariate images
AssigneeSandia Corporation
InventorMichael R. Keenan
Life of this patent
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Abstract
A method for spectrally compressing data sets enables the efficient analysis of very large multivariate images. The spectral compression algorithm uses a factored representation of the data that can be obtained from Principal Components Analysis or other factorization technique. Furthermore, a block algorithm can be used for performing common operations more efficiently. An image analysis can be performed on the factored representation of the data, using only the most significant factors. The spectral compression algorithm can be combined with a spatial compression algorithm to provide further computational efficiencies.
Claims44
A method for analyzing multivariate images, comprising:
- a) providing a data matrix D containing measured spectral data,
- b) reading an ith block of data Di of a total of j data blocks from the data matrix D into the memory of a computer,
- c) computing a block crossproduct matrix DiTDi from the data block Di,
- d) adding the block crossproduct matrix DiTDi to an accumulation of the block crossproduct matrices,
- e) repeating steps b) through d) until all j of the data blocks Di of the data matrix D are read, providing a crossproduct matrix DTD,
- f) performing an eigenanalysis of the crossproduct matrix to obtain eigenvectors V and eigenvalues E,
- g) computing a loadings matrix P, according to P=V,
- h) computing a scores matrix T, according to T=DP, and
- i) performing an image analysis of TPT to obtain a concentration matrix C and a spectral shapes matrix S.
A method for analyzing multivariate images, comprising:
- a) providing a data matrix D containing measured spectral data,
- b) reading an ith block of data Di of a total of j data blocks from the data matrix D into the memory of a computer,
- c) computing a block crossproduct matrix DiDiT from the data block D1,
- d) adding the block crossproduct matrix DiDiT to an accumulation of the block crossproduct matrices,
- e) repeating steps b) through d) until all j of the data blocks Di of the data matrix D are read, providing a crossproduct matrix DDT,
- f) performing an eigenanalysis of the crossproduct matrix to obtain eigenvectors V and eigenvalues E,
- g) computing a scores matrix T, according to T=V,
- h) computing a loadings matrix P, according to PT=TTD, and
- i) performing an image analysis of TPT to obtain a concentration matrix C and a spectral shapes matrix S.
A method for analyzing multivariate images, comprising:
- a) providing a data factor matrix A and a data factor matrix B obtained from a factorization of measured spectral data,
- b) computing a crossproduct data factor matrix ATA from the data factor matrix A,
- c) computing a crossproduct data factor matrix BTB from the data factor matrix B,
- d) performing an eigenanalysis of the product matrix of the crossproduct data factor matrix ATA and the crossproduct data factor matrix BTB to obtain generalized eigenvectors Y and eigenvalues E,
- e) computing a ranked loading matrix {tilde over (P)}, according to {tilde over (P)}=BYr, where Yr is the matrix whose columns are the first r columns of Y, and
- f) computing a ranked scores matrix {tilde over (T)}, according to {tilde over (T)}=A(BTB)Yr.
Dependencies are inferred from the claim text.