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Proceedings Paper

Recovery of constituent spectra using non-negative matrix factorization
Author(s): Paul Sajda; Shuyan Du; Lucas C Parra
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Paper Abstract

In this paper a constrained non-negative matrix factorization (cNMF) algorithm for recovering constituent spectra is described together with experiments demonstrating the broad utility of the approach. The algorithm is based on the NMF algorithm of Lee and Seung, extending it to include a constraint on the minimum amplitude of the recovered spectra. This constraint enables the algorithm to deal with observations having negative values by assuming they arise from the noise distribution. The cNMF algorithm does not explicitly enforce independence or sparsity, instead only requiring the source and mixing matrices to be non-negative. The algorithm is very fast compared to other "blind" methods for recovering spectra. cNMF can be viewed as a maximum likelihood approach for finding basis vectors in a bounded subspace. In this case the optimal basis vectors are the ones that envelope the observed data with a minimum deviation from the boundaries. Results for Raman spectral data, hyperspectral images, and 31P human brain data are provided to illustrate the algorithm's performance.

Paper Details

Date Published: 13 November 2003
PDF: 11 pages
Proc. SPIE 5207, Wavelets: Applications in Signal and Image Processing X, (13 November 2003); doi: 10.1117/12.504676
Show Author Affiliations
Paul Sajda, Columbia Univ. (United States)
Shuyan Du, Columbia Univ. (United States)
Lucas C Parra, Sarnoff Corp. (United States)

Published in SPIE Proceedings Vol. 5207:
Wavelets: Applications in Signal and Image Processing X
Michael A. Unser; Akram Aldroubi; Andrew F. Laine, Editor(s)

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