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Published in:
2011 | OriginalPaper | Chapter
A Recursive Sparse Blind Source Separation Method for Nonnegative and Correlated Data in NMR Spectroscopy
Authors : Yuanchang Sun, Jack Xin
Published in: Computer Analysis of Images and Patterns
Publisher: Springer Berlin Heidelberg
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Motivated by the nuclear magnetic resonance (NMR) spectroscopy of biofluids (urine and blood serum), we present a recursive blind source separation (rBSS) method for nonnegative and correlated data. A major approach to non-negative BSS relies on a strict non-overlap condition (also known as the pixel purity assumption in hyper-spectral imaging) of source signals which is not always guaranteed in the NMR spectra of chemical compounds. A new dominant interval condition is proposed. Each source signal dominates some of the other source signals in a hierarchical manner. The rBSS method then reduces the BSS problem into a series of sub-BSS problems by a combination of data clustering, linear programming, and successive elimination of variables. In each sub-BSS problem, an ℓ
1
minimization problem is formulated for recovering the source signals in a sparse transformed domain. The method is substantiated by NMR data.