Abstract
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 ℓ1 minimization problem is formulated for recovering the source signals in a sparse transformed domain. The method is substantiated by NMR data.
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Sun, Y., Xin, J. (2011). A Recursive Sparse Blind Source Separation Method for Nonnegative and Correlated Data in NMR Spectroscopy. In: Real, P., Diaz-Pernil, D., Molina-Abril, H., Berciano, A., Kropatsch, W. (eds) Computer Analysis of Images and Patterns. CAIP 2011. Lecture Notes in Computer Science, vol 6855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23678-5_8
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DOI: https://doi.org/10.1007/978-3-642-23678-5_8
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