A Recursive Sparse Blind Source Separation Method and Its Application to Correlated Data in NMR Spectroscopy of Biofluids

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. BSS problem arises when one attempts to recover a set of source signals from a set of mixture signals without knowing the mixing process. Various approaches have been developed to solve BSS problems relying on the assumption of statistical independence of the source signals. However, signal independence is not guaranteed in many realworld data like the NMR spectra of chemical compounds. The rBSS method introduced in this paper deals with the nonnegative and correlated signals arising in NMR spectroscopy of biofluids. The statistical independence requirement is replaced by a constraint which requires dominant interval(s) from each source signal over some of the other source signals in a hierarchical manner. This condition is applicable for many real-world signals such as NMR spectra of urine and blood serum for metabolic fingerprinting and disease diagnosis. Exploiting the hierarchically dominant intervals from the source signals, the rBSS method reduces the BSS problem into a series of sub-BSS problems by a combination of data clustering, linear programming, and successive elimination of variables. Then 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 examples from NMR spectroscopy data and is promising towards separation and detection in complex chemical spectra without the expensive multi-dimensional NMR data. ∗Department of Mathematics, University of California at Irvine, Irvine, CA 92697, USA.