A Recursive Sparse Blind Source Separation Method for Nonnegative and Correlated Data in NMR Spectroscopy

Abstract

AbstractMotivated 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.KeywordsNMR spectroscopynon-negative correlated sourcesrecursive blind separation