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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. 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 real-world 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 ℓ
1 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.
KeywordsNonnegative and correlated sources–Blind source separation–Recursive method–Data clustering–
ℓ
1 minimization
Journal of Scientific Computing 04/2012; · 1.56 Impact Factor
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ABSTRACT: In this paper, we develop a novel blind source separation (BSS) method for
nonnegative and correlated data, particularly for the nearly degenerate data.
The motivation lies in nuclear magnetic resonance (NMR) spectroscopy, where a
multiple mixture NMR spectra are recorded to identify chemical compounds with
similar structures (degeneracy).
There have been a number of successful approaches for solving BSS problems by
exploiting the nature of source signals. For instance, independent component
analysis (ICA) is used to separate statistically independent (orthogonal)
source signals. However, signal orthogonality is not guaranteed in many
real-world problems. This new BSS method developed here deals with
nonorthogonal signals. The independence assumption is replaced by a condition
which requires dominant interval(s) (DI) from each of source signals over
others. Additionally, the mixing matrix is assumed to be nearly singular. The
method first estimates the mixing matrix by exploiting geometry in data
clustering. Due to the degeneracy of the data, a small deviation in the
estimation may introduce errors (spurious peaks of negative values in most
cases) in the output. To resolve this challenging problem and improve
robustness of the separation, methods are developed in two aspects. One
technique is to find a better estimation of the mixing matrix by allowing a
constrained perturbation to the clustering output, and it can be achieved by a
quadratic programming. The other is to seek sparse source signals by exploiting
the DI condition, and it solves an $\ell_1$ optimization. We present numerical
results of NMR data to show the performance and reliability of the method in
the applications arising in NMR spectroscopy.
10/2011;
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SIAM J. Scientific Computing. 01/2011; 33:2063-2094.
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Computer Analysis of Images and Patterns - 14th International Conference, CAIP 2011, Seville, Spain, August 29-31, 2011, Proceedings, Part II; 01/2011
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Computer Analysis of Images and Patterns - 14th International Conference, CAIP 2011, Seville, Spain, August 29-31, 2011, Proceedings, Part II; 01/2011
