Article

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

Journal of Scientific Computing (Impact Factor: 1.71). 01/2011; 51(3):1-21. DOI: 10.1007/s10915-011-9528-9

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**ABSTRACT:**Rapid and reliable detection and identification of unknown chemical substances is critical to homeland security. It is challenging to identify chemical components from a wide range of explosives. There are two key steps involved. One is a nondestructive and informative spectroscopic technique for data acquisition. The other is an associated library of reference features along with a computational method for feature matching and meaningful detection within or beyond the library. Recently several experimental techniques based on Raman scattering have been developed to perform standoff detection and identification of explosives, and they prove to be successful under certain idealized conditions. However data analysis is limited to standard least squares method assuming the complete knowledge of the chemical components. In this paper, we develop a new iterative method to identify unknown substances from mixture samples of Raman spectroscopy. In the first step, a constrained least squares method decomposes the data into a sum of linear combination of the known components and a non-negative residual. In the second step, a sparse and convex blind source separation method extracts components geometrically from the residuals. Verification based on the library templates or expert knowledge helps to confirm these components. If necessary, the confirmed meaningful components are fed back into step one to refine the residual and then step two extracts possibly more hidden components. The two steps may be iterated until no more components can be identified. We illustrate the proposed method in processing a set of the so called swept wavelength optical resonant Raman spectroscopy experimental data by a satisfactory blind extraction of a priori unknown chemical explosives from mixture samples.10/2011; - [Show abstract] [Hide abstract]

**ABSTRACT:**Fourier transform is the data processing naturally associated to most NMR experiments. Notable exceptions are Pulse Field Gradient and relaxation analysis, the structure of which is only partially suitable for FT. With the revamp of NMR of complex mixtures, fueled by analytical challenges such as metabolomics, alternative and more apt mathematical methods for data processing have been sought, with the aim of decomposing the NMR signal into simpler bits. Blind Source Separation is a very broad definition regrouping several classes of mathematical methods for complex signal decomposition that use no hypothesis on the form of the data. Developed outside NMR, these algorithms have been increasingly tested on spectra of mixtures. In this review, we shall provide an historical overview of the application of Blind Source Separation methodologies to NMR, including methods specifically designed for the specificity of this spectroscopy.Progress in Nuclear Magnetic Resonance Spectroscopy 01/2014; · 6.02 Impact Factor - [Show abstract] [Hide abstract]

**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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