Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
The approximation power of moving least-squares
Mathematics of Computation
Computer Vision
Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
Blind source separation of positive and partially correlated data
Signal Processing
Hyperspectral Data Exploitation: Theory and Applications
Hyperspectral Data Exploitation: Theory and Applications
Journal of VLSI Signal Processing Systems
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
Journal of Scientific Computing
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Rapid and reliable detection and identification of unknown chemical substances are 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 non-destructive 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. 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. We also test the method on nuclear magnetic resonance (NMR) spectra for chemical compounds identification.