Blind source separation of positive and partially correlated data

Naanaa, Wady

doi:10.1016/j.sigpro.2005.03.006

Cited by 58 publications

(76 citation statements)

References 16 publications

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“…Likewise, Full et al already considered the same simplex volume minimization principle as Craig's in the 1980s [31]. CG has also been independently discovered in other fields such as chemometrics [32] and SP [33], [34]. In all the discoveries or rediscoveries mentioned above, the driving force that led researchers on different backgrounds to devise the same idea seems to be with the geometric elegance of CG and its powerful implications on solving blind unmixing problems.…”

Section: Who Discovered Convex Geometry For Blind Unmixing?mentioning

confidence: 99%

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A Signal Processing Perspective on Hyperspectral Unmixing: Insights from Remote Sensing

Bioucas-Dias

Chan

et al. 2014

IEEE Signal Process. Mag.

421

322

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Blind hyperspectral unmixing (HU), also known as unsupervised HU, is one of the most prominent research topics in signal processing (SP) for hyperspectral remote sensing [1], [2]. Blind HU aims at identifying materials present in a captured scene, as well as their compositions, by using high spectral resolution of hyperspectral images. It is a blind source separation (BSS) problem from a SP viewpoint. Research on this topic started in the 1990s in geoscience and remote sensing [3]- [7], enabled by technological advances in hyperspectral sensing at the time. In recent years, blind HU has attracted much interest from other fields such as SP, machine learning, and optimization, and the subsequent cross-disciplinary research activities have made blind HU a vibrant topic. The resulting impact is not just on remote sensing-blind HU has provided a unique problem scenario that inspired researchers from different fields to devise novel blind SP methods. In fact, one may say that blind HU has established a new branch of BSS approaches not seen in classical BSS studies. In particular, the convex geometry concepts-discovered by early remote sensing researchers through empirical observations [3]- [7] and refined by later research-are elegant and very different from statistical independence-based BSS approaches established in

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Section: Who Discovered Convex Geometry For Blind Unmixing?mentioning

confidence: 99%

“…Since (33) is NP-hard in general, it is natural to seek approximate solutions. Let us consider the popularized 1 , relaxation solution to (33):…”

Section: Sparse Regressionmentioning

confidence: 99%

A Signal Processing Perspective on Hyperspectral Unmixing: Insights from Remote Sensing

Bioucas-Dias

Chan

et al. 2014

IEEE Signal Process. Mag.

421

322

View full text Add to dashboard Cite

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“…The 1 H NMR spectrum of any biological fluid is a superposition of the spectra of great number of compounds. Quantification and identification of the components present in the mixture is a traditional problem not only in NMR spectroscopy [3][4][5] but also in infrared (IR) spectroscopy [6,12], EPR spectroscopy [7,8], mass spectrometry [9,10,12], Raman spectroscopy [11], etc. Identification of the spectra of mixtures proceeds in majority of the cases by matching the mixture's spectra with a library reference compounds, [3,[6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Extraction of multiple pure component 1H and 13C NMR spectra from two mixtures: Novel solution obtained by sparse component analysis-based blind decomposition

Kopriva

Jerić

Smrečki

2009

Analytica Chimica Acta

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Sparse Component Analysis (SCA) is demonstrated for blind extraction of three pure component spectra from only two measured mixed spectra in 13 C and 1 H nuclear magnetic resonance (NMR) spectroscopy. This appears to be the first time to report such results and that is the first novelty of the paper. Presented concept is general and directly applicable to experimental scenarios that possibly would require use of more than two mixtures. However, it is important to emphasize that number of required mixtures is always less than number of components present in these mixtures. The second novelty is formulation of blind NMR spectra decomposition exploiting sparseness of the pure components in the wavelet basis defined by either Morlet or Mexican hat wavelet. This enabled accurate estimation of the concentration matrix and number of pure components by means of data clustering algorithm and pure components § Patent pending under the number PCT/HR2008/000037. 2 spectra by means of linear programming with constraints from both 1 H and 13 C NMR experimental data.The third novelty is capability of proposed method to estimate number of pure components in demanding underdetermined blind source separation (uBSS) scenario. This is in contrast to majority of the BSS algorithms that assume this information to be known in advance. Presented results are important for the NMR spectroscopy-associated data analysis in pharmaceutical industry, medicine diagnostics and natural products research.

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“…This sparseness condition was first known in the 1990s [1,22] in the study of blind hyper-spectral unmixing of remote sensing, where the source condition is called pixel purity assumption (PPA) [2]. In 2005, Naanaa and Nuzillard [14] used this assumption to separate the signals in nuclear magnetic resonance spectroscopy. In fact, this condition is well suited to many chemical substances including those studied in this paper.…”

Section: Convex Blind Source Separationmentioning

confidence: 99%

A sparse semi-blind source identification method and its application to Raman spectroscopy for explosives detection

Sun

Xin

2014

Signal Processing

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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.

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Blind source separation of positive and partially correlated data

Cited by 58 publications

References 16 publications

A Signal Processing Perspective on Hyperspectral Unmixing: Insights from Remote Sensing

A Signal Processing Perspective on Hyperspectral Unmixing: Insights from Remote Sensing

Extraction of multiple pure component 1H and 13C NMR spectra from two mixtures: Novel solution obtained by sparse component analysis-based blind decomposition

A sparse semi-blind source identification method and its application to Raman spectroscopy for explosives detection

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