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

Abstract

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.

Blind Separation of Analytes in Nuclear Magnetic Resonance Spectroscopy and Mass Spectrometry: Sparseness-Based Robust Multicomponent Analysis

“…Moreover, as stated by the authors, the BTEM approach is inapplicable when the number of experimentally measured spectra is less than the number of observed components. Here, as well as in recent publications, [16][17][18] we have demonstrated that the sparseness-based approach successfully estimates pure components when the number of available mixtures is less than the unknown number of components.…”

“…18 The transform T is applied to X row-wise. If mixtures are recorded by higher-dimensional spectroscopic or spectrometric modality (2D NMR for example) a higher-dimensional transform T is applied to each mixture before it is mapped to its one-dimensional counterpart.…”

“…Thus, they are not applicable to the uBSS problem that is of central interest here. To estimate the number of analytes for an identified set of SAPs, we propose to use the clustering function: [16][17][18] ( ) ( )…”

Nonlinear band expansion and nonnegative matrix underapproximation for unsupervised segmentation of a liver from a multi-phase CT image

“…have physical interpretation, factorization indeterminacies must be reduced to TT -1 =PΛ, whereas P is permutation matrix and Λ is diagonal matrix. These are standard indeterminacies in blind source separation and can be achieved if either sparseness, [5,[7][8][9], or statistical independence, [1,3,6], constraints are imposed on S. Sparseness constraints imply that at each pixel location (i 1 ,i 2 ) only few organs exists. In CT imaging, where pixel footprint is small, it is justified to assume that only one organ occupies each pixel footprint.…”

“…The LMM-based representation has been successfully used recently for unsupervised segmentation of multi-spectral image, [3][4][5][6], as well as for blind extraction of analytes from mixtures spectra in NMR spectroscopy [7,8], mass spectrometry [7,9] and FT-IR spectroscopy [10]. In multi-spectral imaging A represents matrix of spectral profiles of the objects present in the image, while S represents matrix of spatial distributions of the same objects.…”