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Model-Free Analysis of Mixtures by NMR Using Blind Source Separation
Abstract
The concept of blind source separation is described and examples of its use in 1D and 2D NMR spectroscopy are presented. The goal of this data processing method is to extract the spectra of components molecules when only mixtures are available. Copyright 1998 Academic Press.
... The case of coloured (i.e. correlated) sources also attracted significant attention; in this case, it was shown that when the source spectra are sufficiently different, the separation can be performed using only order two statistics, for example auto-covariance matrices, while most approaches rely on joint diagonalization of these matrices which means finding the orthonormal change of basis which makes the matrices as diagonal as possible [65,66]. ...
... We can mention as an example the SOBI (Second Order Blind Identification) algorithm, which Nuzillard et al. [66] applied to NMR spectroscopy. SOBI exploits the time coherence of the source signals, in the case of 13 C NMR spectra since there the resonance lines are generally narrow enough to limit the probability of peak superimposition, which fulfill the orthogonality constraint, so that the sources are pairwise decorrelated. ...
... The spectra of mixtures consisted in five 1D 13 C NMR spectra, shown in Fig. 1 (left plot) along with the estimated 13 C NMR spectra of the sources (right plot). Some cross-talk artifacts are visible, especially for the b-glucose spectrum, which were interpreted as arising from small frequency misalignment resulting from a concentration effect [66]. Typically, HSQC is presented as a frequency correlation plot while SOBI was designed to deal with 1D time domain signals, therefore some pre-and post-processing steps were required. ...
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.
... This, respectively, leads to principal component analysis (PCA) [26], independent component analysis (ICA) [27,28], sparse component analysis (SCA) [29,30] and nonnegative matrix factorization (NMF) [31]. These methods have already been applied successfully on analytes extraction from spectroscopic mixtures [32][33][34][35][36][37][38][39]. PCA, ICA and many NMF algorithms require that the unknown number of analytes is less than or equal to the number of mixtures spectra available [32,33,[36][37][38][39]. ...
... These methods have already been applied successfully on analytes extraction from spectroscopic mixtures [32][33][34][35][36][37][38][39]. PCA, ICA and many NMF algorithms require that the unknown number of analytes is less than or equal to the number of mixtures spectra available [32,33,[36][37][38][39]. That is also true for many "deconvolution" methods [40]. ...
... Linear mixture model (LMM) is commonly used in chemometrics [24,[32][33][34][35][36][37][38][39] in general and in NMR spectroscopy in particular [32,[34][35][36][37][38]. It is the model upon which linear instantaneous BSS methods are based [25,[28][29][30][31]. Taking into account the fact that NMR signals are intrinsically time domain harmonic signals with amplitude decaying exponentially with some time constant, [49], linear mixture model in the absence of additive noise reads as: ...
We introduce an improved model for sparseness-constrained nonnegative matrix factorization (sNMF) of amplitude nuclear magnetic resonance (NMR) spectra of mixtures into a greater number of component spectra. In the proposed method, the selected sNMF algorithm is applied to the square of the amplitude of the NMR spectrum of the mixture instead of to the amplitude spectrum itself. Afterwards, the square roots of separated squares of the component spectra and the concentration matrix yield estimates of the true component amplitude spectrum and of the concentration matrix. The proposed model remains linear on average when the number of overlapping components is increasing, while the model based on the amplitude spectra of the mixtures deviates from the linear one when the number of overlapping components is increased. This is demonstrated through the conducted sensitivity analysis. Thus, the proposed model improves the capability of the sparse NMF algorithms to separate correlated (overlapping) component spectra from the smaller number of mixture NMR spectra. This is demonstrated in two experimental scenarios: extraction of three correlated component spectra from two 1H NMR mixture spectra and extraction of four correlated component spectra from three COSY NMR mixture spectra. The proposed method can increase efficiency in a spectral library search by reducing the occurrence of false positives and false negatives. That, in turn, can yield better accuracy in biomarker identification studies, which makes the proposed method important for natural product research and the field of metabolic studies.
... Thereby, of interest are blind source separation (BSS) methods that use only the matrix with recorded mixtures spectra as input information891011. In majority of scenarios, separation of pure components is performed by assuming that mixture spectra are linear combinations of pure components1234. While linear mixture model is adequate for many scenarios, nonlinear model offers more accurate description of processes and interactions occurring in biological systems. Living organisms are best examples of complex nonlinear systems that function far from equilibrium. ...
... 2 Even though the exponential distribution has support on the [0,) interval, by setting =0.01 realizations will be contained in [0, 1] interval with a probability that is close to 1 with an error of 3.7210 -44 . Thus, this justifies a choice of exponential distribution to model sparse distribution of amplitudes s mt on interval [0, 1]. ...
... 2 Even though the exponential distribution has support on the [0,) interval, by setting =0.01 realizations will be contained in [0, 1] interval with a probability that is close to 1 with an error of 3.7210 -44 . Thus, this justifies a choice of exponential distribution to model sparse distribution of amplitudes s mt on interval [0, 1]. where 1 ...
Nonlinear underdetermined blind separation of nonnegative dependent sources consists in decomposing a set of observed nonlinearly mixed signals into a greater number of original nonnegative and dependent component (source) signals. This hard problem is practically relevant for contemporary metabolic profiling of biological samples, where sources (a.k.a. pure components or analytes) are aimed to be extracted from mass spectra of nonlinear multicomponent mixtures. This paper presents a method for nonlinear underdetermined blind separation of nonnegative dependent sources that comply with a sparse probabilistic model, that is, sources are constrained to be sparse in support and amplitude. This model is validated on experimental pure component mass spectra. Under a sparse prior, a nonlinear problem is converted into an equivalent linear one comprised of original sources and their higher-order, mostly second-order, monomials. The influence of these monomials, which stand for error terms, is reduced by preprocessing a matrix of mixtures by means of robust principal component analysis and hard, soft and trimmed thresholding. Preprocessed data matrices are mapped in high-dimensional reproducible kernel Hilbert space (RKHS) of functions by means of an empirical kernel map. Sparseness-constrained nonnegative matrix factorizations in RKHS yield sets of separated components. They are assigned to pure components from the library using a maximal correlation criterion. The methodology is exemplified on demanding numerical and experimental examples related respectively to extraction of eight dependent components from three nonlinear mixtures and to extraction of 25 dependent analytes from nine nonlinear mixture mass spectra recorded in nonlinear chemical reaction of peptide synthesis. Copyright © 2014 John Wiley & Sons, Ltd.
... Mandl et al. presented a linear model to estimate the metabolite concentration in the cingulum bundle using tissue fractions derived from segmentation of GM and WM from T 1 -weighted images and the cingulum from diffusion tensor imaging (8). Statistical analysis methods, such as principal component analysis (9) and independent component analysis (10), perform the spectral factorization by exploiting statistical properties of covariance and independence. Nonnegative matrix factorization method has also been proposed for blind recovery of constituent spectra (11). ...
... Therefore, separation techniques are crucial for reducing the false alarm rate during the annotation process, which increases the accuracy of biomarker identification studies. In this respect, blind source separation (BSS) methods that aim to extract the component spectra using the recorded mixtures mass spectra alone are of special interest [14][15][16][17][18]. While the great majority of BSS methods assume that multicomponent mixtures are linear combinations of, at most, the same number of components [19][20][21][22], recent work in [18] has addressed the underdetermined nonlinear nonnegative BSS problem related to the extraction of a greater number of sparse-dependent nonnegative components from a smaller number of nonlinear mixture mass spectra. ...
The nonlinear, nonnegative single-mixture blind source separation problem consists of decomposing observed nonlinearly mixed multicomponent signal into nonnegative dependent component (source) signals. The problem is difficult and is a special case of the underdetermined blind source separation problem. However, it is practically relevant for the contemporary metabolic profiling of biological samples when only one sample is available for acquiring mass spectra; afterwards, the pure components are extracted. Herein, we present a method for the blind separation of nonnegative dependent sources from a single, nonlinear mixture. First, an explicit feature map is used to map a single mixture into a pseudo multi-mixture. Second, an empirical kernel map is used for implicit mapping of a pseudo multi-mixture into a high-dimensional reproducible kernel Hilbert space. Under sparse probabilistic conditions that were previously imposed on sources, the single-mixture nonlinear problem is converted into an equivalent linear, multiple-mixture problem that consists of the original sources and their higher-order monomials. These monomials are suppressed by robust principal component analysis and hard, soft, and trimmed thresholding. Sparseness-constrained nonnegative matrix factorizations in reproducible kernel Hilbert space yield sets of separated components. Afterwards, separated components are annotated with the pure components from the library using the maximal correlation criterion. The proposed method is depicted with a numerical example that is related to the extraction of eight dependent components from one nonlinear mixture. The method is further demonstrated on three nonlinear chemical reactions of peptide synthesis in which 25, 19, and 28 dependent analytes are extracted from one nonlinear mixture mass spectra. The goal application of the proposed method is, in combination with other separation techniques, mass spectrometry-based non-targeted metabolic profiling, such as biomarker identification studies. Copyright © 2015 John Wiley & Sons, Ltd.
... In the case where both the sources and mixing coefficients are unknown, this problem comes under the heading of blind source separation (BSS). There are many applications in this area [1][2][3][4][5][6][7][8]. ...
A blind source separation method is described to extract sources from data mixtures where the underlying sources are sparse and correlated. The approach used is to detect and analyze segments of time where one source exists on its own. The method does not assume independence of sources and probability density functions are not assumed for any of the sources. A comparison is made between the proposed method and the Fast-ICA and Clusterwise PCA methods. It is shown that the proposed method works best for cases where the underlying sources are strongly correlated because Fast-ICA assumes zero correlation between sources and Clusterwise PCA can be sensitive to overlap between sources. However, for cases of sources that are sparse and weakly correlated with each other, there is a tendency for Fast-ICA and Clusterwise PCA to have better performances than the proposed method, the reason being that these methods appear to be more robust to changes in input parameters to the algorithms. In addition, because of the deflationary nature of the proposed method, there is a tendency for estimates to be more affected by noise than Fast-ICA when the number of sources increases. The paper concludes with a discussion concerning potential applications for the proposed method.
... Linear mixture model is commonly used in chemometrics27282930 in general and in MS in particular [29,30]. It is the model upon which linear instantaneous BSS methods are based1234. ...
Underdetermined blind separation of nonnegative dependent sources consists in decomposing set of observed mixed signals into greater number of original nonnegative and dependent component (source) signals. That is an important problem for which very few algorithms exist. It is also practically relevant for contemporary metabolic profiling of biological samples, such as biomarker identification studies, where sources (a.k.a. pure components or analytes) are aimed to be extracted from mass spectra of complex multicomponent mixtures. This paper presents method for underdetermined blind source separation of nonnegative dependent sources. The method performs nonlinear mixture-wise mapping of observed data in high-dimensional reproducible kernel Hilbert space (RKHS) of functions and sparseness constrained nonnegative matrix factorization (NMF) therein. Thus, original problem is converted into new one with increased number of mixtures, increased number of dependent sources and higher-order (error) terms generated by nonlinear mapping. Provided that amplitudes of original components are sparsely distributed, that is the case for mass spectra of analytes, sparseness constrained NMF in RKHS yields, with significant probability, improved accuracy relative to the case when the same NMF algorithm is performed on original problem. The method is exemplified on numerical and experimental examples related respectively to extraction of ten dependent components from five mixtures and to extraction of ten dependent analytes from mass spectra of two to five mixtures. Thereby, analytes mimic complexity of those components expected to be found in biological samples.
... More recently, there have been efforts to simultaneously exploit the statistical structure of multi-voxel spectra to solve Equation 1 as a blind source separation (BSS) problem. For example, Nuzillard et al. [4] use second order blind identification (SOBI) [5] to separate ¢ ¡ C spectra. Problematic with the approach is the assumption that the constituent spectra are orthogonal, which is required for the SOBI algorithm. ...
In this paper we describe a non-negative matrix factoriza- tion (NMF) for recovering constituent spectra in 3D chem- ical shift imaging (CSI). The method is based on the NMF algorithm of Lee and Seung (1), extending it to include a constraint on the minimum amplitude of the recovered spectra. This constrained NMF (cNMF) algorithm can be viewed as a maximum likelihood approach for finding ba- sis vectors in a bounded subspace. In this case the opti- mal basis vectors are the ones that envelope the observed data with a minimum deviation from the boundaries. Re- sults for P human brain data are compared to Bayesian Spectral Decomposition (BSD) (2) which considers a full Bayesian treatment of the source recovery problem and re- quires computationally expensive Monte Carlo methods. The cNMF algorithm is shown to recover the same con- stituent spectra as BSD, however in about less com- putational time.
... Nuzillard et al. 8 use second order blind identification (SOBI) 9 to separate 13 C spectra. Problematic with the approach is the assumption that the constituent spectra are orthogonal, which is required for the SOBI algorithm. ...
In this paper a constrained non-negative matrix factorization (cNMF) algorithm for recovering constituent spectra is described together with experiments demonstrating the broad utility of the approach. The algorithm is based on the NMF algorithm of Lee and Seung, extending it to include a constraint on the minimum amplitude of the recovered spectra. This constraint enables the algorithm to deal with observations having negative values by assuming they arise from the noise distribution. The cNMF algorithm does not explicitly enforce independence or sparsity, instead only requiring the source and mixing matrices to be non-negative. The algorithm is very fast compared to other "blind" methods for recovering spectra. cNMF can be viewed as a maximum likelihood approach for finding basis vectors in a bounded subspace. In this case the optimal basis vectors are the ones that envelope the observed data with a minimum deviation from the boundaries. Results for Raman spectral data, hyperspectral images, and 31P human brain data are provided to illustrate the algorithm's performance.
... Applications of BSS include signal analysis and processing of speech, image, and biomedical signals, especially, signal extraction, enhancement, denoising, model reduction and classification problems [7]. Recently nonnegative BSS has received a wide attention in various fields such as computer tomography, biomedical image processing, analytical chemistry [2,3,13,16,17,22,24,25,26,27,29,30,28,32] where nonnegative constraints are imposed for the mixing process and/or estimated source signals. The nonnegative BSS problem is defined by the following matrix model ...
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.
... A blind source separation (BSS) problem arises when one attempts to recover source signals from their linear mixtures without detailed knowledge of the mixing process. BSS has received considerable attention in signal analysis and processing of speech, image, and biomedical signals [3,5,6,11,13,15,17,19,20]. The linear BSS model takes the following algebraic form: ...
We study sparse blind source separation (BSS) for a class of positive and partially overlapped signals. The signals are only allowed to have nonoverlapping at certain locations, while they could overlap with each other elsewhere. For nonnegative data, a novel approach has been proposed by Naanaa and Nuzillard (NN) assuming that nonoverlapping exists for each source signal at some location of acquisition variable. However, the NN method introduces errors (spurious peaks) in the output when their nonoverlapping condition is not satisfied. To resolve this problem and improve robustness of separation, postprocessing techniques are developed in two aspects. One is to detect coherent and uncertain components from NN outputs by using multiple mixture data, then removing the uncertain portion to enhance signals. The other is to find better estimation of mixing matrix by leveraging reliable source peak structures in NN output. Numerical results on examples including NMR spectra of a 13C-1-acetylated carbohydrate with overlapping proton spin multiplets show satisfactory performance of the postprocessed sparse BSS and offer promise to resolve complex spectra without using multidimensional NMR methods.
... In practice, the NMF method is randomly initialized [24], while the ALS method is initialized by the results obtained with a non-constrained decomposition method such as principal component analysis (PCA), factor analysis algorithms252627, or using pure variable detection methods such as simple-to-use interactive self modeling mixture analysis (SIMPLISMA) [28] and orthogonal projection approach (OPA) [29]. More recently ICA methods are also used [30, 31] as an initialization method. Similarly to the algebraic methods, additional constraints such as closure, unimodality, selectivity may be added to reduce the set of admissible solutions323334. ...
This paper presents an original method for the analysis of multicomponent spectral data sets. The proposed algorithm is based on Bayesian estimation theory and Markov Chain Monte Carlo (MCMC) methods. Resolving spectral mixture analysis aims at recovering the unknown component spectra and at assessing the concentrations of the underlying species in the mixtures. In addition to non-negativity constraint, further assumptions are generally needed to get a unique resolution. The proposed statistical approach assumes mutually independent spectra and accounts for the non-negativity and the sparsity of both the pure component spectra and the concentration profiles. Gamma distribution priors are used to translate all these information in a probabilistic framework. The estimation is performed using MCMC methods which lead to an unsupervised algorithm, whose performances are assessed in a simulation study with a synthetic data set.
... Similar to factorizing a composite number Various BSS methods have been proposed relying on priori knowledge of source signals such as spatio-temporal decorrelation, statistical independence, sparseness, nonnegativity, etc, [7,8,12,16,19,20,21,25,30,31,32,33]. Recently there have been considerable interests for solving nonnegative BSS problems, which emerge in computer tomography, biomedical image processing, NMR spectroscopy [2,3,14,17,18,23,25,26,27,28,29,30,31,32,33,35]. This work is originated from analytic chemistry, in particular, NMR spectroscopy. ...
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.
... Dennoch sind schon eine Reihe von Erfolgen bei der Anwendung der ICA auf experimentelle Daten erzielt worden, insbesondere in den Gebieten der Akustik [72], Medizin [76,65] und Spektroskopie [5,49]. Dabei handelt es sich z.B. um die Trennung von Gemischen verschiedener Geräusche, die Separation vonÜberlagerungen physiologischer Signale und die Gewinnung der Spektren von Reinsubstanzen aus chemischen Mischungen. ...
... Alternatives to library matching approach are blind decomposition methods, wherein pure components' spectra are extracted using mixtures spectra only. Blind approaches to pure components spectra extraction have been reported in NMR spectroscopy, [8] infrared (IR) [9 – 11] and near infrared (NIR) spectroscopy, [11 – 17] EPR spectroscopy, [18,19] mass spectrometry, [11,16,17] Raman spectroscopy [18,19] etc. In a majority of blind decomposition schemes independent component analysis (ICA) [20 – 22] is employed to solve related blind source separation (BSS) problem. ...
The paper presents sparse component analysis (SCA)-based blind decomposition of the mixtures of mass spectra into pure components, wherein the number of mixtures is less than number of pure components. Standard solutions of the related blind source separation (BSS) problem that are published in the open literature require the number of mixtures to be greater than or equal to the unknown number of pure components. Specifically, we have demonstrated experimentally the capability of the SCA to blindly extract five pure components mass spectra from two mixtures only. Two approaches to SCA are tested: the first one based on l(1) norm minimization implemented through linear programming and the second one implemented through multilayer hierarchical alternating least square nonnegative matrix factorization with sparseness constraints imposed on pure components spectra. In contrast to many existing blind decomposition methods no a priori information about the number of pure components is required. It is estimated from the mixtures using robust data clustering algorithm together with pure components concentration matrix. Proposed methodology can be implemented as a part of software packages used for the analysis of mass spectra and identification of chemical compounds.
... By analyzing individual spectra, these methods fail to exploit the potential benefits of averaging that implicitly occurs when simultaneously fitting multiple spectra. Statistics-based techniques such as principal component analysis (PCA) (12)(13)(14) and independent component analysis (ICA) (14)(15)(16) instead use all spectra simultaneously to extract constituent components. Thus, they exploit the statistical structure of multi-voxel spectra to solve for all rows in Equation [1] simultaneously. ...
Magnetic resonance spectroscopic imaging (MRSI) is currently used clinically in conjunction with anatomical MRI to assess the presence and extent of brain tumors and to evaluate treatment response. Unfortunately, the clinical utility of MRSI is limited by significant variability of in vivo spectra. Spectral profiles show increased variability because of partial coverage of large voxel volumes, infiltration of normal brain tissue by tumors, innate tumor heterogeneity, and measurement noise. We address these problems directly by quantifying the abundance (i.e. volume fraction) within a voxel for each tissue type instead of the conventional estimation of metabolite concentrations from spectral resonance peaks. This 'spectrum separation' method uses the non-negative matrix factorization algorithm, which simultaneously decomposes the observed spectra of multiple voxels into abundance distributions and constituent spectra. The accuracy of the estimated abundances is validated on phantom data. The presented results on 20 clinical cases of brain tumor show reduced cross-subject variability. This is reflected in improved discrimination between high-grade and low-grade gliomas, which demonstrates the physiological relevance of the extracted spectra. These results show that the proposed spectral analysis method can improve the effectiveness of MRSI as a diagnostic tool.
... Some of these are recently developed methods, e.g. artificial neural-networks, 1 Bayesian spectral decomposition 2 and independent component analysis, 3 while others are well known statistical techniques with novel applications to spectroscopy, e.g. principal component analysis, 4 cluster analysis 5 and linear discriminant analysis. ...
The use of principal component analysis (PCA) for simultaneous spectral quantitation of a single resonant peak across a series of spectra has gained popularity among the NMR community. The approach is fast, requires no assumptions regarding the peak lineshape and provides quantitation even for peaks with very low signal-to-noise ratio. PCA produces estimates of all peak parameters: area, frequency, phase and linewidth. If desired, these estimates can be used to correct the original data so that the peak in all spectra has the same lineshape. This ability makes PCA useful not only for direct peak quantitation, but also for processing spectral data prior to application of pattern recognition/classification techniques. This article briefly reviews the theoretical basis of PCA for spectral quantitation, addresses issues of data processing prior to PCA, describes suitable and unsuitable datasets for PCA applications and summarizes the developments and the limitations of the method. Copyright © 2001 John Wiley & Sons, Ltd.
principal component analysis.
... More recently, there have been efforts to simultaneously exploit the statistical structure of multivoxel spectra to solve (1) as a blind source separation (BSS) problem. For example, Nuzillard et al. [25] use second-order blind identification (SOBI) [26] to separate C spectra. Ochs et al. [27] formulate (1) within a Bayesian framework to simultaneously solve for and . ...
We present an algorithm for blindly recovering constituent source spectra from magnetic resonance (MR) chemical shift imaging (CSI) of the human brain. The algorithm, which we call constrained nonnegative matrix factorization (cNMF), does not enforce independence or sparsity, instead only requiring the source and mixing matrices to be nonnegative. It is based on the nonnegative matrix factorization (NMF) algorithm, extending it to include a constraint on the positivity of the amplitudes of the recovered spectra. This constraint enables recovery of physically meaningful spectra even in the presence of noise that causes a significant number of the observation amplitudes to be negative. We demonstrate and characterize the algorithm's performance using 31P volumetric brain data, comparing the results with two different blind source separation methods: Bayesian spectral decomposition (BSD) and nonnegative sparse coding (NNSC). We then incorporate the cNMF algorithm into a hierarchical decomposition framework, showing that it can be used to recover tissue-specific spectra given a processing hierarchy that proceeds coarse-to-fine. We demonstrate the hierarchical procedure on 1H brain data and conclude that the computational efficiency of the algorithm makes it well-suited for use in diagnostic work-up.
... Several BSS approaches have been developed to simultaneously exploit the statistical structure of an MRSI dataset, factorizing Equation 1. For example, ICA (44), second-order blind identification (SOBI) (45), and bayesian spectral decomposition (8) have all been applied to MRSI datasets to decompose observed spectra into interpretable components. ...
Machine learning offers a principled approach for developing sophisticated, automatic, and objective algorithms for analysis of high-dimensional and multimodal biomedical data. This review focuses on several advances in the state of the art that have shown promise in improving detection, diagnosis, and therapeutic monitoring of disease. Key in the advancement has been the development of a more in-depth understanding and theoretical analysis of critical issues related to algorithmic construction and learning theory. These include trade-offs for maximizing generalization performance, use of physically realistic constraints, and incorporation of prior knowledge and uncertainty. The review describes recent developments in machine learning, focusing on supervised and unsupervised linear methods and Bayesian inference, which have made significant impacts in the detection and diagnosis of disease in biomedicine. We describe the different methodologies and, for each, provide examples of their application to specific domains in biomedical diagnostics.
Due to its capability for high-throughput screening 1H nuclear magnetic resonance (NMR) spectroscopy is commonly used for metabolite research. The key problem in 1H NMR spectroscopy of multicomponent mixtures is overlapping of component signals and that is increasing with the number of components, their complexity and structural similarity. It makes metabolic profiling, that is carried out through matching acquired spectra with metabolites from the library, a hard problem. Here, we propose a method for nonlinear blind separation of highly correlated components spectra from a single 1H NMR mixture spectra. The method transforms a single nonlinear mixture into multiple high-dimensional reproducible kernel Hilbert Spaces (mRKHSs). Therein, highly correlated components are separated by sparseness constrained nonnegative matrix factorization in each induced RKHS. Afterwards, metabolites are identified through comparison of separated components with the library comprised of 160 pure components. Thereby, a significant number of them are expected to be related with diabetes type 2. Conceptually similar methodology for nonlinear blind separation of correlated components from two or more mixtures is presented in the Supplementary material. Single-mixture blind source separation is exemplified on: (i) annotation of five components spectra separated from one 1H NMR model mixture spectra; (ii) annotation of fifty five metabolites separated from one 1H NMR mixture spectra of urine of subjects with and without diabetes type 2. Arguably, it is for the first time a method for blind separation of a large number of components from a single nonlinear mixture has been proposed. Moreover, the proposed method pinpoints urinary creatine, glutamic acid and 5-hydroxyindoleacetic acid as the most prominent metabolites in samples from subjects with diabetes type 2, when compared to healthy controls.
Analytical methods for mixtures of small molecules requires specificity (is a certain molecule
present in the mix?) and speciation capabilities. NMR has been a tool of choice for both of these issues since its early days, due to its quantitative (linear) response, sufficiently high resolving power and capabilities of inferring molecular structures from spectral features (even in the absence of a reference database). However, the analytical performances of NMR are being stretched by the increased complexity of the sample at hands, the dynamic range of the components, and the need of a reasonable turnover time. One approach that has been actively pursued for disentangling the composition complexity is the use of 2D NMR spectroscopy. While any of the many experiments from this family will increase the spectral resolution, some are more apt for mixtures, as they are capable to unveil signals belonging to whole molecules or fragments of it. Among the most popular ones one can enumerate HSQC-TOCSY , DOSY and Maximum-Quantum (MaxQ) NMR.
For multicomponent samples, the development of robust mathematical methods of signal decomposition would provide a clear edge towards identification. We have been pursuing, along these lines, Blind Source Separation (BSS). Here, the un-mixing of the spectra is achieved relying on correlations detected on a series of datasets. The series could be associated to samples of different relative composition or in a classically acquired 2D experiment by the mathematical laws underlying the construction of the indirect dimension, the one not recorded by the spectrometer. Many algorithms have been proposed for BSS in NMR since the seminal work of Nuzillard 5 . In this paper, we use rather standard algorithms in BSS in order to disentangle NMR spectra.
We show on simulated data (both 1D and 2D HSQC) that these approaches enable to disentangle accurately multiple components, and provide good estimates for concentrations of compounds.
Furthermore, we show that after proper realignment of the signals, the same algorithms are able to disentangle real 1D NMR spectra. We obtain similar results on 2D HSQC spectra, where BSS algorithms are able to disentangle successfully components, and provide even better estimates for concentrations.
3D DOSY experiments have the potential to provide unique and valuable information, but they are underused, in part because of the lack of efficient processing software. Here, we illustrate the power of 3D DOSY and present MAGNATE, Multidimensional Analysis for the GNAT Environment, an open-source and free software package for the analysis of pulsed field gradient (PFG) 3D NMR diffusion data, distributed under the GNU General Public License. The new software makes it possible for the first time to efficiently analyze and visualize 3D diffusion (e.g., 3D HSQC–DOSY) data using both univariate (e.g., DOSY) and multivariate (e.g., OUTSCORE) methods in a user-friendly graphical interface. The software can be used either independently or as a module in the GNAT program.
Accurate measurement of brain metabolite concentrations with proton magnetic resonance spectroscopy (1H‐MRS) can be problematic because of large voxels with mixed tissue composition, requiring adjustment for differing relaxation rates in each tissue if absolute concentration estimates are desired. Adjusting for tissue‐specific metabolite signal relaxation, however, also requires a knowledge of the relative concentrations of the metabolite in gray (GM) and white (WM) matter, which are not known a priori. Expressions for the estimation of the molality and molarity of brain metabolites with 1H‐MRS are extended to account for tissue‐specific relaxation of the metabolite signals and examined under different assumptions with simulated and real data. Although the modified equations have two unknowns, and hence are unsolvable explicitly, they are nonetheless useful for the estimation of the effect of tissue‐specific metabolite relaxation rates on concentration estimates under a range of assumptions and experimental parameters using simulated and real data. In simulated data using reported GM and WM T1 and T2 times for N‐acetylaspartate (NAA) at 3 T and a hypothetical GM/WM NAA ratio, errors of 6.5–7.8% in concentrations resulted when TR = 1.5 s and TE = 0.144 s, but were reduced to less than 0.5% when TR = 6 s and TE = 0.006 s. In real data obtained at TR/TE = 1.5 s/0.04 s, the difference in the results (4%) was similar to that obtained with simulated data when assuming tissue‐specific relaxation times rather than GM–WM‐averaged times. Using the expressions introduced in this article, these results can be extrapolated to any metabolite or set of assumptions regarding tissue‐specific relaxation. Furthermore, although serving to bound the problem, this work underscores the challenge of correcting for relaxation effects, given that relaxation times are generally not known and impractical to measure in most studies. To minimize such effects, the data should be acquired with pulse sequence parameters that minimize the effect of signal relaxation. Expressions for estimating the molality and molarity of brain metabolites with 1H‐MRS are extended to account for tissue‐specific relaxation of the metabolite signals and examined under different assumptions with simulated and real data. Errors of less than 8% were produced assuming T1 and T2 times for NAA over a range of typical TE and TR values. Using the expressions introduced in this report, these results can be extrapolated to any metabolite or set of assumptions regarding tissue‐specific relaxation.
An observed MR spectrum is composed of a set of metabolites spectrum, baseline and noise. Quantification of metabolites of interest in MR spectrum provides great opportunity for early diagnosis of dangerous disease such as brain tumors. In this paper, a novel spectral factorization approach based on singular spectrum analysis (SSA) is proposed to quantify magnetic resonance spectroscopy (MRS). In addition, baseline removal is performed in this study. The proposed method is a semi-blind spectral factorization algorithm which jointly uses observed signal and prior knowledge about metabolites of interest to improve metabolite separation. In order to incorporate prior knowledge about metabolites of interest, a new covariance matrix is suggested which exploits correlation between the observed NMR signal and prior knowledge. The objectives of the proposed method are i) removing baseline in frequency domain using SSA ii) extracting the underlying components of MRS signal based on the suggested novel covariance matrix and iii) reconstructing metabolite of interest by combining some of the extracted components using a novel cost function. Performance of the proposed method is evaluated using both synthetic and real MRS signals. The obtained results show the effectiveness of proposed technique to accurately remove baseline and extract metabolites of MRS signal.
Principal component analysis (PCA) discovers patterns in multivariate data that include spectra, microscopy, and other biophysical measurements. Direct application of PCA to crowded spectra, images, and movies (without selecting peaks or features) was shown recently to identify their equilibrium or temporal changes. To enable the community to utilize these capabilities with a wide range of measurements, we have developed multiplatform software named TREND to Track Equilibrium and Nonequilibrium population shifts among two-dimensional Data frames. TREND can also carry this out by independent component analysis. We highlight a few examples of finding concurrent processes. TREND extracts dual phases of binding to two sites directly from the NMR spectra of the titrations. In a cardiac movie from magnetic resonance imaging, TREND resolves principal components (PCs) representing breathing and the cardiac cycle. TREND can also reconstruct the series of measurements from selected PCs, as illustrated for a biphasic, NMR-detected titration and the cardiac MRI movie. Fidelity of reconstruction of series of NMR spectra or images requires more PCs than needed to plot the largest population shifts. TREND reads spectra from many spectroscopies in the most common formats (JCAMP-DX and NMR) and multiple movie formats. The TREND package thus provides convenient tools to resolve the processes recorded by diverse biophysical methods.
We introduce a new approach for resolving the NMR spectra of mixtures that relies on the mutual diffusion of dissolved species when a concentration gradient is established within the NMR tube. This is achieved by cooling down a biphasic mixture of triethylamine and deuterated water below its mixing temperature, where a single phase is expected. Until equilibrium is reached, a gradient of concentration, from “pure” triethylamine to “pure” water, establishes within the tube. The amount of time required to reach this equilibrium is controlled by the mutual diffusion coefficient of both species. Moreover, a gradient of concentration exists for each additional compound dissolved in this system, related to the partition coefficient for that compound in the original biphasic state. Using slice selective experiments it was possible to measure these concentration gradients and use them to separate signals from all the present species. We show the results acquired for a mixture composed of n-octanol, methanol, acetonitrile and benzene and compare them with those obtained by PFG-NMR.
NMR is a tool of choice for the measure of diffusion coefficients of species in solution. The DOSY experiment, a 2D implementation of this measure, has proven to be particularly useful for the study of complex mixtures, molecular interactions, polymers, etc. However, DOSY data analysis requires to resort to inverse Laplace transform, in particular for polydisperse samples. This is a known difficult numerical task, for which we present here a novel approach. A new algorithm based on a splitting scheme and on the use of proximity operators is introduced. Used in conjunction with a Maximum Entropy and $\ell_1$ hybrid regularisation, this algorithm converges rapidly and produces results robust against experimental noise. This method has been called PALMA. It is able to reproduce faithfully monodisperse as well as polydisperse systems, and numerous simulated and experimental examples are presented. It has been implemented on the server http://palma. labo.igbmc.fr where users can have their datasets processed automatically.
The use of a blind source separation (BSS) algorithm is demonstrated for the analysis of time series of nuclear magnetic resonance (NMR) spectra. This type of data is obtained commonly from experiments, where analytes are hyperpolarized using dissolution dynamic nuclear polarization (D-DNP), both in in-vivo and in-vitro contexts. High signal gains in D-DNP enable rapid measurement of data sets characterizing the time evolution of chemical or metabolic processes. BSS is based on an algorithm that can be applied to separate the different components contributing to the NMR signal and determine the time dependence of the signals from these components. This algorithm requires minimal prior knowledge of the data - notably, no reference spectra need to be provided - and can therefore be applied rapidly. In a time resolved measurement of the enzymatic conversion of hyperpolarized oxaloacetate to malate, the two signal components are separated into computed source spectra that closely resemble the spectra of the individual compounds. An improvement in the signal-to-noise ratio of the computed source spectra is found compared to the original spectra, presumably resulting from the presence of each signal more than once in the time series. The reconstruction of the original spectra yields the time evolution of the contributions from the two sources, which also corresponds closely to the time evolution of integrated signal intensities from the original spectra. BSS may therefore be an approach for the efficient identification of components and estimation of kinetics in D-DNP experiments, which can be applied at a high level of automation.
Motivated by applications in nuclear magnetic resonance (NMR) spectroscopy, we introduce a novel blind source separation (BSS) approach to treat nonnegative and correlated data. We consider the (over)-determined case where n sources are to be separated from m linear mixtures (m ≥ n). Among the n source signals, there are ℓ 1 partially overlapping (Po) sources and one positive everywhere (Pe) source. This condition is applicable for many real-world signals such as NMR spectra of urine and blood serum for metabolic fingerprinting and disease diagnosis. The geometric properties of the mixture matrix and the sparseness structure of the source signals (in a transformed domain) are crucial to the identification of the mixing matrix and the sources. The method first identifies the mixing coefficients of the Pe source by exploiting geometry in data clustering. Then subsequent elimination of variables leads to a sub-BSS problem of the Po sources solvable by the minimal cone method and related linear programming. The last step is based on solving a convex ℓ 1 minimization problem to extract the Pe source signals. Numerical results on NMR spectra show satisfactory performance of the method.
NMR diffusometry and its flagship layout, DOSY, is versatile for studying mixtures of bioorganic molecules, but a limiting factor of its applicability is the requirement of a mathematical treatment capable of distinguishing molecules with similar spectra or diffusion constants. Mathematical methods developed for other purposes (processing of text, acoustic signals, images) have shown to provide improved performances in the NMR analysis of complex mixtures, such as DOSY. We present here a processing strategy for the DOSY, a synergy of two high-performance Blind Source Separation (BSS) techniques: Non-Negative Matrix Factorization (NMF) using additional Sparse Conditioning (SC), and the JADE (Joint Approximate Diagonalization of Eigenmatrices) declination of Independent Component Analysis (ICA). While the first approach has an intrinsic affinity for NMR data, the latter one can be orders of magnitude computationally faster and can be thus used to simplify the parametrization of the former. To better understand optimal ranges of application of these and any other processing methods, we also propose a framework for evaluation of the quality of DOSY processing, which may be highly dependent of the technical implementation of the algorithms.
Diffusion-ordered spectroscopy (DOSY) is one of the most powerful methods for intact mixture analysis by NMR. However, the separation of overlapped spectra by current DOSY methods typically requires a minimum of 30% difference in diffusion coefficient. Here we present a new algorithm (OUTSCORE) that can improve the situation by almost an order of magnitude, allowing the unmixing of severely overlapped species of similar size, by combining least squares fitting with cross-talk minimisation, maximising spectral difference.
A simple and reliable method for the analysis of mixtures of water- and fat-soluble vitamins in the UV spectral region has
been developed using the chemometrical algorithm of self-modeling curve resolution for the decomposition of the spectra of
mixtures. The influence of various factors on the result of spectra decomposition has been investigated. The proposed method
has been applied to the analysis of model vitamin mixtures as well as multivitamin preparations and energetic drinks.
Different algorithms of the decomposition of spectral curves are compared by the precision of identification and quantitative
analysis of complex mixtures. The available conventional methods of self-modeling curve resolution (SIMPLISMA, MCR-ALS) and
algorithms implementing the independent component analysis (MILCA, SNICA) are used. The results are illustrated by a series
of examples of different spectral signals (UV, IR, Raman, fluorescence).
Keywordschemometrics–spectroscopy–independent component analysis
A variant of the second-order blind identification (SOBI) algorithm is described. It achieves blind source separation of data whose inverse Fourier transform presents the required correlation properties. In a former approach, mixtures were separated using an inverse FT–SOBI–FT processing sequence. The same result is obtained using a new algorithm, named f-SOBI, based on an indirect evaluation of signal correlation functions. The relationship between both approaches is discussed. Their equivalence is established when an appropriate definition of correlation functions in SOBI is used, instead of the currently implemented one.
The paper presents flexible component analysis-based blind decomposition of the mixtures of Fourier transform of infrared spectral (FT-IR) data into pure components, wherein the number of mixtures is less than number of pure components. The novelty of the proposed approach to blind FT-IR spectra decomposition is in use of hierarchical or local alternating least square nonnegative matrix factorization (HALS NMF) method with smoothness and sparseness constraints simultaneously imposed on the pure components. In contrast to many existing blind decomposition methods no a priori information about the number of pure components is required. It is estimated from the mixtures using robust data clustering algorithm in the wavelet domain. The HALS NMF method is compared favorably against three sparse component analysis algorithms on experimental data with the known pure component spectra. Proposed methodology can be implemented as a part of software packages used for the analysis of FT-IR spectra and identification of chemical compounds.
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. A major approach to non-negative BSS relies on
a strict non-overlap condition (also known as the pixel purity assumption in hyper-spectral imaging) of source signals which
is not always guaranteed in the NMR spectra of chemical compounds. A new dominant interval condition is proposed. Each source
signal dominates some of the other source signals in a hierarchical manner. The rBSS method then reduces the BSS problem into
a series of sub-BSS problems by a combination of data clustering, linear programming, and successive elimination of variables.
In each sub-BSS problem, an ℓ1 minimization problem is formulated for recovering the source signals in a sparse transformed domain. The method is substantiated
by NMR data.
In this paper, experiments on previous works of automatic decomposition of MRS based on PCA and ICA were conducted on our
small amount of low SNR dataset. New experimental results were derived. Results show that only PCA cannot decomposes MRS into
meaningful components when small amount of low SNR data are available and that the denoise ability of PCA is limited and heavily
affected result of consequent ICA. A new method combined wavelet with PCA is proposed. Experimental results on the dataset
show the improvement presented by wavelet. The new method is promising to further research, such as MRS interpretation and
classification.
The analysis of series of electron energy-loss spectra recorded with the spectrum-line technique is usually performed with two methods : the spacial difference approach and multivariate statistical analysis. Such spectra are strongly correlated, thus we associate Blind Source Separation techniques to specific pre and post processing. The principale is presented and illustrations are given through a simulation example and an experimental one.
An advanced independent component analysis algorithm (MILCA) is applied for simultaneous chemometric determination of fat- and water-soluble vitamins in complex mixtures. The analysis is based on the decomposition of spectra of multicomponent mixtures in the UV region. The key features of the proposed method are simplicity, accuracy, and reliability. Comparisons between the new algorithm and other established methods (MCR-ALS, SIMPLISMA, other ICA techniques) were made. Our results indicate that in most cases, MILCA is comparable or even outperforms other chemometrics methods taken for comparisons. The influence of different factors (abundance of components, noise, step of spectral scan, and scan speed) on decomposition performance has been investigated. The optimal conditions for spectroscopic registration have been identified. The proposed method was used for analysis of model mixtures and real objects (multivitamin drugs, food additives, and energy drinks). The resolved concentrations match well with the declared amounts and the results of reference methods.
Metabolic profiling of biological samples involves nuclear magnetic resonance (NMR) spectroscopy and mass spectrometry coupled with powerful statistical tools for complex data analysis. Here, we report a robust, sparseness-based method for the blind separation of analytes from mixtures recorded in spectroscopic and spectrometric measurements. The advantage of the proposed method in comparison to alternative blind decomposition schemes is that it is capable of estimating the number of analytes, their concentrations, and the analytes themselves from available mixtures only. The number of analytes can be less than, equal to, or greater than the number of mixtures. The method is exemplified on blind extraction of four analytes from three mixtures in 2D NMR spectroscopy and five analytes from two mixtures in mass spectrometry. The proposed methodology is of widespread significance for natural products research and the field of metabolic studies, whereupon mixtures represent samples isolated from biological fluids or tissue extracts.
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 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.
A complementary approach is proposed for analysing series of electron energy-loss spectra that can be recorded with the spectrum-line technique, across an interface for instance. This approach, called blind source separation (BSS) or independent component analysis (ICA), complements two existing methods: the spatial difference approach and multivariate statistical analysis. The principle of the technique is presented and illustrations are given through one simulated example and one real example.
Spectral reconstruction from multicomponent spectroscopic data is the frequent primary goal in chemical system identification and exploratory chemometric studies. Various methods and techniques have been reported in the literature. However, few algorithms/methods have been devised for spectral recovery without the use of any a priori information. In the present studies, a higher dimensional entropy minimization method based on the BTEM algorithm (Widjaja, E.; Li, C.; Garland, M. Organometallics 2002, 21, 1991-1997.) and related techniques were extended to large-scale arrays, namely, 2D NMR spectroscopy. The performance of this novel method had been successfully verified on various real experimental mixture spectra from a series of randomized 2D NMR mixtures (COSY NMR and HSQC NMR). With the new algorithm and raw multicomponent NMR alone, it was possible to reconstruct the pure spectroscopic patterns and calculate the relative concentration of each species without recourse to any libraries or any other a priori information. The potential advantages of this novel algorithm and its implications for general chemical system identification of unknown mixtures are discussed.
Free radicals play important roles in many physiological and pathological pathways in biological systems. These free radicals can be detected and quantified by their EPR spectra. The measured EPR spectra are often mixtures of pure spectra of several different free radicals and other chemicals. Blind source separation can be applied to estimate the pure spectra of interested free radicals. However, since the pure EPR spectra are often not independent of each other, the approach based on independent component analysis (ICA) cannot accurately extract the required spectra. In this paper, a novel sparse component analysis method for blind source separation, which exploits the sparsity of the EPR spectra, is presented to reliably extract the pure source spectra from their mixtures with high accuracy. This method has been applied to the analysis of EPR spectra of superoxide, hydroxyl, and nitric oxide free radicals, for both simulated data and real world ex vivo experiment. Compared to the traditional self-modeling method and our previous ICA-based blind source separation method, the proposed sparse component analysis approach gives much better results and can give perfect separation for mixtures of superoxide spectrum and hydroxyl spectrum in the ideal noise-free case. This method can also be used in other similar applications of quantitative spectroscopy analysis.
In this paper, we propose a novel approach for electron paramagnetic resonance (EPR) mixture spectra analysis based on blind source separation (BSS) technique. EPR spectrum of a free radical is often superimposed by overlapping spectra of other species. It is important and challenging to accurately identify and quantify the 'pure' spectra from such mixtures. In this study, an automated BSS method implementing independent component analysis is used to extract the components from mixed EPR spectra that contain overlapping components of different paramagnetic centers. To apply this method, there is no requirement to know the component spectra or the number of components in advance. The method is applied to analyze free radical EPR spectra which are collected from standard chemical system, cultured cell suspense, and ex vivo rat kidneys by spin trapping EPR technique. Results show that the BSS method proposed here is capable of identifying the component EPR spectra from mixtures with unknown compositions. The BSS technique can offer powerful aids in resolving spectral overlapping problems in general EPR spectroscopy analysis.
Fully automated methods for analyzing MR spectra would be of great benefit for clinical diagnosis, in particular for the extraction of relevant information from large databases for subsequent pattern recognition analysis. Independent component analysis (ICA) provides a means of decomposing signals into their constituent components. This work investigates the use of ICA for automatically extracting features from in vivo MR spectra. After its limits are assessed on artificial data, the method is applied to a set of brain tumor spectra. ICA automatically, and in an unsupervised fashion, decomposes the signals into interpretable components. Moreover, the spectral decomposition achieved by the ICA leads to the separation of some tissue types, which confirms the biochemical relevance of the components.
In terms of the Heisenberg vector model, heteronuclei undergo a correlated motion via scalar coupling when both have their spins simultaneously in the transverse plane of the doubly rotating reference frame. Several pulse sequences are described in terms of 1H/13C systems. A theoretical analysis of the correlated motions is given for methine (CH), methylene (CH2), and methyl (CH3) groups for the situation when the 'H magnetization vectors are initially placed in the transverse plane of the doubly rotating frame and are allowed to precess freely for (2J)−1 sec, where J is the single-bond 1H-13C coupling constant, prior to the carbon polarization transfer vectors being placed in the transverse plane. The analysis is confirmed experimentally using two-dimensional NMR and the usefulness of the sequences for two-dimensional NMR is assessed. The family of sequences is completed with a theoretical study of sequences which employ polarization transfer in addition to the correlated motion. Experimental verification for the one-dimensional use of these sequences, the exclusive polarization transfer sequence (EPT), in editing 13C spectra is given. Reverse EPT, the inverse of EPT, is also described and is shown to be useful for editing 1H spectra. While it is pointed out that we expect there to be a correspondence between correlated motion and Schroedinger picture multiple-quantum coherence, the details of this correspondence are not explored.
The independent component analysis (ICA) of a random vector consists of searching for a linear transformation that minimizes the statistical dependence between its components. In order to define suitable search criteria, the expansion of mutual information is utilized as a function of cumulants of increasing orders. An efficient algorithm is proposed, which allows the computation of the ICA of a data matrix within a polynomial time. The concept of ICA may actually be seen as an extension of the principal component analysis (PCA), which can only impose independence up to the second order and, consequently, defines directions that are orthogonal. Potential applications of ICA include data analysis and compression, Bayesian detection, localization of sources, and blind identification and deconvolution.
The separation of independent sources from an array of sensors is a classical but difficult problem in signal processing. Based on some biological observations, an adaptive algorithm is proposed to separate simultaneously all the unknown independent sources. The adaptive rule, which constitutes an independence test using non-linear functions, is the main original point of this blind identification procedure. Moreover, a new concept, that of INdependent Components Analysis (INCA), more powerful than the classical Principal Components Analysis (in decision tasks) emerges from this work.ZusammenfassungDie Trennung unabhängiger Quellen stellt ein klassiches jedoch schwieriges Problem bei der Signalverarbeitung dar. Aufgrund neurobiologischer Beobachtungen stellen wir in diesem Artikel einen selbstanpassenden Algorithmus vor, der gleichzeitig alle unbekannten, unabhängigkeitstest unter Anwendung von nicht linearen Funktionen darstellt, ist der zentralste Punkt dieses blindend Identifikationsverfahrens. Ausserdem hebt sich ein neues Konzept, das der unabhängigen Komponenten-Analyse (INCA), leistungsfähiger in den Entscheidungsvorgängen als die Analyse der Hauptkomponenten, aus dieser Arbeit hervor.RésuméLa séparation de sources indépendantes constitue un problème classique mais difficile de traitement du signal. D'après des observations neurobiologiques, nous proposons dans cet article un algorithme auto-adaptatif capable de séparer simultanément toutes les sources indépendantes inconnues. La règle d'adaptation, qui effectue un test d'indépendance grâce à l'utilisation de fonctions non-linéaires, est le point le plus central de cette méthode d'identification aveugle. De plus, un nouveau concept, celui d'analyse en composantes indépendantes (INCA), plus puissant dans les opérations de décision que celui d'analyse en composantes principales, émerge de ce travail.
Multidimensional NMR spectroscopy is a particularly interesting tool for the structural study of macromolecules. However, the assignment of crowded spectra obtained from large molecules is not an easy task, owing to superpositions of signals. We present here a method based on a mathematical analysis of omega2 planes extracted from symmetrical 3D experiments that permits a removal of these degeneracies and an automatic identification of the spin systems.
Separation of sources consists of recovering a set of signals of
which only instantaneous linear mixtures are observed. In many
situations, no a priori information on the mixing matrix is available:
The linear mixture should be “blindly” processed. This
typically occurs in narrowband array processing applications when the
array manifold is unknown or distorted. This paper introduces a new
source separation technique exploiting the time coherence of the source
signals. In contrast with other previously reported techniques, the
proposed approach relies only on stationary second-order statistics that
are based on a joint diagonalization of a set of covariance matrices.
Asymptotic performance analysis of this method is carried out; some
numerical simulations are provided to illustrate the effectiveness of
the proposed method
After a brief theoretical description, new gradient-selected, proton-detected heteronuclear correlation sequences are introduced. The gs-HMBC and gs-Relayed-HMQC are closely related to the original gs-HMQC proposed by Hurd and John. A new approach to obtain pure absorption line shapes in gradient selected spectroscopy is used to measure phase-sensitive gs-HMQC spectra, to carry out multiplicity editing in HSQC spectra and to distinguish direct and long-range correlations in HMQC/HSQC–TOCSY spectra.
This communication presents a simple algebraic method for the extraction of independent components in multidimensional data. Since statistical independence is a much stronger property than uncorrelation, it is possible, using higher-order moments, to identify source signatures in array data without any a-priori model for propagation or reception, that is, without directional vector parametrization, provided that the emitting sources be independent with different probability distributions. We propose such a "blind" identification procedure. Source signatures are directly identified as covariance eigenvectors after data have been orthonormalized and non linearily weighted. Potential applications to Array Processing are illustrated by a simulation consisting in a simultaneous range-bearing estimation with a passive array. INTRODUCTION For a lot of reasons (of various kinds), the most common Signal Processing methods deal with second-order statistics, expressed in terms of covariance matr...
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