Blind Source Separation in Nonlinear Mixtures: Separability and a Basic Algorithm

Ehsandoust, Bahram; Babaie‐Zadeh, Massoud; Rivet, Bertrand; Jutten, Christian

doi:10.1109/tsp.2017.2708025

Cited by 18 publications

(4 citation statements)

References 37 publications

(55 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…when the number of overlapping peaks increases [28]. 2 Compared with the method proposed herein, existing nonlinear BSS methods assume the availability of multiple nonlinear mixtures [29][30][31][32][33][34][35][36][37][38][39][40][41][42].…”

Section: Related and Background Workmentioning

confidence: 99%

Library-assisted nonlinear blind separation and annotation of pure components from a single 1H nuclear magnetic resonance mixture spectra

Kopriva

Jerić

Hadžija

et al. 2019

Analytica Chimica Acta

View full text Add to dashboard Cite

Due to its capability for high-throughput screening 1 H nuclear magnetic resonance (NMR) spectroscopy is commonly used for metabolite research. The key problem in 1 H 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 1 H 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 1 H NMR model mixture spectra; (ii) annotation of fifty five metabolites separated from one 1 H 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.

show abstract

Section: Related and Background Workmentioning

confidence: 99%

Library-assisted nonlinear blind separation and annotation of pure components from a single 1H nuclear magnetic resonance mixture spectra

Kopriva

Jerić

Hadžija

et al. 2019

Analytica Chimica Acta

View full text Add to dashboard Cite

show abstract

“…It is often considered in the Fourier transform domain where it is translated to a set of instantaneous mixtures, which can be treated as the jBSS problem [39]- [41]. Some specific nonlinear mixing models have been studied, e.g., in [42], [43].…”

Section: B State-of-the-artmentioning

confidence: 99%

Double Nonstationarity: Blind Extraction of Independent Nonstationary Vector/Component from Nonstationary Mixtures -- Algorithms

Koldovsky¹,

Kautský²,

Tichavský³

2022

Preprint

View full text Add to dashboard Cite

In this article, nonstationary mixing and source models are combined for developing new fast and accurate algorithms for Independent Component or Vector Extraction (ICE/IVE), one of which stands for a new extension of the well-known FastICA. This model allows for a moving sourceof-interest (SOI) whose distribution on short intervals can be (non-)circular (non-)Gaussian. A particular Gaussian source model assuming tridiagonal covariance matrix structures is proposed. It is shown to be beneficial in the frequency-domain speaker extraction problem. The algorithms are verified in simulations. In comparison to the state-of-the-art algorithms, they show superior performance in terms of convergence speed and extraction accuracy.

show abstract

“…Sparse signal representation (SSR) is used in many applications, such as image and tensor denoising, tensor compression, tensor completion, face and audio signal recognition, blind source separation, inverse synthetic aperture radar (ISAR) image formation and classification, and so on [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. This area of signal processing consists of two fundamental principles, proper selection of basis signals (called atoms) which is known as Dictionary Learning (DL), and introducing efficient methods for computing the sparse representation of the signals over the set of obtained atoms (dictionary) called Sparse Coding (SC).…”

Section: Introductionmentioning

confidence: 99%

3D inverse synthetic aperture radar image quality improvement using sparse signal representation

Mehrpooya

Karbasi

Nazari

et al. 2022

IET Radar Sonar & Navi

View full text Add to dashboard Cite

Generalisation of one‐dimensional dictionary learning (1DDL) algorithms to Multidimensional (MD) mode and its utilisation in MD data applications, increases the speed and reduces the computational complexity. An example of such an application is 3D inverse synthetic aperture radar (ISAR) image reconstruction and noise reduction. In this study, in addition to MD mode generalisation, the formulation structure of the multidimensional dictionary learning (MDDL) problem is discussed followed by two novel algorithms to solve it. The first one is based on the K‐singular value decomposition algorithm for 1DDL, which uses alternating minimisation and singular value decomposition. The second algorithm is the extension of the sequential generalisation of K‐means 1DDL algorithm to the MD mode. Moreover, the MD tensor denoising method based on the MDDL algorithm (MDDL‐ALG) is proposed. As an application, the proposed method is used to denoise the 3D ISAR image. The numerical simulations reveal that the proposed methods, in addition to reducing the memory consumption and the computational complexity, also enjoy higher convergence rate in comparison to 1D algorithms. Specifically, convergence speed of MD algorithms, depending on the training data size, is up to at least 10 times faster than the equivalent 1D counterparts. As revealed through the simulations, the amount of signal to noise ratio recovered by the proposed methods is almost 2 dB higher than the case using a pre‐designed dictionary for denoising. Moreover, it outperforms about 10 dB over the case with the conventional 3D‐IFFT method for image construction.

show abstract

Blind Source Separation in Nonlinear Mixtures: Separability and a Basic Algorithm

Cited by 18 publications

References 37 publications

Library-assisted nonlinear blind separation and annotation of pure components from a single 1H nuclear magnetic resonance mixture spectra

Library-assisted nonlinear blind separation and annotation of pure components from a single 1H nuclear magnetic resonance mixture spectra

Double Nonstationarity: Blind Extraction of Independent Nonstationary Vector/Component from Nonstationary Mixtures -- Algorithms

3D inverse synthetic aperture radar image quality improvement using sparse signal representation

Contact Info

Product

Resources

About