dAMUSE : a new tool for denoising and blind source separation

In this work a generalized version of AMUSE, called dAMUSE is proposed. The main modification consists in embedding the observed mixed signals in a high-dimensional feature space of delayed coordinates. With the embedded signals a matrix pencil is formed and its generalized eigendecomposition is computed similar to the algorithm AMUSE. We show that in this case the uncorrelated output signals are filtered versions of the unknown source signals. Further, denoising the data can be achieved conveniently in parallel with the signal separation. Numerical simulations using artificially mixed signals are presented to show the performance of the method. Further results of a heart rate variability (HRV) study are discussed showing that the output signals are related with LF (low frequency) and HF (high frequency) fluctuations. Finally, an application to separate artifacts from 2D NOESY NMR spectra and to denoise the reconstructed artefact-free spectra is presented also.info:eu-repo/semantics/publishedVersio

Denoising using local projective subspace methods

In this paper we present denoising algorithms for enhancing noisy signals based on Local ICA (LICA), Delayed AMUSE (dAMUSE) and Kernel PCA (KPCA). The algorithm LICA relies on applying ICA locally to clusters of signals embedded in a high-dimensional feature space of delayed coordinates. The components resembling the signals can be detected by various criteria like estimators of kurtosis or the variance of autocorrelations depending on the statistical nature of the signal. The algorithm proposed can be applied favorably to the problem of denoising multi-dimensional data. Another projective subspace denoising method using delayed coordinates has been proposed recently with the algorithm dAMUSE. It combines the solution of blind source separation problems with denoising efforts in an elegant way and proofs to be very efficient and fast. Finally, KPCA represents a non-linear projective subspace method that is well suited for denoising also. Besides illustrative applications to toy examples and images, we provide an application of all algorithms considered to the analysis of protein NMR spectra.info:eu-repo/semantics/publishedVersio

A review of blind source separation in NMR spectroscopy

27 pagesInternational audienceFourier 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

Técnicas não lineares baseadas em componentes principais no estudo de séries temporais

Mestrado em Engenharia Electrónica e TelecomunicaçõesEste trabalho teve como objectivo estudar técnicas não lineares para a eliminação de ruído em séries temporais. O estudo efectuado baseou-se nos algoritmos SSA e KPCA. É apresentado um novo algoritmo, designado por Local SSA, que representa uma extensão do SSA. O algoritmo KPCA é descrito numa abordagem diferente da apresentada na literatura. Os algoritmos foram aplicados a sinais artificiais para estudar a influência dos parâmetros na performance dos mesmos. Foi efectuado um estudo preliminar da aplicação destes algoritmos a sinais EEG para eliminação de artefactos, nomeadamente, do sinal EOG.The main goal of this work was to study non linear techniques to remove noise in time series. The study was based on Singular Spectrum Analysis (SSA) and Kernel Principal Component Analysis (KPCA) algorithms. A new algorithm is presented, named as Local SSA, which consists on extension of the SSA. KPCA algorithm is described in a different approach from the one presented in the literature. The performance of the algorithms, with distinct parameters, was studied using artificial signals. A preliminary study was carried out, applying these algorithms to EEG signals in order to remove high amplitude artefacts like the interference of the EOG signal

Técnicas não lineares baseadas em componentes principais no estudo de séries temporais

Este trabalho teve como objectivo estudar técnicas não lineares para a eliminação de ruído em séries temporais. O estudo efectuado baseou-se nos algoritmos SSA e KPCA. É apresentado um novo algoritmo, designado por Local SSA, que representa uma extensão do SSA. O algoritmo KPCA é descrito numa abordagem diferente da apresentada na literatura. Os algoritmos foram aplicados a sinais artificiais para estudar a influência dos parâmetros na performance dos mesmos. Foi efectuado um estudo preliminar da aplicação destes algoritmos a sinais EEG para eliminação de artefactos, nomeadamente, do sinal EOG