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

Single-channel electroencephalogram analysis using non-linear subspace techniques

In this work, we propose the correction of univariate, single channel EEGs using projective subspace techniques. The biomedical signals which often represent one dimensional time series, need to be transformed to multi-dimensional signal vectors for the latter techniques to be applicable. The transformation can be achieved by embedding an observed signal in its delayed coordinates. We propose the application of two non-linear subspace techniques to the obtained multidimensional signal. One of the techniques consists in a modified version of Singular Spectrum Analysis (SSA) and the other is kernel Principal Component Analysis (KPCA) implemented using a reduced rank approximation of the kernel matrix. Both nonlinear subspace projection techniques are applied to an electroencephalogram (EEG) signal recorded in the frontal channel to extract its prominent electrooculogram (EOG) interference.info:eu-repo/semantics/publishedVersio

Brain status data analysis by sliding EMD

Biomedical signals are in general non-linear and non-stationary which renders them difficult to analyze with classical time series analysis techniques. Empirical Mode Decomposition (EMD) in conjunction with a Hilbert spectral transform, together called Hilbert-Huang Transform, is ideally suited to extract informative components which are characteristic of underlying biological or physiological processes. The method is fully adaptive and generates a complete set of orthogonal basis functions, called Intrinsic Mode Functions (IMFs), in a purely data-driven manner. Amplitude and frequency of IMFs may vary over time which renders them different from conventional basis systems and ideally suited to study non-linear and non-stationary time series. However, biomedical time series are often recorded over long time periods. This generates the need for efficient EMD algorithms which can analyze the data in real time. No such algorithms yet exist which are robust, efficient and easy to implement. The contribution shortly reviews the technique of EMD and related algorithms and develops an on-line variant, called slidingEMD, which is shown to perform well on large scale biomedical time series recorded during neuromonitoring