Matthias Böhm

How to Apply Nonlinear Subspace Techniques to Univariate Biomedical Time Series

In this paper, we propose an embedding technique for univariate single-channel biomedical signals to apply projective subspace techniques. Biomedical signals are often recorded as 1-D time series; hence, they need to be transformed to multidimensional signal vectors for subspace techniques to be applicable. The transformation can be achieved by embedding an observed signal in its delayed coordinates. We propose the application of two nonlinear subspace techniques to embedded multidimensional signals and discuss their relation. The techniques consist of modified versions of singular-spectrum analysis (SSA) and kernel principal component analysis (KPCA). For illustrative purposes, both nonlinear subspace projection techniques are applied to an electroencephalogram (EEG) signal recorded in the frontal channel to extract its dominant electrooculogram (EOG) interference. Furthermore, to evaluate the performance of the algorithms, an experimental study with artificially mixed signals is presented and discussed.

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.

On the use of simulated annealing to automatically assign decorrelated components in second-order blind source separation

In this paper, an automatic assignment tool, called BSS-AutoAssign,for artifact-related decorrelated components within a second-order blind source separation (BSS) is presented. The latter is based on the recently proposed algorithm dAMUSE, which provides an elegant solution to both the BSS and the denoising problem simultaneously. BSS-AutoAssign uses a local principal component analysis (PCA)to approximate the artifact signal and defines a suitable cost function which is optimized using simulated annealing. The algorithms dAMUSE plus BSS-AutoAssign are illustrated by applying them to the separation of water artifacts from two-dimensional nuclear overhauser enhancement (2-D NOESY)spectroscopy signals of proteins dissolved in water

An algorithm for automatic assignment of artifact-related independent components in biomedical signal analysis

In this work an automatic assignment tool for estimated independent components within an independent component analysis is presented. The tool is applied to the problem of removing the water resonance and related artifacts from multi-dimensional proton NMR spectra. The algorithm uses local PCA to approximate the water artifact and defines a suitable cost function which is optimized using simulated annealing. The blind extraction of artifact-related source signals is effected by a recently developed algorithm called dAMUSE.

A hybridization of simulated annealing and local PCA for automatic component assignment within ICA

Independent component analysis (ICA) as well as blind source separation (BSS) often faces the problem of assigning the independent or uncorrelated components estimated with ICA or BSS techniques to underlying source signals, artifacts or noise contributions. In this work an automatic assignment tool is presented which uses a priori knowledge about the form of some of the signals to be extracted. The algorithm is applied to the problem of removing water artifacts from 2D NOESY NMR spectra. The algorithm uses local PCA to approximate the water artifact and defines a suitable cost function which is optimized using simulated annealing. The blind source separation of the water artifact from the remaining protein spectrum is done with the recently developed algorithm dAMUSE.

AutoAssign: an automatic assignment tool for independent components

In this work an automatic assignment tool for estimated independent components within an independent component analysis is presented. The algorithm is applied to the problem of removing the water artifact from 2D NOESY NMR spectra. The algorithm uses local PCA to approximate the water artifact and defines a suitable cost function which is optimized using simulated annealing. The blind source separation of the water artifact from the remaining protein spectrum is done with the recently developed algorithm dAMUSE.