Biosignal Processing Mari Karsikas

Transcription

1 Independent component analysis, ICA Biosignal Processing Mari Karsikas

2 After PCA studies

3 Motivation

4 Motivation Independent component analysis (ICA) is a statistical and computational technique for revealing hidden factors that underlie sets of random variables, measurements, or signals. cocktail-party problem several signal sources the sensors measure some unknown mixtures of sources how to recover original source signals? See figures on the right: There is an overlap of the frequency content of these signals making it difficult to separate these using spectral filtering techniques. Due to this there is a need for new signal separation techniques such as ICA. (i) Electromyogram (EMG), (ii) Electrocardiogram (ECG), (iii) Electro-oculargram (EOG), (iv) Electro-encephlogram (EEG), (v) magneto-encelogram (MEG)

5 Assumptions and limitations of ICA The success of ICA to estimate independent sources is dependent on the fulfilment of the following conditions. The sources must be statistically independent. The sources must have non Gaussian distributions. However, ICA can still estimate the sources with small degree of non-gaussianity. The number of available mixtures N must be at least the same as the number of the independent components M. The mixtures must be (can be assumed as) linear combination of the independent sources. There should be no (little) noise and delay in the recordings. ICA also suffers from the following unavoidable ambiguities. The order of the independent components cannot be determined (it may change each time the estimation starts). The exact amplitude (scale) and sign of the independent components cannot be determined.

6 Whitening: a preprocessing to ICA

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9 More on ICA Nongaussianity can be determined by: - Maximum positive transform of kurtosis - Minimum differential entropy =~ Maximum Negentropy, Gaussians have max. diff. entr. - Gram-Charlier expansion Ambiguities in ICA Signal sign, energy and order cannot be recovered Interesting software: FastICA ICA can be derived in various ways By maximization of nongaussianity (as above) By maximum likelihood estimation By minimization of mutual information By tensorial methods By nonlinear decorrelation and nonlinear PCA By methods using time structure

10 PCA vs. ICA

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12 Independent component analysis (ICA) for removing artefact and noise from recorded biosignals. For example: * Researchers have also attempted to use ICA to isolate the electro- oculography (EOG) artefact from electroenchepalography (EEG) data to identify and remove electrocardiography (ECG) artefact from surface electromyography (SEMG) for separation of breathing artefacts in ECG signal. Example 1 Artefact removing by ICA

13 Example 2 Removing blink and muscle artifacts The figure shows a 3-sec portion of the recorded EEG time series and its ICA component activations, the scalp topographies of four selected components, and the artifact- corrected EEG signals obtained by removing four selected EOG and muscle noise components from the data. The eye movement artifact at 1.8 sec in the EEG data (left) is isolated to ICA components 1 and 2 (left middle). The scalp maps (right middle) indicate that these two components account for the spread of EOG activity to frontal sites.

14 Example 3

15 ICASSO= ICA repeatability analysis

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17 Independent Component Analysis Demo Jon Shlens, 13 Feb 2003 [ matlab ] A step-by-step tutorial and sofware demo that examines what ICA does, the advantage of ICA over PCA and the limits of ICA

18 Literature Hyvärinen A, Karhunen J, Oja E. Independent component analysis, John Wiley & Sons, Inc., New York, 2001, p Material in: Limitations of ICA for Artefact Removal PCA vs. ICA, and other important information: T. He, G. Clifford, and L. Tarassenko, Application of ica in the separation of breathing artifacts in ecg signals, Neural Computing and Applications, 2002.