Biomedical Engineering Reference
In-Depth Information
Fig. 1
EEG contaminated with EOG producing spikes
N
is the noise and
E
represents the recorded signal.
The presence of these noises introduces spikes which can be confused with
neurological rhythms. They also mimic EEG signals overlying these signals
resulting in signal distortion (Fig. 1 ). Correct analysis is therefore impossible,
resulting in misdiagnosis in the case of some patients. Noise must be eliminated or
attenuated.
The method of cancellation of the contaminated segments, although practice
can lead to considerable information loss, thus other methods such as principal
component analysis (PCA) and more recently ICA and WT have been utilized [ 3 ].
Data Adaptive Transform Domain Image Denoising
Method: ICA
Definitions of ICA: We can define the ICA as it is a random vector X which
consists of finding a linear transform as in Eq. ( 2 ):
X ¼ AS
ð 2 Þ
so that the components s i are as independent as possible w.r.t. some maximum
function that measures independence. This definition is known as a general defi-
nition where no assumptions on the data are made. Independent component
analysis (ICA) is the decomposition of a random vector in linear components
which are ''as independent as possible''. Here, 'independence' should be under-
stood in its strong statistical sense: it goes beyond second order decorrelation and
thus involves the non-gaussianity of the data. The ideal measure of independence
is the higher order cumulants like kurtosis and mutual information.
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