Biomedical Engineering Reference
In-Depth Information
Non-Data Adaptive Transform Domain-Based Denoising
(Wavelet Denoising)
We know that Fast ICA are expected to correspond to artifacts only, on the other
hand, some brain action might escape to these gathered signals. The purpose of
conventional filtering is to process raw EEG data x(t) to eliminate 50 Hz line noise,
baseline values, artifacts inhabiting very low frequencies and high frequency sensor
noise v(t), and this phase may include mixture of different existing notch, lowpass,
and/or highpass filters. As artifacts have a frequency overlap with the brain signals,
the conventional filtering technique cannot be utilized, and therefore this paper
focuses on using Wavelet Denoising to explore brain activity from gathered inde-
pendent components [ 1 ].
Image
signal
and
noise
signal
by
the
wavelet
transform
have
different
characteristics:
1. In the wavelet transform, the noise energy reduces rapidly as scale increases,
but the image signal does not reduce rapidly.
2. Noise is not highly relevant at different scales of the wavelet transform. But the
wavelet transform of image signal generally has a strong correlation, the scale
of the adjacent local maxima almost appear in the same position and have the
same symbol.
The two above-mentioned points will separate image signal and noise signal,
that is to say they are the base of image denoising [ 6 ].
Wavelet Domain-Based Denoising Algorithm
An image is often corrupted by noise in its acquisition or transmission. Wavelet
provides an appropriate basis for separating noisy signal from image signal. The
motivation is that as the wavelet transform is good at energy compaction, small
coefficient is more likely due to noise and large coefficient due to important signal
features. These small coefficients can be threshold without affecting the significant
features of the images.
The problem that arises is how to find an optimal threshold such that the mean
squared error between the signal and its estimate is minimized. The wavelet
decomposition of an image is done as the image is split into 4 subbands, namely
the HH, HL, LH, and LL subbands as shown in Fig. 2 . The HH subband gives the
diagonal details of the image; the HL subband gives the horizontal features while
the LH subband represents the vertical structures. The LL subband is the low
resolution residual consisting of low frequency components and it is this subband
which is further split at a higher level of decomposition as shown in Fig. 2 [ 7 ].
The low pass filters represent the ''approximation'' of the signal or its dc
component and the high pass filters represent the ''details'' or its high frequency
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