79 CHAPTER 4 WAVELET ANALYSIS OF ELECTROGASTROGRAM SIGNALS 4.1 INTRODUCTION Biosignals are used in the biomedical field mostly for the investigation of the subject’s biological system by extracting its features. Electrogastrogram [EGG], a non-stationary signal acquired cutaneously is a non-invasive method of detecting the disorders of a digestive system. The physician may have this as a preliminary investigation before going for the Endoscopic procedure. In this chapter, investigation is performed to identify the digestive system disorders present in EGG signals using Wavelet Transform. The signal is analyzed using Continuous Wavelet Transform (CWT) and Discrete Wavelet Transform (DWT). In CWT, the subjects are classified according to number of peaks obtained. In DWT, the EGG signal is first decomposed and then it is reconstructed to find the threshold value to classify the different digestive disorder subjects. The EGG signals are subjected to 3 levels of decomposition using Daubechies mother wavelet. Wavelet Transform (WT) was introduced at the beginning of the 1980s by Morlet et al Since then, various types of wavelet transforms have been developed, and many other applications have been found (Burrus et al 1998). The continuous-time wavelet transform, also called the Integral Wavelet Transform (IWT), finds most of its applications in data analysis, where it yields an affine invariant time-frequency representation. DWT has
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79
CHAPTER 4
WAVELET ANALYSIS OF ELECTROGASTROGRAM
SIGNALS
4.1 INTRODUCTION
Biosignals are used in the biomedical field mostly for the
investigation of the subject’s biological system by extracting its features.
Electrogastrogram [EGG], a non-stationary signal acquired cutaneously is a
non-invasive method of detecting the disorders of a digestive system. The
physician may have this as a preliminary investigation before going for the
Endoscopic procedure. In this chapter, investigation is performed to identify
the digestive system disorders present in EGG signals using Wavelet
Transform. The signal is analyzed using Continuous Wavelet Transform
(CWT) and Discrete Wavelet Transform (DWT). In CWT, the subjects are
classified according to number of peaks obtained. In DWT, the EGG signal is
first decomposed and then it is reconstructed to find the threshold value to
classify the different digestive disorder subjects. The EGG signals are
subjected to 3 levels of decomposition using Daubechies mother wavelet.
Wavelet Transform (WT) was introduced at the beginning of the
1980s by Morlet et al Since then, various types of wavelet transforms have
been developed, and many other applications have been found (Burrus et al
1998). The continuous-time wavelet transform, also called the Integral
Wavelet Transform (IWT), finds most of its applications in data analysis,
where it yields an affine invariant time-frequency representation. DWT has
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excellent signal compaction properties for many classes of real-world signals
while being computationally very efficient. Therefore, it has been applied to
almost all technical fields including image compression, denoising, numerical
integration, and pattern recognition.
WT has similarities with the Short-Time Fourier Transform, but it
also possesses a time-localization property that generally renders it superior
for analyzing non-stationary signals such as EGG. WT also decompose a
signal into a set of “frequency bands” (referred to as scales) by projecting the
signal onto an element of a set of basic functions. Although the scales do not
live in the frequency domain, projection of the signal onto different scales is
equivalent to bandpass filtering with a bank of constant-Q filters. The basic
functions are called wavelets. Wavelets in a basis are all similar to each other,
varying only by dilation and translation. In wavelet analysis, one looks at the
signals at different scales or resolution. A rough approximation of the signal
might look stationary; while at a detailed level when using small window,
discontinuities become evident.
4.2 LITERATURE REVIEW
Akhilesh Bijalwan et al (2012) deals with the threshold estimation
method for image denoising in the wavelet transform domain. The technique
is based upon the discrete wavelet transform analysis where the algorithm of
wavelet threshold is used to calculate the value of threshold. Experimental
results on several test images are compared with denoising techniques based
on Peak Signal to Noise ratio (PSNR), Root Mean Square Error (RMSE) and
Correlation of Coefficient (CoC). Rui Rodrigues and Paula Couto (2012)
proposed an ECG denoising method based on a feed forward neural network
with three hidden layers. Particularly useful for very noisy signals, this
approach uses the available ECG channels to reconstruct a noisy channel by
adding noise to an existing signal and measure the RMSE of the denoised
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signal relative to the original signal. Shantanu Godbole (2012) has shown
various ways in which the notion of similarity amongst subsets of classes
from the confusion matrix can be exploited. First, the author has provided a
mechanism of generating more meaningful intermediate levels of hierarchies
in large at sets of classes. Secondly, the author has demonstrated on how large
multi-class classification tasks can be scaled up with the number of classes.
Barroso-Alvarado et al (2011) reported db4 wavelet analysis on
EGG database. Classical parameters namely mean, standard deviation,
dominant frequency and dominant power are analyzed. Suman et al (2011)
proposed the adaptive noise canceller that has been optimized with Modified
Memetic Algorithm (MMA) to remove power line interference in the ECG
signals. The performance of these algorithms has been analyzed on the basis
of parameters viz., improvement in signal to noise ratio, normalized
correlation coefficient (NCC) and root mean square error (RMSE).
Nagendra.H (2011) has provided an overview of some wavelet techniques
namely CWT, DWT, Stationary WT, Fractional WT. Performance is
evaluated using RMSE. Powers, D.M.W (2011) used evaluation measures
including Recall, Precision, F-Measure and Accuracy for concepts of
Informedness, Markedness, Correlation and Significance, as well as analyzed
the intuitive relationships of Recall and Precision, and outlined the extension
from the dichotomous case to the general multi-class case.
Curilem et al (2010) compared ANN and SVM for EGG analysis
and showed SVM classifier is faster, requires less memory than ANN. Wei
Ding et al (2010) utilized Electrogastrography to detect slow wave of gastric
digest motility after test meal and the authors used multiresolution method
with the Daubechies wavelet function to decompose EGG signal. Abdel-
Reman et al (2010) used the high pass filtering for noisy signal before
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reconstruction by inverse discrete wavelet transform (IDWT). This algorithm
is very robust for noise removal in Electrocardiogram (ECG).
Chacon et al (2009) analyzed neural network structures to classify
the wavelet coefficient for healthy and dyspepsia patients. The classifier
achieved 78.6 % sensitivity and 92.9 % specificity and Classification
Accuracy of 82.1%. TanYun-fu et al (2009) used Daubechies and Symlet
wavelets for the removal of various kinds of noises present in the ECG signal
and reconstructed ECG signal with minimum distortion at a faster rate.
Saritha et al (2008) identified different types of abnormalities in ECG using
daubechies wavelets in MATLAB environment.
Wei Zhang et al (2008) used the multiresolution concept along with
adaptive filters to detect effectively, the weak ECG signal in strong noisy
environment. Cheng Peng et al (2007) applied independent component
analysis with references to separate the gastric signal from noises. Mahumut
Tokmakei (2007) analyzed EGG using discrete wavelet transform and
statistical methods to detect gastric dysrhytmia. Kania et al (2007) studied the
importance of the proper selection of mother wavelet with appropriate number
of decomposition levels for reducing the noise in ECG signal. The authors
claim that they obtained good quality signal for the wavelet db1 at first and
fourth level of decomposition and at fourth level of decomposition for sym3.
Dirgenali et al (2006) compared wavelet method and short-time
Fourier transform method to find abnormalities of EGG signals and showed
that WT sonograms can be used to classify patients successfully. Kara et al
(2006) developed a method for EGG classification based on DWT and ANN.
This method achieved 98.5% sensitivity and 94.5% specificity. Tchervensky
et al (2006) utilized wavelet-based decomposition technique to process
multichannel EGG signals. The authors considered this to be an effective
method for enhancing the clinical utility of EGG. Choukari et al (2006) used
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second level decomposition for detecting QRS complex and fourth and fifth
level of decomposition for detecting P and T waves in ECG. Brij Singh and
Arvind Tiwari (2006) presented a selection procedure of mother wavelet
basis functions applied for denoising of the ECG signal in wavelet domain
while retaining the signal peaks close to their full amplitude. The obtained
wavelet based denoised ECG signals retain the necessary diagnostics
information contained in the original ECG signal. The experimental results
have revealed suitability of Daubechies mother wavelet of order 8 to be the
most appropriate wavelet basis function for the denoising application (Parmod
and Devanjali 2010).
Kara et al (2005) performed wavelet packet analysis of EGG
signals and estimated gastric rhythm differences of normal and diabetic
subjects. Liang (2005) used a combined method of stages combined method
with independent component analysis and adaptive signal enhancement for
extraction of gastric slow waves from EGG or to detect propagation of gastric
slow waves from multichannel EGG. Amit C. Patel and Mia K. Markey
(2005) empirically compared the methods that have been proposed to evaluate
the performance of N-class classifiers (N>2). Morteza Moazami-Goudarzi
(2005) assessed the functionality of the different multiwavelets in
compressing ECG signals, in addition to known factors such as Compression
Ratio (CR), Percent Root Difference (PRD), Distortion (D), and Root Mean
Square Error (RMSE) in compression literature.
De Sobral Cintra (2004) proposed that matching a wavelet to a
class of signals can be of interest in feature detection and classification based
on wavelet representation. The authors provided a quantitative approach and
wavelets generated from the optimal parameterization values were similar to
the standard db3 wavelet and were used to the problem of matching a wavelet
to EGG signals. Hualou Liang and Zhiyue Lin (2002) provided a description
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of two multiresolution methods for electrogastric signal processing, namely,
wavelet transform and empirical mode decomposition in their paper. Zhenghu
et al (2000) developed a new method for processing EGG signals based on
wavelet transform which has a very good application perspective because it is
found to be simple and a convenient way to provide precise charts and
recognition about frequency characteristic to a refinement. Han-Chang Wu
(1998) considered EGG to be more important due to its non-invasive
measurement and the authors have developed a new method based on discrete
wavelet transform (DWT) to analyze the power distribution of the EGG
signals. Jie Liang (1997) applied Nonorthogonal Multiresolution Wavelet
Analysis (NOMRWA) on EGG noise detection and denoising.
4.3 CONTINUOUS WAVELET TRANSFORM
Continuous Wavelet Transform (CWT) was developed as an
alternative approach to the FT to reduce the difficulty in extracting
information from the signals. The term wavelet means a small wave. The
smallness refers to the condition that this function is of finite length. The
wave refers to the condition that this function is oscillatory. For getting the
CWT of a signal, the signal is multiplied with a function (wavelet), and the
transform is computed separately for different segments of the time domain
signal.
Continuous Wavelet Transform is defined by Equation (4.1)
dts
ttxs
ssCWT xx
*1,, (4.1)
where,
τ : translation parameter
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s : scaling parameter
(t) : mother wavelet
tx : input signal
The transformed signal is a function of two variables ‘τ’ and ‘s’,
the translation and scale parameters, respectively. Thus, the wavelet transform
is computed as the inner product of x (t) and translated and scaled versions of
a single function (t), which is called wavelet. (t) is the transforming
function, and it is called the mother wavelet. The term mother implies that the
functions with different region of support that are used in the transformation
process are derived from one main function, or the mother wavelet. The
mother wavelet is a prototype for generating the other window functions. The
term translation refers to the location of the window, as the window is shifted
through the signal.
In wavelet analysis, high scales correspond to a non-detailed view
of the signal, and low scales correspond to a detailed view. Similarly, in terms
of frequency, low frequencies (high scales) correspond to a global
information of a signal (that usually spans the entire signal), whereas high
frequencies (low scales) correspond to a detailed information of a hidden
pattern in the signal (that usually lasts a relatively short time).
In most of the bio-signals, low scales (high frequencies) do not last
for the entire duration of the signal, but they usually appear from time to time
as short bursts, or spikes. High scales (low frequencies) usually last for the
entire duration of the signal. Scaling, as a mathematical operation, either
dilates or compresses a signal. Larger scales correspond to dilated (or
stretched out) signals and small scales correspond to compressed signals.
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4.3.1 Analysis of EGG using CWT
Figure 4.1 shows the flowchart of the CWT technique used for the
classification of EGG signals.
Figure 4.1 Flow chart for Classification EGG with CWT
CWT is applied to the denoised EGG signal. The output is a 3-D
plot with Time in second in the X-axis, EGG sample in the Y-axis and
Amplitude in mV in the Z-axis. The plot gives a clear view of the number of
peaks in the signal. Taking 3 Cycle Per Minute (cpm) as reference for
normal EGG (Parkman et al 2003), the peaks are counted to detect
abnormalities. 3-D plot is obtained by the meshc command in MATLAB
using db4 wavelet . MATLAB performs a linear transformation on the data in
C to obtain colors from the current colormap. If X, Y, and Z are matrices,
they must be the same size as C. Figure 4.3 represents the CWT of the
normal subject. It clearly shows that the signal exhibits 3cpm. CWT, when
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applied to raw EGG data and showed unclear peaks for normal EGG as in
Figure 4.2. Due to the presence of unclear peaks, the Classification Accuracy
was found to be 61.71% for normal EGG. Hence all the signal were denoised
and then analysed.
Figure 4.2 CWT of raw EGG for Normal Subject
The reference signal obtained from the physician for normal and
dysarrthymic EGG signals when subjected to CWT analysis showed distinct
peaks for each type of EGG as depicted in Figure.4.3 for normal subjects,
Figure.4.4 for bradygastria subjects, Figure.4.5 for dyspepsia subjects,
Figure.4.6 for nausea subjects , Figure.4.7 for ulcer subjects , Figure.4.8 for
tachygastria subjects and Figure.4.9 for vomiting subjects. The cpm
determined by the the 3-D plot for various disorders is tabulated in Table 4.1
and this is used for the classification of disorders.