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CHAPTER 1

INTRODUCTION

1.1 Introduction

Signal and system are the two major components in signal processing. A signal is a physical

quantity having the characteristics of varying w.r.t. time and space and the system is a process

whose input and output is a signal. The signal could be of any type. This chapter gives the brief

introduction about the biomedical signals and the various transformation techniques used for de-

noising of the non-stationary signals. The chapter also gives an idea about biomedical signals

and various methods used for the analysis of these signals. A wide study of literature has been

presented followed by the outcome from the literature and objectives of the thesis.

1.2. Biomedical Signals and Analysis

Biomedical signal generally represents a collective electrical signal attained from any organ,

signifying a physical variable of interest. This signal can be expressed with respect to its

amplitude, frequency and phase as well as it is on the whole a function of time. In common, the

observations gained from the physiological activities such as gene and protein sequences, neural

and cardiac rhythms, tissue and organ images of organisms are said to be biomedical signals.

Depending upon their source, application or signal characteristics, the biomedical signals are

classified. They can be either continuous or discrete. A number of signal sources may result into

a biomedical signal. Those sources are bioelectric Signals, bioimpedance signals, bioacoustic

signals, biomagnetic signals, biochemical signals and bio-optical signals.

Biomedical signal covers a wide range of signals including Electro-Oculogram (EOG) signal,

Electroneurogram (ENG) signal, Electrogastrogram (EGG) signal, Phonocardiogram (PCG)

signal, Carotid Pulse (CP) signal, Vibromyogram (VMG) signal, Vibroarthogram (VAG) signal,

Electrocardiogram (ECG), Electroencephalogram (EEG) and Electromyography (EMG) signal.

More precisely, the significant and widely applied biomedical signals are Electrocardiogram

(ECG), Electroencephalogram (EEG) and Electromyography (EMG).

Once the biomedical signals are recorded, they need to be analysed. The major operations of

signal processing include:

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1) Signal acquisition and reconstruction,

2) Quality improvement including filtering, smoothing and digitization,

3) Feature extraction,

4) Signal compression,

5) Prediction.

In other words, the analysis includes, information gathering i.e. inferring a system by phenomena

measurement, diagnosis of malfunction or deformity and monitoring the system for continuous

or periodic information. Therapy and control which is modifying the system behaviour with

respect to the result of the above listed activities guarantees a definite result and finally the

evaluation which is to make it able to meet functional requirements, perform quality control, or

qualify the treatment effectiveness.

Biomedical signal processing aid the biologists to discover new biology and doctors in

monitoring diverse diseases. However the major problem faced by the entire signal processing

applications is noise. Noise is an unwanted signal superimposed over a pure signal [1]. A noise

can be differentiated according to its time and frequency domain properties. Types of noises are

white noise, uniform noise, and Gaussian noise. White noise is mainly hard to distinguish and to

eliminate because it is located in all frequencies. Uniform noise has a constant probability

density over a finite interval whereas Gaussian noise is defined over an infinite interval by just

two factors, average and spread. Additive white Gaussian noise is a special type of white and

Gaussian noises, which is a ubiquitous model in the context of statistical image restoration.

Fractional Gaussian noise (fGn) is the simplification of white noise. As an effect of these noises,

the information in a noisy signal will be misunderstood. Thus, in almost all signal processing and

communications applications, it is a significant task that the noise is eliminated totally from such

signals. This task is referred to as denoising.

There are various denoising techniques such as Fourier Transform, Time-Frequency analysis[2],

Wavelet Transform, Neural Network, Independent Component Analysis (ICA), Unscented

Kalman Filter (UKF) ), Empirical Mode Decomposition (EMD) [3], Canonical Correlation

Analysis (CCA) [30], Principal Component Analysis (PCA), Adaptive Impulse Correlated Filter

(AICF) [4], Time Sequence Adaptive Filter (TSAF), Signal-Input Adaptive Filter (SIF) [5] [6],

Adaptive Filters, Wiener filter, Singular Value Decomposition (SVD), FIR or IIR digital filters.

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Wavelets commonly used for denoising biomedical signals include the Daubechies ‘db2’, ‘db8’

and ‘db6’ wavelets and orthogonal Meyer wavelet. Even though there are several techniques for

signal denoising, the common ones are the Fourier and Wavelet Transforms. Biomedical data

processing becomes more and more vital these days, because of its property of relevance and

support to the specialists for making decisions in their respective domains. The processing

techniques of biomedical signals generally employ standard algorithms for the purpose of

denoising.

Denoising using Wavelet Transform has different approaches; among them the mostly adopted

method is the one where the signals are decomposed into wavelets followed by thresholding and

shrinkage application for noise removal. The work focuses on Wavelet based denoising for the

biomedical signals ECG, EEG and EMG. Each signal has its unique feature and is adopted in a

wide range of applications. These biomedical signals are studied one by one in detail.

Denoising an EEG signal is a tricky preprocessing step prior to qualitative or quantitative

analysis. A blind source separation (BSS) problem is defined as disturbance minimization due to

muscular activity in EEG signals which consists of estimating the original sources underlying the

multichannel, without a prior knowledge about the sources and mixing process.

The noise reduction in electrocardiography signals is one of the important problems, which

appear during the analysis of this data. ECG signal is a non-stationary biological signal in nature

and plays a big role in diagnostics of human diseases [8]. One of the most serious problems in

the registration of electrocardiographic (ECG) signals is the parasite interference of muscle

active potentials – electromyography (EMG) signals. Because of EMG wide spectrum, it is

considered as white noise.Therefore the electrocardiography signals need an effective denoising.

Generally, adequate ECG denoising algorithms and procedures should have the following

properties :a) Improve signal-to-noise ratio (SNR), b) Preserve the original shape of the signal

and especially the sharp Q, R, and S peaks, without distorting the P and T waves and the smooth

transition of the ST-T segment. The noise presence problem is partially avoided by low-pass

(LP) filtering, FIR or IIR digital filters. Ensemble Averaging (EA) for the extraction of small

cardiac components from the noise contaminated ECG. As an improvement over EA, classical

Adaptive Filter (AF) with varying impulse response of the signal for the noise cancellation of

ECGs containing baseline wander, power line interference, EMG noise, and motion artifacts.

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Wavelet analysis is often very effective because it provides a simple approach for dealing with

the local aspects of a signal. Electromyography (EMG) signals can be used for

clinical/biomedical applications, Evolvable Hardware Chip (EHW) development, and modern

human computer interaction. EMG signals acquired from muscles require advanced methods for

detection, decomposition, processing, and classification.

EMG signal denoising is mainly based on wavelet transform since it is the most useful tool to

remove noises in myoelectric recognition system. Wavelet denoising in analysis of EMG signal

is studied in the last decade, particularly in the engineering application such as the control of

upper-limb and lower-limb prostheses. The WT decomposes a signal into several multi-

resolution components according to a basic function which is called a wavelet function. As

discussed before, filters are one of the most widely used signal processing functions. The

resolution of the signal, which is a measure of the amount of detail information in the signal, is

determined by the filtering operations, and the scale is determined by up sampling and down

sampling operations. Wavelet function, level of wavelet decomposition, estimation function of

threshold value, and transformation (shrinkage) function of threshold value with wavelet

coefficients are the four important things that are considered for achieving the optimal wavelet

denoising algorithm for EEG signal.

1.3. Wavelet Transforms

The earlier method of ECG signal analysis was based on time domain method. But this is not

always sufficient to study all the features of ECG signals. So, the frequency representation of a

signal is required. To accomplish this, FFT (Fast Fourier Transform) technique is applied. But

the unavoidable limitation of this FFT is that the technique failed to provide the information

regarding the exact location of frequency components in time [11] [13] [14]. A method for ECG

denoising based on Wavelet Shrinkage approach using Time-Frequency Dependent Threshold

(TFDT) has been proposed in[93]. Generally speaking, the TFDT is high for the non-informative

wavelet coefficients, and low for the informative coefficients representing the important signal

features [69]. Donoho and Johnstone proposed Wavelet thresholding de-noising method based on

discrete wavelet transform (DWT) is suitable for non-stationary signals [12].

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The Fourier transform is less useful in analyzing non-stationary signal (a non-stationary signal is

a signal where there is change in the properties of the signal) i.e., there is no repetition within the

region sampled. Fourier transform is only localized in frequency domain. The main drawback of

Fourier transform is that we lose our time information which is very important [10]. Fourier

transform cannot provide any information about the spectrum changes with respect to time.

Fourier transform assumes the signal to be stationary, but speech signal is always non-stationary.

To overcome this deficiency, a modified method-Short Time Fourier transform allows

representing the signal in both time and frequency domain through time windowing functions.

The usage of windowing with the Fourier Transform is called the Short Time Fourier Transform,

(STFT). The problem with this is that adequate understanding of the contents of the signal is

required to make appropriate windowing. This is hardly ever the case and many times, these

assumptions lead to problems. Moreover the STFT is time and frequency localized; there are

issues with the frequency time resolution [10]. Although the Fourier transforms tells how much

its frequency exists in a signal, it does not tell when in time these frequency components occur.

This information is required when the signal is non-stationary. All the real world signals are not

stationary, since their frequency changes in time. So what happen to a non-stationary signal

when it is processed, to view it in a frequency domain? All these are the major issues in signal

processing using Fourier transform techniques. Because of all the above said limitations, Fourier

Transform is not applied for denoising signals in the thesis. Moreover all these drawbacks are

overcome by Wavelet Transform technique and thus make wavelet a logical choice of denoising

technique in the thesis.

All types of signal transmission are based on transmission of a series of numbers. For signal

transmission or signal storage, the first step is to convert the given information to a series of

numbers. To do this the coefficients of the series need to be stored and only the coefficients are

sent. The wavelet tool is the new tool to perform this function. In the wavelet transform one

does not lose the time information, which is useful in many contexts [17]. In wavelet transform,

a signal is analyzed and expressed as a linear combination of the sum of the product of the

wavelet coefficients and mother wavelet. Wavelets are localized in both the frequency and the

time. This makes it possible to better localize properties of the analyzed signal. The result is a

well known ability of the wavelet transforms to pack the main signal information into a very

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small number of large wavelet coefficients. A wavelet is simply a small wave which has energy

concentrated in time to give a tool for the analysis of transient, non stationary or time-varying

phenomena. A Wavelet transform uses a set of transform basis function called wavelets to

decompose a signal.Proper selection of wavelet basis function plays a vital role in denoising

[18].

Wavelets are a powerful statistical tool which can be used for a wide range of applications,

namely signal processing, data compression, smoothing and de-noising, fingerprint verification,

biology for cell membrane recognition, blood-pressure, heart-rate and ECG analysis etc.

There are many types of wavelets in the family. The Daubechies wavelet is described by a

maximal number of vanishing moments for some given support. Haar wavelet is an order of

rescaled square shaped function. Symlet wavelets are an improved version of Daubechies

wavelets with increased symmetry. Coiflets wavelets have scaling functions with vanishing

moments. The biorthogonal family wavelets are signed as bior. In Legendre wavelet, the

Legendre function have common applications in which spherical coordinate system are suitable.

Among the various wavelet families are defined in the literature, Daubechies wavelets are the

most popular wavelets. The Daubechies wavelets are used in different applications. The Haar,

Daubechies, Symlets and Coiflets are compactly supported orthogonal wavelets. These wavelets

along with Meyer wavelets are capable of perfect reconstruction. The Meyer, Morlet and

Mexican Hat wavelets are symmetric in shape. The wavelets filters are selected based on their

ability to analyze the signal and their shape in an application [20] [23] [27] [29].

The signals are reconstructed using Inverse DWT. The IDWT is applied as a reverse process to

the decomposed signal and the original signal is reconstructed. The IDWT is obtained by the

quadrature filter bank [32]. On the other hand a classifier achieves its objective by making a

classification decision based on some characteristics. The application of Artificial Neural

Network enables the selection of the best wavelet type for each type of biomedical signal [33].

The denoised signal is compressed by a hybrid wavelet Shannon-Fano coding for reducing its

storage size [41].

Now a brief introduction about signal processing, biomedical signals and the nature of various

signal denoising techniques has been given. In this section, several studies proposed especially

for denoising are to be discussed. Moreover, the nature and applications of wavelet techniques

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and different classifiers, which were exploited in a wide area of research other than denoising are

to be presented. A detailed survey about the various techniques designed for denoising and the

methods proposed for signal compression in the literature referred earlier is given in the next

section.

1.4. State of Art/ Literature Survey:

In this section, some of the studies based on signal processing have been presented. It is stated in

the previous sections that denoising is applied extensively for biomedical signals, images, and

for audio, video signals. So, a detailed review of literature has been done in which various

methods for denoising, compression, reconstruction and classification have been studied.

Stephane G. Mallat (1989) studied the properties of the operator which approximates a signal at a

given resolution. He showed that the difference of information between the approximation of a

signal at the resolutions 2’+’

and 2j can be extracted by decomposing this signal on a wavelet

orthonormal basis of L2(R

n). This decomposition defines an orthogonal multiresolution

representation called a wavelet representation. [3]

Metin Akay (1995) compared various methods for biomedical signal processing only to conclude

that wavelet transform is the best among all these methods. He gave the advantages and

disadvantages of all the techniques used in the signal processing and proposed wavelet transform

for biomedical signals as they are non-stationary in nature. [11]

Michael Unser (1996) emphasized on the statistical properties of the wavelet transform and

discusses some recent examples of application in medicine and biology. The redundant forms of

the transform (CWT and wavelet frames) are well suited for detection tasks (e.g., spikes in EEG,

or micro-calcifications in mammograms). The CWT, in particular, can be interpreted as a pre-

whitening multi-scale matched filter. Redundant wavelet decompositions are also very useful for

the characterization of singularities as well as the time-frequency analysis of non-stationary

signals. Some examples of applications in Phonocardiography, ECG and EEG are also discussed

in the paper. [14]

Nikolay Nikolaev and Atanas Gotchev (1998) investigated a method for ECG denoising based

on wavelet shrinkage approach. They proposed a shrinkage threshold which was high for the

non-informative wavelet coefficients and low for the informative coefficients. [23]

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Arthur Petrosian et al., (2000) applied recurrent neural networks (RNN) combined with signal

wavelet decomposition to the problem of predicting the onset of epileptic seizure which is an

important and difficult biomedical problem. [33].

Tom Chau (2001) presented a review paper in which, part 1 explored applications of fuzzy,

multivariate statistical and fractal methods to gait data analysis and part 2 extended this critical

review to the applications of ANN and wavelets to gait data analysis. The review concluded with

a practical guide to the selection of alternative gait data analysis methods. [39]

Claude Robert et al. (2002) presented more than 100 current neural network applications

dedicated to EEG processing. They demonstrated the importance of neural network in medicine

and biology involving EEG signal processing. Positive results obtained in most applications had

shown relevance for processing electroencephalograms. Works were categorized according to

their objective. [45]

Thierry Blu and Michael Unser (2002) showed that the wavelets and radial basis functions are

the two types of representation which were closely linked together through fractals. They

identified and characterized the whole class of self-similar radial basis functions that could be

localized to yield conventional multi-resolution wavelet bases. They also proved that for any

compactly supported scaling function, there existed a one-sided central basis function, which

spanned the same multi-resolution subspaces. [80]

Alka Yadav et al. (2003) proposed a new approach to filter the ECG signal from noise using

Multi resolution Technique based on Wavelet Transform . They proposed decomposition method

using the Stationary Wavelet Transform and by selecting db wavelet, the noisy signal had been

decomposed, in the 4th decomposition level. As a result approximate coefficients aj and detail

coefficients dj were obtained. They showed that their method gave better results than the other

technique applied in this field. [172]

Andrew P. Bradley (2003) reviewed a number of approaches to reduce, or remove, the problem

of shift variance in the discrete wavelet transform (DWT). He described a generalization of the

critically sampled DWT and the fully sampled algorithm ‘A TROUS’ that provided approximate

shift-invariance with an acceptable level of redundancy. [49]

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Minos Garofalakis and Amit Kumar (2004) proposed a novel, computationally efficient schemes

for deterministic maximum-error wavelet thresholding in one and multiple dimensions. For one-

dimensional wavelets, they introduced an optimal, low polynomial-time thresholding algorithm

based on a new Dynamic Programming formulation that can be used to minimize either the

maximum relative error or the maximum absolute error in the data approximation [52]

Pawel Costka and Ewaryst Tkacz (2004) presented Wavelet-neural systems (WNS) which

inherited the properties of neural networks, belong to the class of universal approximators of

unknown functions. Classifier structures described in their work fulfilled the role of

approximators of functions, which were able to assign the input signal to a particular class with a

given accuracy. [54]

S.A. Chouakri et al. (2005) presented an algorithm of filtering the noisy real ECG signal in this

paper. The classical wavelet denoising process, based on the Donoho et al. algorithm, at the 4th

level, appears clearly the P and T waves whereas the R waves undergo considerable distortion.

This is due to the interference of the WGN and the free noise ECG detail sequences at level 4. To

overcome this drawback, the key idea is to estimate the corrupted WGN and consequently

remove the noise interfering R waves at the 4th level detail sequence. [65]

Mohammad Pooyan et al. (2005) presented a novel approach for wavelet compression of

electrocardiogram (ECG) signals based on the set partitioning in hierarchical trees (SPIHT)

coding algorithm. SPIHT algorithm had achieved prominent success in image compression. They

used a modified version of SPIHT for one dimensional signal. [64]

Vangelis P. Oikonomou and Dimitrios I. Fotiadis (2006) proposed the Bayesian approach for

biomedical signal denoising. This approach mainly deals with the biomedical signals affected by

white Gaussian noise. To obtain a meaningful solution, they introduced many constraints in the

problem. They selected the desired signal to belong to the class of smooth signals. The

introduction of constraints led them to a bayesian formalism of the problem.

Reza Sameni et.al (2006) proposed a nonlinear Bayesian filtering framework for the filtering of

single channel noisy ECG recordings. Within this framework several suboptimal filtering

schemes were developed. The necessary dynamic models of the ECG were based on a modified

nonlinear dynamic model, previously suggested for the generation of a highly realistic synthetic

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ECG. A modified version of this model was used in several Bayesian filters, including the

Extended Kalman Filter, Extended Kalman Smoother, and Unscented Kalman Filter. An

automatic parameter selection method was also introduced, to facilitate the adaptation of the

model parameters to a vast variety of ECGs. [78]

Jong Yong A. Foo (2006). In this paper it is shown that Photoplethysmography (PPG) can be

used in time-related measurements such as heart rate (HR) and pulse transit time (PTT)

estimations in the medical fields. This paper compares the capabilities of two signal processing

techniques; digital adaptive filtering and discrete wavelet transformation, in restoring artifact-

induced PPG signals during two regulated mild movements. [68]

P. Kukharchik et al. (2007) presented an initial study of feature extraction based on wavelets and

pseudo wavelets in the task of vocal pathology diagnostic. A new type of feature vector, based

on continuous wavelet and wavelet-like transform of input audio data was proposed. Support

vector machine had been used as a classifier for testing the feature extraction procedure. The

proposed scheme revealed, that features based on continuous wavelet transform and continuous

pseudo wavelet transform had potential for future usage for vocal fold pathology detection when

working with realistic records, that were not previously processed or prepared. [86]

Omid Sayadi and Mohammad B. Shamsollahi (2007) presented a new modified wavelet

transform, called the multiadaptive bionic wavelet transform (MABWT), that could be applied to

ECG signals in order to remove noise from them under a wide range of variations for noise. This

proposed thresholding rule had been applied and worked successfully in denoising the ECG. [76]

Orlando Jos´e Ar´evalo Acosta and Matilde Santos Pe˜nas (2007). This contribution consists of

the application of a hybrid technique of signals digital processing and artificial intelligence, to

classify two kinds of biomedical spectra, normal brain and meningioma tumor. Each signal is

processed to extract the relevant information within the range of interest. Then, a Haar 4 wavelet

transform is applied to reduce the size of the spectrum without losing its main features. This

signal approximation is coded in a binary set which keeps the frequencies that could have

representative amplitude peaks of each signal. [81]

Laurent Brechet et.al (2007) proposed a novel scheme for signal compression based on the

discrete wavelet packet transform (DWPT) decomposition. The mother wavelet and the basis of

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wavelet packets were optimized and the wavelet coefficients were encoded with a modified

version of the embedded zero tree algorithm. This signal dependant compression scheme was

designed by a two-step process. The first (internal optimization) was the best basis selection that

was performed for a given mother wavelet. The second (external optimization) was the selection

of the mother wavelet based on the minimal distortion of the decoded signal given a fixed

compression ratio. [82]

Ilker Bayram, Ivan W. Selesnick (2007) The author discusses the 2-band discrete wavelet

transform (DWT) which provides an octave-band analysis in the frequency domain, but might

not be ‘optimal’ for a given signal. In this paper, a method to implement a dual-tree complex

wavelet packet transform (DTCWPT) has been discussed. To find the best complex wavelet

packet frame for a given signal, the author adapts the basis selection algorithm by Coifman and

Wickerhauser, providing a solution to the basis selection problem for the DT-CWPT. [83]

Alain de Cheveigne and Jonathan Z. Simon (2008) introduced a denoising method based on

spatial filtering for removing unwanted components of biological origin from neurophysiologic

recordings such as Magnetoencephalography (MEG), electroencephalography (EEG), or

multichannel electrophysiological or optical recordings. A spatial filter was designed to partition

recorded activity into Stimulus-related and stimulus-unrelated components, based on a criterion

of stimulus-evoked reproducibility. Components that are not reproducible were projected out to

obtain clean data. [96]

Yannis Kopsinis and Stephen (Steve) McLaughlin (2008), used Empirical Mode Decomposition

(EMD) based denoising techniques of the major wavelet thresholding principle in the

decomposition modes resulting from applying EMD to a signal. They showed that although a

direct application of this principle in the EMD case was not feasible, it could appropriately

adapted by exploiting the special characteristics of the EMD decomposition modes. [94]

Leandro Aureliano da Silva et al. (2008) proposed the technique used for noise reduction during

the reconstruction of speech signals, particularly for biomedical applications. They implemented

and compared two algorithms for speech denoising: the Kalman’s filter in the time domain

(FKT) and in the frequency domain (FKF). Comparison with discrete Kalman filter in the

frequency domain showed better performance of the proposed technique. [98]

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Guoshen Yu et al. (2008) introduced a block thresholding estimation procedure which adjusted

all the parameters adaptively to signal property by minimizing a Stein estimation of the risk

calculated from the data. The resulting algorithm was robust to variations of signal structures

such as short transients and long harmonics. [95]

Omid Sayadi and Mohammad Bagher Shamsollahi (2008) proposed a study in which they

presented efficient denoising and lossy compression schemes for electrocardiogram (ECG)

signals based on a modified extended Kalman filter (EKF) structure. The new EKF structure was

used not only for denoising, but also for compression, since it provided estimation for each of the

new 15 model parameters. [97]

Hariharan Nalatore et al. (2009) attempted to apply a state-space smoothing method, based on

the combined use of the Kalman filter theory and the Expectation–Maximization algorithm, to

denoise two datasets of local field potentials recorded from monkeys. Their main goal was to

establish that the denoising procedure based on a simple data model works on actual neural data.

After denoising, the discrepancy between the two subjects was significantly reduced. [107]

Slavy G. Mihov et al. (2009) investigated the use of wavelet transform for denoising speech

signals contaminated with common noises. They showed the basic principles of wavelet

transform as an alternative to the Fourier transform. The practical results obtained were based on

processing a large dedicated database of reference speech signals contaminated with various

noises in several SNRs. [112]

G. Umamaheswara Reddy et al. (2009) proposed a new thresholding technique for denoising of

ECG signal. This new denoising method was called as improved thresholding denoising method

and could be regarded as a compromising between hard- and soft thresholding denoising

methods. The proposed method selected the best suitable wavelet function based on DWT at the

decomposition level of 5, using mean square error (MSE) and output SNR. The advantage of the

improved thresholding denoising method was that it retained both the geometrical characteristics

of the original ECG signal and variations in the amplitudes of various ECG waveforms

effectively. [111]

Sana Ktata et al. (2009) proposed a wavelet ECG data codec, based on the Set Partitioning in

Hierarchical Trees (SPIHT) compression algorithm. The SPIHT algorithm had achieved notable

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success in still image coding. They modified the algorithm for the one-dimensional (1-D) case

and applied it to compression of ECG data. By this compression method, small percent root

mean square difference (PRD) and high compression ratio with low implementation complexity

were achieved. [114]

M. Murugesan and R. Sukanesh (2009) presented an effective system for classification of

electroencephalogram (EEG) signals that contain credible cases of brain tumor. The

classification technique support vector machine (SVM) was utilized in the proposed system for

detecting brain tumors. Initially, the artifacts present in the EEG signal were removed using

adaptive filtering. Then the spectral analysis method was applied for extracting generic features

embedded in an EEG signal. The key advent of the proposed approach was that it enabled early

detection of brain tumors initiating quicker clinical responses. [109]

I. Omerhodzic et al. (2009) discussed a wavelet-based neural network (WNN) classifier which

was implemented and tested for recognizing three sets of EEG signals. First, the DWT with the

MRA was applied to decompose EEG signal at resolution levels of the components of the EEG

signal and the Parseval’s theorem were employed to extract the percentage distribution of energy

features of the EEG signal at different resolution levels. Second, the neural network (NN)

classified those extracted features to identify the EEGs type according to the percentage

distribution of energy features. The results showed that the proposed classifier had the ability of

recognizing and classifying EEG signals efficiently. [110]

Mojtaba Bandarabadi et al. (2010) proposed a method for electrocardiogram signal (ECG)

denoising. The basis of this method was achieved through filtering Singular Values (SV) of the

signal. It was based on enhancing and optimizing the SV for omitting noise from ECG. The

advantage of this proposed method was its capability in enhancing the signal very well. Using

different quantitative and qualitative parameters, the efficacy of the method was evaluated. [131]

Wasim Ahmad et al. (2010) proposed a shift-invariant analysis scheme which was non

redundant. This scheme combined minimum-phase (MP) reconstruction with the DWT so that

the resultant scheme provided a shift-invariant transform. The detailed properties of MP signal

and different methods to reconstruct it were explained. The proposed scheme could be used for

the analysis-synthesis, classification, and compression of transient sound signals. [127]

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A.N. Akansu et.al (2010) highlighted inherently built-in approximation errors of discrete-time

signal processing techniques employing WT framework. Then, they presented an overview of

emerging analog signal processing applications of wavelet transform along with its still active

research topics in more matured discrete-time processing applications. It was shown that analog

wavelet transform was successfully implemented in biomedical signal processing for design of

low-power pacemakers and also in ultra-wideband (UWB) wireless communications. [123]

Dimitri Van De Ville et al. (2010) introduced a family of elementary singularities that were

point-Holder-regular. These singularities were self-similar and were the Green functions of

fractional derivative operators; i.e., by suitable fractional differentiation, one retrieved a Dirac

function at the exact location of the singularity. They showed that the wavelet coefficients of the

(non-redundant) decomposition could be fitted in a multiscale fashion to retrieve the parameters

of the underlying singularity. They proposed an algorithm based on stepwise parametric fitting

and the feasibility of the approach to recover singular signal representations. [129]

Abdel Rahman et al. (2010), proposed a new approach to filter the ECG signal from noise using

Wavelet Transform. Different ECG signals were used and the method had been evaluated using

MATLAB software. The aim of the paper was to adapt the discrete wavelet transform (DWT) to

enhance the ECG signal. The presented method showed good results when compared to

conventional methods particularly in ECG signal case. This method had better performance than

Donoho’s discrete wavelet thresholding coefficients and FIR filter. [121]

A. Phinyomark et al. (2010) proposed the selection of the modified wavelet shrinkage functions

which was based on the improving of recognition in EMG signal from upper-limb motions.

Seven kinds of modified shrinkage functions and two traditional shrinkage functions were

compared by calculating classification accuracy of denoised EMG signal estimated from the

shrinkage functions. In addition, the denoising effects of the different shrinkage functions for

different levels of noise were proposed. The experimental results showed that the highest

classification accuracy can be reached using the firm wavelet shrinkage function. [122]

Minfen Shen et al. (2010) proposed a new local spatio-temporal prediction method based on

support vector machines (SVMs). Combining with the local prediction method, the sequential

minimal optimization (SMO) training algorithm, and the wavelet kernel function, a local SMO-

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wavelet SVM (WSVM) prediction model was developed to enhance the efficiency,

effectiveness, and universal approximation capability of the prediction model. This method

greatly increased the computational speed and more effectively captured the local information of

the signal. [126]

Andreas Spanias et al. (2010), considered features extracted from the Fourier, wavelet and Walsh

power spectra of the ion-channel signals. They compared the performance of all the three sets of

features using support vector machines. They performed classification of signals from simulated

and real ion-channels and presented the results. Results obtained showed that the transform

domain features achieved high classification rates in addition to high sensitivity and specificity

rates. [74]

Corina Sararu et al. (2010) described a new classification methodology based on the use of

Independent Component Analysis and Wavelet decomposition (ICAW) techniques. An ensemble

system of classifiers was built such that each classifier independently decided the assignation of

the test examples on several representations resulted by taking projections computed by wavelets

and Independent Component Analysis (ICA). [119]

Rui Hou et al. (2011) proposed a quantitative evaluation model of denoising methods for surface

Plasmon resonance imaging signal. Their model allowed one to get the optimized denoising

method. The method can be used to suppress the noise in SPRI signals effectively. The wavelet

transform based denoising methods was used to process SPRI signals constructed from

theoretical simulated kinetic curves of bio molecular interactions. Application of the optimized

denoising method obtained from the model to SPRI signals helped to improve the resolution of

SPRI instrument. [142]

Jeremy Terrien et al. (2011) proposed an algorithm for the automatic selection of the modes

containing the signal of interest. This algorithm was based on statistical analysis describing the

noise repartition between IMFs. This algorithm used an estimate of the signal noise content from

the energy of the first IMF, which was supposed to contain a specific part of the total noise and

to contain noise only. They proposed to use mode mixing detection based on a stationary test

applied to the first IMF. [143]

16

Anil Chacko and Samit Ari (2011), proposed a denoising technique for ECG signals based on

Empirical Mode Decomposition (EMD). The noisy ECG signal was initially decomposed into a

set of Intrinsic Mode Functions (IMFs) using EMD method. In the proposed technique, the IMFs

which are dominated by noise were automatically determined using Spectral Flatness (SF)

measure and then filtered using butterworth filters to remove noise. [144]

Ibrahim Missaoui and Zied Lachiri (2011) addressed the problem of blind separation of speech

mixtures. They proposed a new blind speech separation system, which integrated a perceptual

filter bank and independent component analysis (ICA) and using kurtosis criterion. Their

proposed technique consisted on transforming the observations signals into an adequate

representation using UWPD and Kurtosis maximization criterion in a new preprocessing step in

order to increase the non Gaussianity which was a pre-requirement for ICA. [149]

B. Mohan Kumar and R. Vidhya Lavanya in 2011 used CL Multiwavelet with soft thresholding

by universal threshold selection rule for denoising the real time signals. The approach was

incorporated with time domain and frequency domain analysis. The objective of the work was to

enhance the noisy speech signal using CL Multiwavelet with soft threshold method in real time

mobile speech communication. The noise was estimated and thresholding was done according to

the estimated noise. Denoising was done for both stationary and non-stationary signals with

different noise levels. [147]

N. M. Sobahi (2011) applied wavelet transform for removing noise from the surface EMG and

provided a brief introduction of the wavelet transform in EMG signals processing. Wavelet

denoising method was expected to offer a powerful compliment to conventional filtering

techniques like notch filters and frequency domain filtering methods, which would have been

very efficient for EMG signal analysis. [133]

Om Prakash Yadav et al. (2011) presented Wavelet Based Encoder/Decoder for Compression of

ECG Signal and three compression algorithms. In EZW algorithm, 3-level decomposition was

performed to the original ECG samples, and the wavelet coefficients at different sub-band

representing the same spatial location in the ECG samples were loaded into a spanning tree.

[148]

17

Catalina Monica Fira et al. (2011). An electrocardiographic signal (ECG) compressed sensing

(CS) method, its reconstruction using specific dictionaries of cardiac pathologies and method

evaluation testing using classical measures as well as by classification error of the reconstructed

patterns based on the K-Nearest Neighbor classifier (KNN) were presented in the paper. For

compressed sensing, a random matrix with standard normal distribution had been used, followed

by a classification of compressed signals in one of eight possible pathological classes. [136]

Mingsheng Liu et al. (2011) presented a risk assessment method which combined wavelet neural

network (WNN) and entropy-grey correlation, created a WNN model and described a simulation

experiment by Matlab 7. In addition, comparisons were made in terms of convergent speed,

training precision and forecasting effect between WNN and other traditional estimation methods

such as BP-NN (Back Propagation Neural Network), FCM (Fuzzy Clustering Method) and SPR

(Statistical Pattern Recognition). [150]

Oumar Niang et.al (2012) presented a new signal denoising method based on the classical three

step procedure analysis-threshold- synthesis and the Spectral Intrinsic Decomposition (SID).

This method consists of an iterative thresholding of the SID components. The SID-based

removal method reduced noise and could retain useful discontinuities of the signal as effectively

as the wavelet techniques based on soft thresholding. [166]

Chinmay Chandrakar et al. (2012) considered adaptive filters to reduce the ECG signal noises

like PLI and Base Line Interference. Recursive Least Squares (RLS) algorithm was proposed for

removing artifacts preserving the low frequency components and tiny features of the ECG. [114]

L. N. Sharma et al. (2012) applied Multiscale Principal Component Analysis (MSPCA) for

quality controlled de-noising of Multichannel Electrocardiogram (MECG) signals. Collecting

wavelet coefficients of all ECG channels at a wavelet scale multivariate data matrices were

formed. Principal Component Analysis (PCA) was performed on these matrices for signal

denoising. [167]

Akanksha Mishra et al. in 2012 introduced a comparison of the reconstructed 10 ECG signals

based on different wavelet families, by evaluating the performance measures as MSE (Mean

Square Error), PSNR (Peak Signal To Noise Ratio), PRD (Percentage Root Mean Square

Difference) and CoC (Correlation Coefficient). L1 minimization was used as the recovery

18

algorithm. The reconstruction results were comprehensively analyzed for three compression

ratios. [171]

Hossein Rabbani and Saeed Gazor (2012) investigated the local probability density function

(pdf) of natural signals in sparse domains. The statistical properties of natural signals were

characterized more accurately in the sparse domains. Their experiments on 3D data in 3D

discrete complex wavelet transform (DCWT) domain showed that a conditionally (given locally

estimated variance and shape) independent Bessel K-form distribution (BKFD) locally fitted the

sparse domain’s coefficients of natural signals, accurately. [159]

Zoltan Germans Saollo and Calin Ciufudean, (2012) dealt with the design of waveform-adapted

analyzing function in order to have a good wavelet decomposition of the analyzed signal. The

proposed procedure led to obtain discrete sequences as discrete wavelet function to perform

denoising, those met certain mathematical criteria. Discrete Wavelet Transform based denoising

was performed. That study introduced a waveform-adapted wavelet transform based noise

suppression procedures and presented the obtained results. [161]

Md. Ashfanoor Kabir and Celia Shahnaz, (2012) Comparison of ECG signal denoising

algorithms in EMD and wavelet domains presented a detail analysis on the Electrocardiogram

(ECG) denoising approaches based on noise reduction algorithms in Empirical Mode

Decomposition (EMD) and Discrete Wavelet Transform (DWT) domains. This study provided

the performance analyses of ECG signal denoising algorithms in EMD and wavelet domains thus

compared the effectiveness in reducing the noise. [163]

Hari Mohan Rai and Anurag Trivedi (2012) dealt with the noise removal of ECG signal using

three different wavelet families. The different noise structure (unscaled white noise, scaled white

noise and non white noise) had been selected for ECG signals and was compared their statistical

parameter to find out the best result. The wavelet families used for De-noising were Haar,

Daubechies and Symlets. They decomposed the ECG signal into 5 levels. The experiment

showed that the Daubechies4(Db4) of level 5 for scaled white noise structure gave the best result

as compared to other wavelet family and Haar wavelet gave the worst result for Unscaled white

noise structure. [174]

19

P. Karthikeyan (2012) They considered that the Discrete Wavelet Transform (DWT) based

wavelet denoising had incorporated using different thresholding techniques to remove three

major sources of noises from the acquired ECG signals namely, power line interference, baseline

wandering, and high frequency noises. Three wavelet functions ("db4", "coif5" and "sym7") and

four different thresholding methods were used to denoise the noise in ECG signals. [170]

Maedeh Kiani Sarkaleh and Asadollah Shahbahrami (2012), proposed an expert system for ECG

arrhythmia classification. Discrete wavelet transform was used for processing ECG recordings,

and extracting some features, and the Multi-Layer Perceptron (MLP) neural network performed

the classification task. Two types of arrhythmias could be detected by the proposed system.

Some recordings of the MIT-BIH arrhythmias database had been used for training and testing

our neural network based classifier. [162]

Prajakta S. Gokhale (2012) showed the effect of the wavelet thresholding on the quality

reconstruction of an ECG signal. By applying IIR notch filter directly to the non-stationary

signal like ECG gives ringing effect which can be eliminated through wavelet transform among

which Db4 performed better than other methods to de-noise the noisy ECG signal. [175]

Apoorv Gautam and Maninder kaur (2012) proposed algorithm which utilizes morphological

filtering and continuous wavelet transform with a dedicated wavelet. They showed that the multi-

resolution analysis based on the CWT can enhance small differences when the signal is

simultaneously observed at the most appropriate scales. [172]

L. Senhadji et al. (2013) introduced a model-based Bayesian denoising framework for

phonocardiogram (PCG) signals. The denoising framework was founded on a new dynamical

model for PCG, which was capable of generating realistic synthetic PCG signals. The extended

Kalman smoother (EKS) is the Bayesian filter that was used in their study. The results of the

EKS demonstrated better performance than WD over a wide range of PCG SNRs. [187]

Md. Mamun et al. (2013) employed discrete wavelet transform to remove noise from EEG

signal. Root mean square difference had been used to find the usefulness of the noise

elimination. Four different discrete wavelet functions had been used by them to remove noise

from the EEG signal gotten from two different types of patients (healthy and epileptic) to show

the effectiveness of DWT on EEG noise removal. [177]

20

E. Castillo et al. (2013) One-step wavelet-based processing for wandering and noise removing in

ECG signals technique illustrated the application of the Discrete Wavelet Transform (DWT) to

the processing of electrocardiogram (ECG) for wandering and noise suppression in this paper.

The proposed scheme allowed reducing the computational complexity, while its fixed-point

modeling showed the expected performance of possible future portable hardware

implementations. The system had been tested using synthetic ECG signals, which allowed to

accurately measuring the effect of the proposed processing. [182]

Maryam Ahmadi and Rodrigo Quian Quiroga (2013) presented an automatic denoising method

based on the wavelet transform to obtain single trial evoked potentials. The method was based on

the inter and intra-scale variability of the wavelet coefficients and their deviations from baseline

values. The performance of the method was tested with simulated event related potentials (ERPs)

and with real visual and auditory ERPs. The proposed method provided a simple, automatic and

fast tool that allowed the study of single trial responses and their correlations with behavior.

[180]

Sandeep Sharma et al. (2013) developed a technique to automatically detect and mark the basic

waveforms of ECG signal. Recently developed PCA had been used for this purpose. [181]

Amita A. Shinde and Pramod M. Kanjalkar (2013) presented an algorithm for wavelet based

ECG signal compression, where db7 was selected as the mother wavelet for analysis.

Thresholded wavelet coefficients were coded with RLC. One of the main advantages of this

method was lower calculation complexity in comparison with other methods. This algorithm was

tested for different records from MIT–BIH arrhythmia database. [185]

Vahid Majidnezhad and Igor Kheidorov (2013). In this paper, an ANN-Based method for vocal

fold pathology diagnosis was proposed so that in the proposed scheme, Mel-Frequency-Cepstral-

Coefficients along with the wavelet packet decomposition were used for feature extraction phase.

Also PCA method for the feature reduction phase was used. And finally the Artificial neural

network (ANN) was used for the classification phase. [186]

Mandavi1 et al. (2013). An efficient composite method had been developed for data compression

of ECG signals in this paper. After carrying out detailed studies of different data compression

algorithms, they used back propagation algorithm to analyze the artificial neural networks.

21

Twelve significant features were extracted from an echocardiogram (ECG). The features of

samples were used as input to the neural network. [184]

1.5. Outcome from Literature / Gaps

From the extensive literature survey, it is observed that different denoising techniques give

significantly varying performance for each of the biomedical signals, and the main problems

encountered are as follows.

In the previous studies, while denoising the biomedical signals such as ECG, EEG and

EMG, the trained system is unable to automatically detect the best wavelet suitable for

denoising.

The Fourier transform analysis is inadequate and is localized only in the frequency band.

The major drawback of Short Term Fourier Transform for signal denoising is that the

time frequency precision is not optimal.

Digital filters and adaptive methods can be applied only to signals whose statistical

characteristics are stationary in many cases and cannot be applied to non-stationary

signals because of loss of information. The best method that offers efficient denoising for

each of the biomedical signals such as ECG, EEG and EMG had not been predefined in

the literature.

Although, some of the authors exploited different wavelet for denoising different signals,

their trained system was unable to automatically detect the best wavelet suitable for

denoising. Even though much of the schemes discussed in literature survey provided

better performance in denoising, they compromised either space or time.

For compression of biomedical signals several studies have been addressed in the existing

literature. EZW, MEZW, SPIHT coding, RLC algorithm, Wavelet transform with SPHIT,

Wavelet and huffman, JPEG 2000, Shannon fano are the few compression techniques

addressed in the literature.

1.6. Problem Formulation / Objectives

From the literature it is obvious that there is a strong need of an efficient classifier for deciding

the optimal wavelet family for denoising different biomedical signals. Since each biomedical

22

signal has its unique nature and characteristics, the classifier must be trained in an efficient way

with the nature of each signal for accurate classification of optimal wavelet. Moreover we are in

need of an effective biomedical signal compression algorithm achieving best CR and PRD

values.

Based upon the above listed directions, the problem for this work is formulated as:

To find the optimal wavelet for biomedical signal.

To focus on reducing time and storage space, however at the same time signals must be

denoised efficiently with the optimal wavelet.

Once the optimal wavelet is found, biomedical signals will be denoised using this wavelet with

focus on reducing time and storage space. Biomedical signals considered will be ECG, EEG and

EMG.

1.7 Methodology Used to Achieve Objectives

The main motive of the thesis lies on denoising signals with the most suitable wavelet, which is

classified using Artificial Neural network. It results in less overhead time, since the classification

algorithm is already trained for almost all of the members of wavelet family. Moreover a hybrid

compression algorithm is applied after the denoising process and thus a less space is needed for

storing compressed information and is used for reconstruction of the original signal. Thus the

objectives of minimum space and less time are achieved in the thesis only by using simple

methods for denoising, classification and compression. The following steps will be carried out to

achieve the objectives:

Discrete Wavelet Transformation for the signals will be applied, which will be performed

by means of a low pass and a high pass filter, yielding approximation and detailed

coefficients respectively. This process continues for a fixed number of decomposition

levels.

The signal will be decomposed using the Shift Invariant method.

Then for each level of decomposition, the wavelet frequency thresholding for the detailed

and approximation coefficients will be applied resulting in denoised signal.

23

The artificial neural network will be trained initially with the properties of each wavelet

and the nature of the biomedical signals. By using the parameters the optimized wavelet

transform will be selected which is best suitable for denoising using the neural network

classifier.

As there is a strong need of an effective biomedical signal compression algorithm for

achieving the best CR and PRD values. For this purpose, both Shannon Fano algorithm

and wavelet transform will be combined. The signals obtained after classifications will

then be compressed using hybrid wavelet Shannon-Fano coding algorithm.

These steps can be represented in the form of Block Diagram shown in Figure 1.1 whereas

detailed representation by flow chart in Figure 1.2

Figure 1.1: Main steps of the proposed system

Decomposition

Denoising Signal

Compression

Input

Signal

ANN

24

Figure 1.2: Flow chart of the proposed system

Wavelet

reconstruction

TRAINING SYSTEM

Input Biomedical

Signals (ECG, EEG

and EMG)

Selection of the best

Wavelet using Artificial

Neural Network

Wavelet Frequency

Thresholding

Apply hybrid

wavelet Shannon

Fano compression

Denoised signal

Apply Discrete

Wavelet Transform

(DWT)

Train the features in

Artificial Neural

Network

TESTING SYSTEM

Input Biomedical Signal

(ECG, EEG or EMG)

25

1.8. Organization of the Thesis

The thesis is organized as follows.

Chapter 1 presents an introduction of the proposed system model followed by the introduction

of biomedical signals and wavelet transform. Chapter also deals with a detailed survey of the and

outcome from the literature studied. The problems of the existing studies have been presented

followed by the main objectives of this thesis. The methodology used to achieve the objectives

has also been discussed in the chapter.

Chapter 2 gives the detail description about the biomedical signals used for analysis in the

thesis. The origin and recording of the ECG, EEG and EMG signals has been studied in this

chapter. The Wavelet transformation scheme will also be explained with detailed mathematical

representation followed by their types. Types of wavelet transform such as Continuous Wavelet

Transforms (CWT) and the Discrete Wavelet Transforms (DWT) will be given. Followed by

DWT, wavelet filters will conclude the second chapter.

Chapter 3 deals with the various decomposition and denoising techniques in mathematical and

diagrammatic representations. The chapter explains the different thresholding techniques for

denoising. Wavelet frequency thresholding based denoising is used in the thesis and its details

will be presented in this chapter. The chapter concludes with the graphical results of denoising

for the three biomedical signals.

Chapter 4 Signal Reconstruction and compression techniques are given in this chapter.

Reconstruction by IDWT is explained in detail followed by the signal compression by Shannon

Fano algorithm. The evaluation criteria for compression (PRD and CR) have been demonstrated

through Graphical representation.

Chapter 5 presents the general conclusions of the thesis and proposes possible improvements

and directions of future research work followed by references and Appendix A and Appendix B.