Wavelet Families Research Articles

General model for best feature extraction of EEG using discrete wavelet transform wavelet family and differential evolution

Wavelet family and differential evolution are proposed for categorization of epilepsy cases based on electroencephalogram (EEG) signals. Discrete wavelet transform is widely used in feature extraction step because it efficiently works in this field, as confirmed by the results of previous studies. The feature selection step is used to minimize dimensionality by excluding irrelevant features. This step is conducted using differential evolution. This article presents an efficient model for EEG classification by considering feature extraction and selection. Seven different types of common wavelets were tested in our research work. These are Discrete Meyer (dmey), Reverse biorthogonal (rbio), Biorthogonal (bior), Daubechies (db), Symlets (sym), Coiflets (coif), and Haar (Haar). Several kinds of discrete wavelet transform are used to produce a wide variety of features. Afterwards, we use differential evolution to choose appropriate features that will achieve the best performance of signal classification. For classification step, we have used Bonn databases to build the classifiers and test their performance. The results prove the effectiveness of the proposed model.

Application of Wavelet Based Security and Compression Techniques for Biomedical Instrumentation Signals

The reliably creating amounts of restorative computerized pictures and the need to share them among bosses and facilities for better and continuously exact end require that patients' security be guaranteed. Biomedical signs from various sources including heart, cerebrum and endocrine structure speak to a test to analysts who may need to confine delicate signs getting in contact from various sources spoiled with antiquated rarities and fuss. Biomedical signs as a result of its colossal moderations are extensively associated in a couple of restorative applications; Electrocardiogram, Electroencephalogram and Electromyogram are to give a few precedents. Regardless, these signs experience the development of racket and result in an inefficient presentation. In the present open society and with the advancement of human rights, people are progressively increasingly stressed over the security of their information and other basic information. This examination uses electrocardiography (ECG) information in order to verify singular information. An ECG flag can't solely be used to analyze ailment, yet furthermore to give critical biometric information to unmistakable evidence and affirmation. ECG watermarking can ensure the security and immovable nature of a customer's information while reducing the proportion of information. In the appraisal, we apply as far as possible, piece botch rate (BER), motion to-disturbance extent (SNR), pressure extent (CR), and stuffed flag to commotion extent (CNR) strategies to assess the proposed . In the present work a solidified arrangement of applying denoising and pressure for biomedical signs using wavelets has been presented. An unequivocal examination of Discrete Wavelet Transform (DWT) denoising using distinctive wavelet families on biomedical signs (ECG, EMG and EEG) is shown in the hypothesis. The standard desire for the work is to explore the wavelet work that is perfect in perceiving and denoising the diverse biomedical signs.

Fault detection in smart grids with time-varying distributed generation using wavelet energy and evolving neural networks

Online monitoring systems have been developed for real-time detection of high impedance faults in power distribution networks. Sources of distributed generation are usually ignored in the analyses. Distributed generation imposes great challenges to monitoring systems. This paper proposes a wavelet transform-based feature-extraction method combined with evolving neural networks to detect and locate high impedance faults in time-varying distributed generation systems. Empirically validated IEEE models, simulated in the ATPDraw and Matlab environments, were used to generate data streams containing faulty and normal occurrences. The energy of detail coefficients obtained from different wavelet families such as Symlet, Daubechies, and Biorthogonal are evaluated as feature extraction method. The proposed evolving neural network approach is particularly supplied with a recursive algorithm for learning from online data stream. Online learning allows the neural models to capture novelties and, therefore, deal with nonstationary behavior. This is a unique characteristic of this type of neural network, which differentiate it from other types of neural models. Comparative results considering feed-forward, radial-basis, and recurrent neural networks as well as the proposed hybrid wavelet-evolving neural network approach are shown. The proposed approach has provided encouraging results in terms of accuracy and robustness to changing environment using the energy of detail coefficients of a Symlet-2 wavelet. Robustness to the effect of distributed generation and to transient events is achieved through the ability of the neural model to update parameters, number of hidden neurons, and connection weights recursively. New conditions could be captured on the fly, during the online operation of the system.

Novel design of a fractional wavelet and its application to image denoising

This paper proposes a new wavelet family based on fractional calculus. The Haar wavelet is extended to fractional order by a generalization of the associated conventional low-pass filter using the fractional delay operator Z-D. The high-pass fractional filter is then designed by a simple modulation of the low-pass filter. In contrast, the scaling and wavelet functions are constructed using the cascade Daubechies algorithm. The regularity and orthogonality of the obtained wavelet basis are ensured by a good choice of the fractional filter coefficients. An application example is presented to illustrate the effectiveness of the proposed method. Thanks to the flexibility of the fractional filters, the proposed approach provides better performance in term of image denoising.

Transmission of Audio over LTE Packet Based Wireless Networks Using Wavelets

In the present study, the main goal is to analyse the performance of audio data for wireless VOIP (Voice Over IP) proposed model utilizing wavelets. This treatise represents a performance study of wireless VOIP for recorded audio signal using different wavelet families such as Coiflet, Daubechies family (Db2, Db4, Db6, Db8, and Db10), Haar and Symlet. The performance was approximated with the subsequent procedure. Firstly, the recorded audio data was decomposed up to 4-levels by means of wavelet transform. From simulation results it is clear that wavelets are more practical and dominant tool meant for analyzing audio signals, as it exhibits multi-resolution property with a considerable decrease in the time complexity for removing resolution problems. Furthermore, it was concluded that Coiflet performs best at 1st and 3rd decomposition levels, while Haar and Db8 (Daubechies 8) performs the best among the other wavelets at 2nd and 4th decomposition levels respectively. Further, the parameters such as SNR (Signal/Noise Ratio), PSNR (Peak S/N Ratio), NRMSE (Normalized Root Mean Square Error), PRSE (Percentage of Retained Signal Energy) and Compression Ratio are used to investigate the performance. Additionally, transmission capabilities are also analyzed using packet loss and delay. Finally, ANOVA (Analysis of Variance) statistical tool has been applied to test the effectiveness of recorded data on 4 groups.

Parameters of a class of complex continuous wavelet family

In this paper, we have established the relationship between the wavelet scale and equivalent Fourier wavelength for the family of the new complex continuous wavelet. The same relation is used to relate the maximum of the Scalogram of each coefficient obtained from the wavelet transform of the signal to its amplitude. The relationship was applied to a synthetic signal and the simulated results show the effectiveness of using the proper wavelet transform definition to this proposed family of wavelets.

Extension of proposed family of one-dimensional continuous wavelets to two-dimensional continuous wavelets

Extension of proposed family of one-dimensional continuous wavelets to two-dimensional continuous wavelets

Haar wavelet collocation method for linear first order stiff differential equations

In general, there are countless types of problems encountered from different disciplines that can be represented by differential equations. These problems can be solved analytically in simpler cases; however, computational procedures are required for more complicated cases. Right at this point, the wavelet-based methods have been using to compute these kinds of equations in a more effective way. The Haar Wavelet is one of the appropriate methods that belongs to the wavelet family using to solve stiff ordinary differential equations (ODEs). In this study, The Haar Wavelet method is applied to stiff differential problems in order to demonstrate the accuracy and efficacy of this method by comparing the exact solutions. In comparison, similar to the exact solutions, the Haar wavelet method gives adequate results to stiff differential problems.

Analysis on Wavelet Family based Channel Estimation for MIMO-OFDM System

Channel estimation for (MIMO-OFDM) is an important part for present and future generation broadband wireless communications. OFDM, which uses for the spaced subcarriers to improving the performance. The channel estimation schemes based on pilot reduces the transmission rate and spectral efficiency. Many conventional schemes of channel estimation are not effective in reducing noise. It leads to poor quality signals at receiver at final stage. To rectify this problem, in this paper a wavelet family based channel estimation technique, is proposed and analyzed. The proposed research aims to estimate channels and reconstruct signal via wavelet transform, dyadic wavelet transform and fractional spline wavelet transform which enhances the spectrum efficiency and transmission rate. Simulation results shows that the fractional spline wavelet transform performs well for channel estimation and data signal reconstruction.

Agro Image De Noising (Aid) for Enhanced Agricultural Images

Several Noises may be present in acquired images. This is an undesired feature for image processing techniques that analyze these images. Image de-noising helps improve efficiency of image processing. Many image de-noising methods have been proposed and exist in literature. Image de-noising methods for agricultural images have been proposed to a lesser extent when compared to the bright medical or photographic images. This paper proposes Agricultural Image De-noising (AID) which uses a discrete wavelet transform (DWT) to eliminate noise in agricultural images. This study uses specific kind of wavelet family spline wavelet transforms with appropriate decomposition level and the wavelet coefficients are analysed with hard and soft threshold methods. The denoised image using various spline wavelets is compared of hard threshold and soft threshold are assessed. The performance of AID is calculated using the peak signal to noise ratio (PSNR) and signal to noise ratio (SNR).

Solving Fredholm integral equations of the first kind by using wavelet bases

In this paper, we used a project technique for solving integral equation of the first kind by wavelet families via regularization approach and we proved the convergence for the numerical method and error consideration. Semi-orthogonal B-spline scaling functions and wavelets of degree 4 and their dual functions are presented to approximate the solutions to integral equations. Sparse matrix will product of semi-orthoganality and vanishing moment properties of B-spline wavelets.

Construction of a family of non-stationary biorthogonal wavelets

The family of exponential pseudo-splines is the non-stationary counterpart of the pseudo-splines and includes the exponential B-spline functions as special members. Among the family of the exponential pseudo-splines, there also exists the subclass consisting of interpolatory cardinal functions, which can be obtained as the limits of the exponentials reproducing subdivision. In this paper, we mainly focus on this subclass of exponential pseudo-splines and propose their dual refinable functions with explicit form of symbols. Based on this result, we obtain the corresponding biorthogonal wavelets using the non-stationary Multiresolution Analysis (MRA). We verify the stability of the refinable and wavelet functions and show that both of them have exponential vanishing moments, a generalization of the usual vanishing moments. Thus, these refinable and wavelet functions can form a non-stationary generalization of the Coifman biorthogonal wavelet systems constructed using the masks of the D–D interpolatory subdivision.

Ringing artifacts in wavelet based image fusion: Analysis, measurement and remedies

In this paper, we investigate an issue of the ringing artifacts inherent to wavelet based image fusion. A thorough analysis of the ringing phenomenon, by experimenting with different types of images and different wavelet families, with varying lengths of filters and varying levels of decomposition is performed to obtain deeper insights of the ringing artifacts. It is experimentally shown that wavelet based fusion results in the modification of the intra- and inter-scale dependencies, with the inter-scale dependency being the dominating factor causing the ringing artifacts. Also, these ringing artifacts are localized in the Fourier domain. Subsequently, a quantitative measure using structural dissimilarity is proposed to measure the ringing artifacts due to wavelet based fusion. Two possible solutions to compensate for the ringing artifacts are then proposed. In the first strategy, a filtering based method is proposed to reduce these ringing artifacts. It takes advantage of the localized nature of the ringing artifacts. Furthermore, the intra- and inter-scale dependencies are modeled using order-zero entropy. A second strategy using the inter-scale dependency is then proposed to reduce the ringing artifacts. Experimental results show that both these methods are able to reduce the ringing artifacts significantly and have further scope for improvement. Another critical finding of this work is selection of the wavelet filter and its levels of decomposition for the process of fusion.

Performance of Extreme Learning Machine Kernels in Classifying EEG Signal Pattern of Dyslexic Children in Writing

Dyslexia is a specific learning disability that causes leaners to have difficulties to process letters and number during reading, writing and doing mathematics. Early identification of dyslexic characteristic is crucial so that early intervention given could overcome learner difficulties. A process of writing involves areas in brain learning pathway and motor cortex. This activity could be recorded using electroencephalogram (EEG) non-invasively. Using this information, a study has been conducted to distinguish EEG signal of normal, poor and capable dyslexic children. In this work, EEG signals were recorded from eight channels; C3, C4, P3, P4, FC5, FC6, T7 and T8. The signals were extracted using discrete wavelet transform (DWT) with Daubechies wavelet family order 2, 4, 6 and 8 to acquire beta and theta band features. The coefficient of beta band power and the ratio of theta/beta band power were input features of expert learning machine (ELM) classifier. Four types of kernels namely linear, radial basis function (RBF), polynomial and wavelet were applied as output weight in connecting hidden node and the output node of ELM. Parameters were varied to optimize each kernel to obtain the best classification accuracy. Results show that db2 gives the highest classification performance for all kernel among other Daubechies family. RBF and wavelet kernel yield the highest accuracy at 89% compared with other ELM kernels. This work reveals that ELM with RBF and wavelet kernel together with beta band power and ratio of theta/beta band power extracted from db2 could distinguish normal, poor and dyslexic children during writing.

A NOVEL APPROACH TO CLASSIFY THE SHOULDER MOTION OF UPPER LIMB AMPUTEES

Wavelet transform (WT) is a powerful statistical tool used in applied mathematics for signal and image processing. The different mother wavelet basis function has been compared to select the optimal wavelet function that represents the Electromyogram signal characteristics of upper limb amputees. Four different EMG electrode has placed on different location of shoulder muscles. Twenty-one wavelet functions from different wavelet families were investigated. These functions included Daubechies (db1–db10), Symlets (sym1–sym5), Coiflets (coif1–coif5) and Discrete Meyer. Using mean square error value, the significance of the mother wavelet functions has been determined for Teres, Pectorials and Infraspinatus around shoulder muscles. The most compatible wavelet families Daubechies families were selected to achieve the classification of the shoulder movement.

A structural property of the wavelet packet transform method to localise incoherency of a signal

This paper proves a general structural property of the wavelet tree for a given seminorm in the context of the wavelet packet transform method. This structural property can be used in denoising algorithms of different applications to guarantee the optimality of novel search strategies. The property holds for any input signals using any orthogonal analysing wavelet families. The property holds for any norms, which results to be a convex function through the wavelet tree. Using a defined norms, seminorms or pseudonorms, this property can be used to detect incoherent parts of an input signal by using the minimal depth of the tree. In this sense the proposed denoising procedure works without thresholds for the localisation of different kinds of noise, as well as for a stop criterium for an optimal representation of the incoherency. The proof of this property is performed by mathematical induction and the demonstration is based on orthonormality with the help of the multiresolution framework aspects of the wavelets packet tree. The Theorem is independent of the definition of the adopted norm and of the incoherent part of an input signal. In this sense, the discovered property is a general one, which is related to any norm and any nature of the signal incoherence. It can be used in different applications, in which a minimum of a norm is required to be calculated through the wavelet tree.

Detection and classification of microcalcification from digital mammograms with firefly algorithm, extreme learning machine and non‐linear regression models: A comparison

AbstractIn this study, abnormalities in medical images are analysed using three classifiers, and the results are compared. Breast cancer remains a major public health problem among women worldwide. Recently, many algorithms have evolved for the investigation of breast cancer diagnosis through medical imaging. A computer‐aided microcalcification detection method is proposed to categorise the nature of breast cancer as either benign or malignant from input mammogram images. The standard mammogram image corpus, the Mammogram Image Analysis Society database is utilised, and feature extraction is performed using five different wavelet families at level 4 and level 6 decomposition. The work is accomplished through firefly algorithm (FA), extreme learning machine (ELM) and least‐square‐based non‐linear regression (LSNLR) classifiers. The performance of the classifiers is compared by benchmark metrics, such as total error rate, specificity, sensitivity, area under the receiver operating characteristic curve, precision, F1 score and the Matthews correlation coefficient. As validation of the classifier results, a kappa analysis is included to determine the agreement among classifiers. The LSNLR classifier attains a 3% to 7% improvement in average accuracy compared with the average classification accuracy of the FA (86.75%) and ELM (90.836%) classifiers.

Quantifying near fault pulses using generalized Morse wavelets

Recently, a family of analytic wavelets known as generalized Morse wavelets (GMW) has been established in the literature. This versatile wavelet family uses two parameters (γ and β) to adjust its frequency or time domain properties. By varying these two parameters, this wavelet family includes many commonly used analytic wavelets. In this paper, GMW are examined, along with the continuous wavelet transform (CWT), to determine their suitability for extraction of ground motion pulses from a suite of acceleration records. GMW are compared to a popular pulse model that has recently been adapted for wavelet analysis in the literature. It is shown, based on two different metrics, that GMW performs comparably with the other model for this suite of ground motions. Since CWT is repeated with different wavelet parameters for each ground motion, the parameter selection and pulse extraction process are examined. It is shown that using the maximum wavelet coefficient alone does not allow for the extraction of pulses that best match the time series or the spectral response. Alternative criteria are proposed in order to optimize pulse selection using performance-based metrics.

Performance comparison of sparsifying basis functions for compressive speech enhancement

Speech enhancement using Compressive Sensing algorithm is a different paradigm from the conventional enhancement and compression techniques. Compressive Sensing requires very less number of samples compared to the Nyquist sampling for the purpose of reconstructing the signal. This work provides a comparative analysis of three sparsifying basis functions DFT, DCT and DWT for compressive speech enhancement on the basis of five objective measures. The objective measures used are: Signal to Noise Ratio, Segmental Signal to Noise Ratio, Log-Likelihood Ratio, Perceptual Evaluation of Speech Quality and processing time. Experimental analysis concludes that DWT as a basis function performs better than the others for compressive speech enhancement. As orthogonal wavelets are suitable for signal denoising, this work further investigates the performance of the four orthogonal wavelet families: Daubechies, Coiflets, Symlets and Fejer-Korovkin as basis functions for the purpose of compressive speech enhancement.

Mother wavelet selection in the discrete wavelet transform for condition monitoring of wind turbine drivetrain bearings

AbstractAlthough the discrete wavelet transform has been used for diagnosing bearing faults for two decades, most work in this field has been done with test rig data. Since field data starts to be made more available, there is a need to shift into application studies.The choice of mother wavelet, ie, the predefined shape used to analyse the signal, has previously been investigated with simulated and test rig data without consensus of optimal choice in literature. Common between these investigations is the use of the wavelet coefficients' Shannon entropy to find which mother wavelet can yield the most useful features for condition monitoring.This study attempts to find the optimal mother wavelet selection using the discrete wavelet transform. Datasets from wind turbine gearbox accelerometers, consisting of enveloped vibration measurements monitoring both healthy and faulty bearings, have been analysed. The bearing fault frequencies' excitation level has been analysed with 130 different mother wavelets, yielding a definitive measure on their performance. Also, the applicability of Shannon entropy as a ranking method of mother wavelets has been investigated.The results show the discrete wavelet transforms ability to identify faults regardless of mother wavelet used, with the excitation level varying no more than 4%. By analysing the Shannon entropy, broad predictions to the excitation level could be drawn within the mother wavelet families but no direct correlation to the main results. Also, the high computational effort of high order Symlet wavelets, without increased performance, makes them unsuitable.