Wavelet Concept Research Articles

Digital image processing to detect adaptive evolution.

In recent years, advances in image processing and machine learning have fueled a paradigm shift in detecting genomic regions under natural selection. Early machine learning techniques employed population-genetic summary statistics as features, which focus on specific genomic patterns expected by adaptive and neutral processes. Though such engineered features are important when training data is limited, the ease at which simulated data can now be generated has led to the recent development of approaches that take in image representations of haplotype alignments and automatically extract important features using convolutional neural networks. Digital image processing methods termed α-molecules are a class of techniques for multi-scale representation of objects that can extract a diverse set of features from images. One such α-molecule method, termed wavelet decomposition, lends greater control over high-frequency components of images. Another α-molecule method, termed curvelet decomposition, is an extension of the wavelet concept that considers events occurring along curves within images. We show that application of these α-molecule techniques to extract features from image representations of haplotype alignments yield high true positive rate and accuracy to detect hard and soft selective sweep signatures from genomic data with both linear and nonlinear machine learning classifiers. Moreover, we find that such models are easy to visualize and interpret, with performance rivaling those of contemporary deep learning approaches for detecting sweeps.

Variant of the charged system search algorithm for the design of optimal linear phase finite impulse response filters

ABSTRACT Digital signal filtering is one of the prime area which is frequently used in practical applications. In the class of digital filters, the prominent filters include – filters with finite impulse response (FIR) and filters with infinite impulse response (IIR). Low pass, high pass, band pass and band stop filters are the different types of filters that are currently employed for carrying out filtering actions. Filters are used for practical applications to reduce the noise incurred while processing the signals received, whether it may be an audio signal, video signal, bio-medical signal and so on. The key features for the design of filters include the optimization of coefficients and in turn the design of coefficients is based on attaining maximum stop band attenuation with less ripple rates. This paper proposes the soft computing based wavelet concept being introduced in the charged system search algorithm at the updation process. The scaling factor in the updation equation is implemented with a wavelet introduced to improve the exploration and exploitation capability of the algorithm. This introduction of wavelet into the algorithm results in faster convergence of the algorithm and proves its effectiveness in comparison with that of the other approaches as available in the literature.

Artificial Intelligence in Classifying High Impedance Faults in Electrical Power Distribution System

The Proposed work deals with the different types of artificial intelligence based classifiers for fault classification. A feature extraction method proposed on new wavelet concept based dual tree wavelet complex transform that is combined with the neural network. Detecting high impedance fault is toughest challenge for the electrical engineers in recent days.High impedance faults (HIF) are not identified byconventional over current protection system like conventional over current relay protection scheme due its uniqueness in magnitude of fault current, nature and characteristics.In this paper transient signal is analyzed using dual tree wavelet complex transform feature extraction method, coefficients are extracted under the scale 3 .In this paper HIF , L-G , L-L-G are classified by neural network based classifiers. The method is applied to IEEE33 standard radial Distribution network and the MATLAB simulation work is carried out necessary results.

Identification of relevant wavelet functions for multiscale characterization of manufactured surfaces using a genetically optimized neural network

Multiscale surface characterization is a powerful tool that is used for process monitoring, surface quality control, and manufacturing optimization by establishing a link between process variables and functional performances. The multiscale decomposition approach using continuous and discrete wavelets is widely applied to take into account scales dependency. However, the optimal choice of the analysis wavelet function and the number of decomposition level is still a big issue. In this article, the artificial neural network theory was combined with the wavelet concept and was optimized based on the genetic algorithm to identify the relevant wavelet function for multiscale characterization of abraded surface topographies. Then, an extensive wavelet function library was developed and the proposed algorithm was applied to topographic data obtained from various abrasive finishing processes. The results show the pertinence of this approach to select the relevant wavelet, and a universal relevant wavelet function for abraded surface characterization was determined.

A Hybrid Digital Watermarking Approach Using Wavelets and LSB

The present paper proposed a novel approach called Wavelet based Least Significant Bit Watermarking (WLSBWM) for high authentication, security and copyright protection. Alphabet Pattern (AP) approach is used to generate shuffled image in the first stage and Pell’s Cat Map (PCM) is used for providing more security and strong protection from attacks. PCM applied on each 5×5 sub images. A wavelet concept is used to reduce the dimensionality of the image until it equals to the size of the watermark image. Discrete Cosign Transform is applied in the first stage; later N level Discrete Wavelet Transform (DWT) is applied for reducing up to the size of the watermark image. The water mark image is inserted in LH<sub>n</sub> Sub band of the wavelet image using LSB concept. Simulation results show that the proposed technique produces better PSNR and similarity measure. The experimental results indicate that the present approach is more reliable and secure efficient.The robustness of the proposed scheme is evaluated against various image-processing attacks.

Bidirectional relationship between investor sentiment and excess returns: new evidence from the wavelet perspective

ABSTRACTWe propose to use the wavelet concept of the phase angle to determine the lead–lag relationship between investor sentiment and excess returns that are related to the bubble component of stock prices. The wavelet phase angle allows for decoupling short- and long-run relations and is additionally capable of identifying time-varying comovement patterns. Based on the monthly S&P500 index and two alternative monthly US sentiment indicators, we find that in the short run (until 3 months), sentiment is leading returns whereas for periods above 3 months the opposite can be observed. Moreover, the initially strong positive relationship becomes less pronounced with increasing time horizon, thereby indicating that the over- or undervaluation in the short run is gradually corrected in the long run.

On hyperbolic wavelets

AbstractA hyperbolic wavelet concept that can be used to describe, represent, and identify signals belonging to the space of functions H2 on the unit disc is constructed. The wavelet is derived as the voice-transform belonging to the unitary representation of the Blaschke group upon H2 on the disc. An alternative for discretization is also proposed and an efficient algorithm is constructed to compute the wavelet coefficients.

Pan-sharpening of QuickBird satellite images using multiresolution techniques: wavelets, contourlets, and curvelets

The Pan-sharpening technique is of special interest in remote sensing because satellites usually take panchromatic (PAN) and multispectral (MS) images separately; therefore, later fusion is necessary. In the present study, we focus on the satellite QuickBird because its images are among those that have the highest spatial resolution and are useful for regional analysis and high-resolution thematic cartography. Also, we perform the fusion task by multiresolution techniques, as numerous studies have demonstrated that the wavelet method (the origin of multiresolution methods) is one of the best for Pan-sharpening. Nevertheless, other multiresolution methods which inherited the wavelet concept, such as contourlet and curvelet, have scarcely been used in Pan-sharpening. In our study, we use undecimated algorithms in wavelets and contourlets while using a decimated algorithm for curvelets. The decimated algorithm presents an inhomogeneous colour distribution at a particular resolution level. We found that, for each method, more than one resolution level is suitable for Pan-sharpening. On the other hand, all methods at all the resolution levels present good spatial resolution when they are evaluated visually. Nevertheless, there are spectral differences between methods and resolution levels. Finally, from the analysis and discussion of the results, we recommend two methods for their functionality, these methods being the wavelet at resolution level 2 and the contourlet at resolution level 4.

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Time-space multiscale analysis by use of tensor product wavelets and its application to hydrology and GRACE data

This paper presents a wavelet analysis of temporal and spatial variations of the Earth’s gravitational potential based on tensor product wavelets. The time-space wavelet concept is realized by combining Legendre wavelets for the time domain and spherical wavelets for the space domain. In consequence, a multiresolution analysis for both temporal and spatial resolution is formulated within a unified concept. The method is then numerically realized by using first synthetically generated data and finally two real data sets.

Compact Representation of Green Function Using Discrete Wavelet Concept for Fast Field Analysis

A compact representation of the Green function is proposed by applying the discrete wavelet concept in the k-domain, which can be used for the acceleration of scattered field calculations in integral equation methods. A mathematical expression of the Green function based on the discrete wavelet concept is derived and its characteristics are discussed.

An integrated wavelet concept of physical geodesy

For the determination of the earth's gravity field many types of observations are nowadays available, including terrestrial gravimetry, airborne gravimetry, satellite-to-satellite tracking, satellite gradio-metry, etc. The mathematical connection between these observables on the one hand and gravity field and shape of the earth on the other is called the integrated concept of physical geodesy. In this paper harmonic wavelets are introduced by which the gravitational part of the gravity field can be approximated progressively better and better, reflecting an increasing flow of observations. An integrated concept of physical geodesy in terms of harmonic wavelets is presented. Essential tools for approximation are integration formulas relating an integral over an internal sphere to suitable linear combinations of observation functionals, i.e. linear functionals representing the geodetic observables. A scale discrete version of multiresolution is described for approximating the gravitational potential outside and on the earth's surface. Furthermore, an exact fully discrete wavelet approximation is developed for the case of band-limited wavelets. A method for combined global outer harmonic and local harmonic wavelet modelling is proposed corresponding to realistic earth's models. As examples, the role of wavelets is discussed for the classical Stokes problem, the oblique derivative problem, satellite-to-satellite tracking, satellite gravity gradiometry and combined satellite-to-satellite tracking and gradiometry.

A fast multiresolution moment‐method algorithm using wavelet concepts

AbstractA fast multiresolution moment‐method algorithm is developed based on the spectral‐domain wavelet concept. The computational savings are achieved by taking advantage of the multiscale feature of the spectral‐domain Green's function. It is shown that the multiresolution algorithm leads to reduced computational complexity in the matrix‐vector multiplication operation. © 1995 John Wiley & Sons, Inc.

On the efficient representation of the electrodynamic green's function using multiresolution wavelet concepts

AbstractA multiresolution wavelet concept is applied to efficiently represent the electrodynamic Green's function. In the joint spectral‐spatial representation, the multiscale feature of the spectral‐domain Green's function is clearly revealed. Due to this multiscale feature in the spectral domain, a wavelet application in the spectral domain (KDWT) is more appropriate in representing the Green's function than the wavelet transform applied in the space domain (SDWT). We present a multiresolution implementation of the KDWT and show that the KDWT representation results in a sparser moment impedance matrix than the SDWT representation. © 1995 John Wiley & Sons, Inc.

Data Compression and Wavelet Transforms

Efficient data compression needs analyzing functions to recognise the local resolution of the signal. They are provided by the wavelet concept. The optimal wavelet (best information concentration) is defined by the image model of the application. For the most common images in astronomy the H-transform is optimal (in the sense of Karhunen-Loeve transform). The role of the H-transform in 2-dimensional processing is the same as the Haar-transform in 1-dimension, but it is not the ‘2-dimensional Haar-transform’ found in text books.

Time-frequency digital filtering based on an invertible wavelet transform: an application to evoked potentials

This paper presents a method to analyze and filter digital signals of finite duration by means of a time-frequency representation. This is done by defining a purely invertible discrete transform, representing a signal either in the time or in the time-frequency domain, as simply as possible with the conventional discrete Fourier transform between the time and the frequency domains. The wavelet concept has been used to build this transform. To get a correct invertibility of this procedure, we have proposed orthogonal and periodic basic discrete wavelets. The properties of such a transform are described, and examples on brain-evoked potential signals are given to illustrate the time-frequency filtering possibilities.

Diffraction from a wavelet point of view

The system impulse response representing the Fresnel diffraction is shown to form a wavelet family of functions. The scale parameter of the wavelet family represents the depth (distance). This observation relates the diffraction-holography-related studies and the wavelet theory. The results may be used in various optical applications such as designing robust volume optical elements for optical signal processing and finding new formulations for optical inverse problems. The results also extend the wavelet concept to the nonbandpass family of functions with the implication of new applications in signal processing. The presented wavelet structure, for example, is a tool for space–depth analysis.