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11	A Survey of the Development of Daubechies Scaling Functions Age, Amber E 06 July 2010 (has links) Wavelets are functions used to approximate data and can be traced back to several different areas, including seismic geology and quantum mechanics. Wavelets are applicable in many areas, including fingerprint and data compression, earthquake prediction, speech discrimination, and human vision. In this paper, we first give a brief history on the origins of wavelet theory. We will then discuss the work of Daubechies, whose construction of continuous, compactly supported scaling functions resulted in an explosion in the study of wavelets in the 1990's. These scaling functions allow for the construction of Daubechies' wavelets. Next, we shall use the algorithm to construct the Daubechies D4 scaling filters associated with the D4 scaling function. We then explore the Cascade Algorithm, which is a process that uses approximations to get possible representations for the D2N scaling function of Daubechies. Lastly, we will use the Cascade Algorithm to get a visual representation of the D4 scaling function. Daubechies Cascade Algorithm Scaling Functions Multiresolution Analysis Wavelet American Studies Arts and Humanities
12	Remo??o de ru?dos s?smicos utilizando transformada de wavelet 1D e 2D com software em desenvolvimento Ecco, Daniel 05 April 2011 (has links) Made available in DSpace on 2014-12-17T14:08:44Z (GMT). No. of bitstreams: 1 DanielE_DISSERT.pdf: 1217613 bytes, checksum: edb565b9e30a0c09780fcf4efd4a52dc (MD5) Previous issue date: 2011-04-05 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / In the Hydrocarbon exploration activities, the great enigma is the location of the deposits. Great efforts are undertaken in an attempt to better identify them, locate them and at the same time, enhance cost-effectiveness relationship of extraction of oil. Seismic methods are the most widely used because they are indirect, i.e., probing the subsurface layers without invading them. Seismogram is the representation of the Earth s interior and its structures through a conveniently disposed arrangement of the data obtained by seismic reflection. A major problem in this representation is the intensity and variety of present noise in the seismogram, as the surface bearing noise that contaminates the relevant signals, and may mask the desired information, brought by waves scattered in deeper regions of the geological layers. It was developed a tool to suppress these noises based on wavelet transform 1D and 2D. The Java language program makes the separation of seismic images considering the directions (horizontal, vertical, mixed or local) and bands of wavelengths that form these images, using the Daubechies Wavelets, Auto-resolution and Tensor Product of wavelet bases. Besides, it was developed the option in a single image, using the tensor product of two-dimensional wavelets or one-wavelet tensor product by identities. In the latter case, we have the wavelet decomposition in a two dimensional signal in a single direction. This decomposition has allowed to lengthen a certain direction the two-dimensional Wavelets, correcting the effects of scales by applying Auto-resolutions. In other words, it has been improved the treatment of a seismic image using 1D wavelet and 2D wavelet at different stages of Auto-resolution. It was also implemented improvements in the display of images associated with breakdowns in each Auto-resolution, facilitating the choices of images with the signals of interest for image reconstruction without noise. The program was tested with real data and the results were good / Na atividade explorat?ria de hidrocarbonetos a grande inc?gnita ? a localiza??o das jazidas. Grandes esfor?os s?o empreendidos na tentativa de melhor identific?-las, localiz?-las e, ao mesmo tempo, otimizar a rela??o custo-benef?cio da extra??o de Petr?leo. Os m?todos s?smicos s?o os mais utilizados pelo fato de serem indiretos, isto ?, sondam as camadas de subsuperf?cie sem invadi-las. O sismograma ? a representa??o do interior da Terra e de suas estruturas atrav?s de um arranjo convenientemente disposto dos dados obtidos por meio da s?smica de reflex?o. Um grande problema nessa representa??o ? a intensidade e variedade de ru?dos presentes no sismograma, como o ru?do de rolamento superficial que contamina os sinais relevantes e pode mascarar as informa??es desejadas, trazidas por ondas espalhadas em regi?es mais profundas das camadas geol?gicas. Desenvolvemos uma ferramenta para suprimir estes ru?dos que usa transformadas Wavelets 1D e 2D. O programa, em linguagem Java, faz a separa??o das imagens S?smicas considerando as dire??es (horizontal, vertical e mistas ou locais) e faixas de comprimentos de ondas que formam essas imagens, usando Wavelets de Daubechies, Autoresolu??o que duplica o comprimento das ondas e Produto Tensorial das bases de Wavelets. Desenvolvemos a op??o, em uma mesma imagem, de usar o produto tensorial de Wavelets de dimens?o 2 ou produto tensorial de Wavelets de dimens?o 1 pelas identidades. Neste ?ltimo caso, temos a Decomposi??o em Wavelets de um sinal bidimensional em uma ?nica dire??o. Esta decomposi??o permite alongar numa determinada dire??o as Wavelets bidimensionais, corrigindo efeitos de escalas ao aplicarmos Autoresolu??es. Em outras palavras, aperfei?oamos o tratamento de uma imagem s?smica, usandoWavelet 1D eWavelet 2D em etapas diferentes de Autoresolu??es. Tamb?m implementamos melhorias na visualiza??o das imagens associadas ?s decomposi??es em cada Autoresolu??o, facilitando as escolhas das imagens com os sinais de interesse para reconstru??o da imagem sem os ru?dos. O programa foi testado com dados reais e os resultados obtidos foram de boa qualidade Transformada wavelet Wavelet daubechies Autoresolu??o linguagem java Produto tensorial Removing of surface bearing noise Wavelet transform Wavelet daubechies Auto-resolution Java language Tensor product CNPQ::ENGENHARIAS
13	Monitoring PC Hardware Sounds in Linux Systems Using the Daubechies D4 Wavelet. Henry, Robert Karns 17 December 2005 (has links) Users of high availability (HA) computing require systems that run continuously, with little or no downtime. Modern PCs address HA needs by monitoring operating system parameters such as voltage, temperature, and hard drive status in order to anticipate possible system failure. However, one modality for PC monitoring that has been underutilized is sound. The application described here uses wavelet theory to analyze sounds produced by PC hard drives during standard operation. When twenty-nine hard drives were tested with the application and the results compared with the drives' Self-Monitoring, Analysis, and Reporting Technology (S.M.A.R.T.) data, the binomial distribution's low p-value of 0.012 indicated better than chance agreement. While the concurrence between the two systems shows that sound is an effective tool in detecting hardware failures, the disagreements between the systems show that the application can complement S.M.A.R.T. in an HA system. failure prediction Linux ALSA SM.A.R.T. Monitor DSP Daubechies Wavelet remote vibration analysis. Computer Sciences Physical Sciences and Mathematics
14	Návrh algoritmu pro anonymizaci ultrazvukových dat na úrovni snímku / Design of algorithm for anonymization of ultrasound data Bugnerová, Pavla January 2017 (has links) This master’s thesis is focused on anonymization of ultrasound data in DICOM format. Haar wavelet belonging to Daubechies wavelet family is used to detect text areas in the image. Extraction of the text from the image is done using a free tool - tesseract OCR Engine. Finally, detected text is compared to sensitive data from DICOM metadata using Levenshtein - edit distance algorithm.
15	Application of Wavelets to Filtering and Analysis of Self-Similar Signals Wirsing, Karlton 30 June 2014 (has links) Digital Signal Processing has been dominated by the Fourier transform since the Fast Fourier Transform (FFT) was developed in 1965 by Cooley and Tukey. In the 1980's a new transform was developed called the wavelet transform, even though the first wavelet goes back to 1910. With the Fourier transform, all information about localized changes in signal features are spread out across the entire signal space, making local features global in scope. Wavelets are able to retain localized information about the signal by applying a function of a limited duration, also called a wavelet, to the signal. As with the Fourier transform, the discrete wavelet transform has an inverse transform, which allows us to make changes in a signal in the wavelet domain and then transform it back in the time domain. In this thesis, we have investigated the filtering properties of this technique and analyzed its performance under various settings. Another popular application of wavelet transform is data compression, such as described in the JPEG 2000 standard and compressed digital storage of fingerprints developed by the FBI. Previous work on filtering has focused on the discrete wavelet transform. Here, we extended that method to the stationary wavelet transform and found that it gives a performance boost of as much as 9 dB over that of the discrete wavelet transform. We also found that the SNR of noise filtering decreases as a frequency of the base signal increases up to the Nyquist limit for both the discrete and stationary wavelet transforms. Besides filtering the signal, the discrete wavelet transform can also be used to estimate the standard deviation of the white noise present in the signal. We extended the developed estimator for the discrete wavelet transform to the stationary wavelet transform. As with filtering, it is found that the quality of the estimate decreases as the frequency of the base signal increases. Many interesting signals are self-similar, which means that one of their properties is invariant on many different scales. One popular example is strict self-similarity, where an exact copy of a signal is replicated on many scales, but the most common property is statistical self-similarity, where a random segment of a signal is replicated on many different scales. In this work, we investigated wavelet-based methods to detect statistical self-similarities in a signal and their performance on various types of self-similar signals. Specifically, we found that the quality of the estimate depends on the type of the units of the signal being investigated for low Hurst exponent and on the type of edge padding being used for high Hurst exponent. / Master of Science Hurst Exponent Threshold Function Vanishing Moment Stationary Wavelet Transform Discrete Wavelet Transform Symlet Coiflet Daubechies Wavelet White Noise Red Noise Pink Noise Long Memory Self-Similarity Fractal
16	Detekce a sledování malých pohybujících se objektů / Detection and Tracking of Small Moving Objects Filip, Jan Unknown Date (has links) Thesis deals with the detection and tracking of small moving objects from static images. This work shows a general overview of methods and approaches to detection and tracking of objects. There are also described some other approaches to the whole solution. It also included basic definitions, such a noise, convolution and mathematical morphology. The work described Bayesian filtering and Kalman filter. It described the theory of Wavelets, wavelets filters and transformations. The work deals with different ways of the blob`s detection. It is here the design and implementation of applications, which is based on the wavelets filters and Kalman filter. It`s implemented several methods of background subtraction, which are compared by testing. Testing and application are designed to detect vehicles, which are moving faraway (at least 200 m away).
17	EEG Data acquisition and automatic seizure detection using wavelet transforms in the newborn EEG. Zarjam, Pega January 2003 (has links) This thesis deals with the problem of newborn seizre detection from the Electroencephalogram (EEG) signals. The ultimate goal is to design an automated seizure detection system to assist the medical personnel in timely seizure detection. Seizure detection is vital as neurological diseases or dysfunctions in newborn infants are often first manifested by seizure and prolonged seizures can result in impaired neuro-development or even fatality. The EEG has proved superior to clinical examination of newborns in early detection and prognostication of brain dysfunctions. However, long-term newborn EEG signals acquisition is considerably more difficult than that of adults and children. This is because, the number of the electrodes attached to the skin is limited by the size of the head, the newborns EEGs vary from day to day, and the newborns are reluctant of being in the recording situation. Also, the movement of the newborn can create artifact in the recording and as a result strongly affect the electrical seizure recognition. Most of the existing methods for neonates are either time or frequency based, and, therefore, do not consider the non-stationarity nature of the EEG signal. Thus, notwithstanding the plethora of existing methods, this thesis applies the discrete wavelet transform (DWT) to account for the non-stationarity of the EEG signals. First, two methods for seizure detection in neonates are proposed. The detection schemes are based on observing the changing behaviour of a number of statistical quantities of the wavelet coefficients (WC) of the EEG signal at different scales. In the first method, the variance and mean of the WC are considered as a feature set to dassify the EEG data into seizure and non-seizure. The test results give an average seizure detection rate (SDR) of 97.4%. In the second method, the number of zero-crossings, and the average distance between adjacent extrema of the WC of certain scales are extracted to form a feature set. The test obtains an average SDR of 95.2%. The proposed feature sets are both simple to implement, have high detection rate and low false alarm rate. Then, in order to reduce the complexity of the proposed schemes, two optimising methods are used to reduce the number of selected features. First, the mutual information feature selection (MIFS) algorithm is applied to select the optimum feature subset. The results show that an optimal subset of 9 features, provides SDR of 94%. Compared to that of the full feature set, it is clear that the optimal feature set can significantly reduce the system complexity. The drawback of the MIFS algorithm is that it ignores the interaction between features. To overcome this drawback, an alternative algorithm, the mutual information evaluation function (MIEF) is then used. The MIEF evaluates a set of candidate features extracted from the WC to select an informative feature subset. This function is based on the measurement of the information gain and takes into consideration the interaction between features. The performance of the proposed features is evaluated and compared to that of the features obtained using the MIFS algorithm. The MIEF algorithm selected the optimal 10 features resulting an average SDR of 96.3%. It is also shown, an average SDR of 93.5% can be obtained with only 4 features when the MIEF algorithm is used. In comparison with results of the first two methods, it is shown that the optimal feature subsets improve the system performance and significantly reduce the system complexity for implementation purpose. electroencephalogram seizure newborn detection classification time frequency scale signals automatic discrete wavelet seizure detection rate false alarm rate non-seizure detection rate optimisation mutual information mutual information evaluation function mutual information feature selection decomposition level wavelet coefficients detail components approximate components classifier feature extraction Daubechies artificial neural network
18	Contribution à la théorie des ondelettes : application à la turbulence des plasmas de bord de Tokamak et à la mesure dimensionnelle de cibles / Contribution to the wavelet theory : Application to edge plasma turbulence in tokamaks and to dimensional measurement of targets Scipioni, Angel 19 November 2010 (has links) La nécessaire représentation en échelle du monde nous amène à expliquer pourquoi la théorie des ondelettes en constitue le formalisme le mieux adapté. Ses performances sont comparées à d'autres outils : la méthode des étendues normalisées (R/S) et la méthode par décomposition empirique modale (EMD).La grande diversité des bases analysantes de la théorie des ondelettes nous conduit à proposer une approche à caractère morphologique de l'analyse. L'exposé est organisé en trois parties.Le premier chapitre est dédié aux éléments constitutifs de la théorie des ondelettes. Un lien surprenant est établi entre la notion de récurrence et l'analyse en échelle (polynômes de Daubechies) via le triangle de Pascal. Une expression analytique générale des coefficients des filtres de Daubechies à partir des racines des polynômes est ensuite proposée.Le deuxième chapitre constitue le premier domaine d'application. Il concerne les plasmas de bord des réacteurs de fusion de type tokamak. Nous exposons comment, pour la première fois sur des signaux expérimentaux, le coefficient de Hurst a pu être mesuré à partir d'un estimateur des moindres carrés à ondelettes. Nous détaillons ensuite, à partir de processus de type mouvement brownien fractionnaire (fBm), la manière dont nous avons établi un modèle (de synthèse) original reproduisant parfaitement la statistique mixte fBm et fGn qui caractérise un plasma de bord. Enfin, nous explicitons les raisons nous ayant amené à constater l'absence de lien existant entre des valeurs élevées du coefficient d'Hurst et de supposées longues corrélations.Le troisième chapitre est relatif au second domaine d'application. Il a été l'occasion de mettre en évidence comment le bien-fondé d'une approche morphologique couplée à une analyse en échelle nous ont permis d'extraire l'information relative à la taille, dans un écho rétrodiffusé d'une cible immergée et insonifiée par une onde ultrasonore / The necessary scale-based representation of the world leads us to explain why the wavelet theory is the best suited formalism. Its performances are compared to other tools: R/S analysis and empirical modal decomposition method (EMD). The great diversity of analyzing bases of wavelet theory leads us to propose a morphological approach of the analysis. The study is organized into three parts. The first chapter is dedicated to the constituent elements of wavelet theory. Then we will show the surprising link existing between recurrence concept and scale analysis (Daubechies polynomials) by using Pascal's triangle. A general analytical expression of Daubechies' filter coefficients is then proposed from the polynomial roots. The second chapter is the first application domain. It involves edge plasmas of tokamak fusion reactors. We will describe how, for the first time on experimental signals, the Hurst coefficient has been measured by a wavelet-based estimator. We will detail from fbm-like processes (fractional Brownian motion), how we have established an original model perfectly reproducing fBm and fGn joint statistics that characterizes magnetized plasmas. Finally, we will point out the reasons that show the lack of link between high values of the Hurst coefficient and possible long correlations. The third chapter is dedicated to the second application domain which is relative to the backscattered echo analysis of an immersed target insonified by an ultrasonic plane wave. We will explain how a morphological approach associated to a scale analysis can extract the diameter information Ondelettes Principe d'incertitude de Heisenberg Pavage temps-Fréquence Moments Régularité Support compact Fonction d'échelle Fonction d'ondelette Approximations Détails Résolution Filtre QMF Coefficients de Daubechies Analyse Reconstruction Précurseur Algorithme de Mallat Convolution Décimation Symétrisation Orthogonalisation Gram Schmidt Filtres frontières Complexité Décomposition modale empirique Méthode R/S Analyse des fluctuations redressées Fractal Auto-Similarité Plasma Bruit Gaussien fractionnaire Mouvement Brownien fractionnaire Ultrason Wavelets Heisenberg uncertainty principle Time-Frequency tiles Vanishing moments Regularity Compact support Scaling function Wavelet function Approximations Details Resolution QMF filters Daubechies coefficients Analysis Reconstruction Precursor Mallat algorithm Convolution Decimation Mirroring Orthogonalization Gram Schmidt Boundary filters Complexity Empirical Modal Decomposition R/S method Detrended fluctuations Analysis Fractal Self-Similarity Plasma Fractional Gaussian noise Fractional Brownian motion Ultrasound 530.44 515.243 3

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