In this thesis, a target detection technique using a rotational invariant wavelet-based scheme is presented. The technique is evaluated on Synthetic Aperture Rader (SAR) imaging and compared with a previously developed fractal-based technique, namely the extended fractal (EF) model. Both techniques attempt to exploit the textural characteristics of SAR imagery. Recently, a wavelet-based fractal feature set, similar to the proposed one, was compared with the EF feature for a general texture classification problem. The wavelet-based technique yielded a lower classification error than EF, which motivated the comparison between the two techniques presented in this paper. Experimental results show that the proposed techniques feature map provides a lower false alarm rate than the previously developed method.

Aplicações computacionais voltadas para o auxílio ao diagnóstico (Computer-Aided Diagnosis - CAD) estão se tornando cada vez mais freqüentes. O objetivo dessas aplicações é fornecer ao profissional da área médica ferramentas que auxiliem na detecção precoce de patologias diversas. Nesse contexto, algoritmos que satisfaçam o interesse do usuário em encontrar imagens semelhantes a um caso específico podem ser desenvolvidos. Essas buscas devem ser feitas por similaridade, considerando a informação visual da imagem e não utilizando os recursos do processo convencional de busca textual, o qual compara parâmetros fornecidos pelo usuário com valores de atributos armazenados. As técnicas que permitem esse desenvolvimento são descritas na literatura como recuperação de imagens baseada em conteúdo (Content-Based Image Retrieval - CBIR). O maior desafio nessa abordagem é determinar o conjunto de características que descrevem o conteúdo da imagem adequadamente. No presente trabalho foram implementados algoritmos para extrair as características das imagens médicas utilizando as transformadas Wavelet e Wavelet Packet. A transformada Wavelet Packet tem maior capacidade para distinguir as freqüências quando comparada com a transformada Wavelet \"tradicional\". Esse estudo explora tal propriedade e analisa o desempenho dessas abordagens matemáticas na recuperação das imagens médicas por conteúdo. Ao final do estudo pôde-se estabelecer um comparativo entre os resultados obtidos com os vetores gerados a partir dos dados extraídos por ambas transformadas. Considerando-se que na área médica a precisão na obtenção das informações tem importância fundamental, a transformada Wavelet Packet revelou vantagens relevantes sobre os métodos tradicionais que aplicam a transformada Wavelet. Gráficos recall x precision e confusion matrix forneceram medidas da eficácia de recuperação. / Computer-Aided Diagnosis (CAD) applications are becoming more frequent each day. This application\'s objective is to provide tools for the medical professional that help in the precocious detection of different pathologies. On this context, algorithms that satisfy the user interest to find similar images related to a singular case can be developed. Such searches must be done considering the visual information instead of using common resources employed in textual conventional procces\'s searches, which compares parameters provide by the user to attribute\'s values stored. The techniques that admit such development are depicted in the literature as Content-Based Image Retrieval (CBIR). The great challenge here is to define the features that represent the image appropriately. In the present research were implemented algorithms to extract the images features using the Wavelet transform and Wavelet Packet transform. A Wavelet Packet transform distinguish frequencies better than the \"tradicional\" Wavelet transform. Therefore this study explores such properties and analyze the both mathematics approaches performance in the medical images retrieval. A comparative can be estabilished between the results obtained with the vectors produced using extracted data in both transforms. Considering that in the medical area the precision to obtain informations has fundamental importance, the Wavelet Packet transform revealed relevant advantages compared to the traditional methods that use the Wavelet transform. Recall x precision graphs and confusion matrix provides retrieval efficiency measures.

Wavelets are functions that are useful for representing signals and approximating other functions. Wavelets sets are defined in terms of Fourier transforms of certain wavelet functions. In this paper, we provide an introduction to wavelets and wavelets sets, examine the preexisting literature on the subject, and investigate an algorithm for creating wavelet sets. This algorithm creates single wavelets, which can be used to create bases for L2(Rn) through dilation and translation. We investigate the convergence properties of the algorithm, and implement the algorithm in Matlab.

acase@tulane.edu / In this thesis, we tackle the statistical problem of demixing a multivariate stochastic process made up of independent, fractional process entries. We consider both Gaussian and non-Gaussian frameworks. The observable, mixed process is then a multivariate fractional stochastic process. In particular, when the components of the unmixed process are self-similar, the mixed process is operator self-similar. Multivariate mixed fractional processes are parameterized by a vector of Hurst parameters and a mixing matrix. We propose a 2-step wavelet-based estimation method to produce estimators of both the demixing matrix and the Hurst parameters. In the first step, an estimator of the demixing matrix is obtained by applying a classical joint diagonalization algorithm to two wavelet variance matrices of the mixed process. In the second step, a univariate-like wavelet regression method is applied to each entry of the demixed process to provide estimators of each individual Hurst parameter. The limiting distribution of the estimators is established for both Gaussian and nonGaussian (Rosenblatt-like) instances. Monte Carlo experiments show that the finite sample estimation performance is very satisfactory. As an application, we model bivariate series of annual tree ring measurements from bristlecone pine trees in White Mountains, California. / 1 / Hui Li

This degree project deals with Wavelet transform and Karhunen-Loeve transform. Through the mathematic description to understand and simulation to investigate the denoise ability of WT and the de-correlation ability of KLT. Mainly prove that the new algorithm which is the joint of these two algorithms is feasible.

Electrocardiogram is a pictorial representation of the electrical activity of heart beats. Because of the direct relationship between the ECG waveform and interval of the heart beats, it is possible that doctor can diagnose cardiac disease and monitor patient conditions from the unusual ECG waveforms. Based on the wavelet transform, this work introduces an algorithm to detect QRS complex. In particular, the quadratic spline wavelet has been adopted. The thesis first reviews wavelet transform briefly, then develops a QRS detention algorithm, which is then tested by using the MIT-BIH arrhythmia database. It is hoped that the proposed QRS detection algorithm can be a useful tool for medical personnel who are interested in using QRS information to explore their research work.

In multiresolution analysis(MRA)by wavelet function Daubechies (db), we decompose the signal in two parts, the low and high-frequency content,respectively. We remove the high-frequency content and reconstruct a new ¡§de-noise¡¨ signal by using inverse wavelet transform. In order to improve the forecasting accuracy of ANN (Artificial Neural Network) model ,we use the concept of tidal constituent phase-lags, and the new ¡§de-noise¡¨ signal was used as the input data set of ANN. Besides, we also use wavelet spectrum, conventional energy spectrum (Fast Fourier Transform, FFT),and harmonic analysis to analyze the character of tidal data . The results show that the concept of tidal constituent phase-lags can improve ANN model of tidal forecasting and supplement, but in the wavelet analysis , the improvement is insignificant .The reason is that the energy of higher frequency noise is very small compared to the energy of the diurnal and the semi- diurnal tidal components. In other word , the ANN model has a certain tolerance of noise effect .

Particle Image Velocimetry (PIV) and pressure measurement techniques were performed to investigate the drag reduction due to microbubble injection in the boundary layer of a fully developed turbulent channel flow. Two-dimensional full-field velocity components in streamwise-near-wall normal plane of a turbulent channel flow at Reynolds number of 5128 based on the half height of the channel were measured. The influence of the presence of microbubbles in the boundary layer was assessed and compared with single phase channel flow characteristics. A drag reduction of 38.4% was achieved with void fraction of 4.9%. The measurements were analyzed by studying the turbulence characteristics utilizing wavelet techniques. The wavelet cross-correlation and auto-correlation maps with and without microbubbles were studied and compared. The two-dimensional and threedimensional wavelet maps were used to interpret the results. The following observations were deduced from this study: 1. The microbubble injection within the boundary layer increases the turbulent energy of the streamwise velocity components of the large scale (large eddy size, low frequency) range and decreases the energy of the small scale (small eddy size, high frequency) range. 2. The wavelet cross-correlation maps of the normal velocities indicate that the microbubble presence decrease the turbulent energy of normal velocity components for both the large scale (large eddy size, low frequency) and the small scale (small eddy size, high frequency) ranges. 3. The wavelet auto-correlation maps of streamwise velocity shows that the intensities at low frequency range were increased with microbubble presence and the intensities at high frequency range were decreased. 4. The turbulent intensities for the normal fluctuating velocities at both low frequency and high frequency range were decreased with microbubble injection. This study presents the modifications in the characteristics of the boundary layer of channel flow which are attributed to the presence of microbubbles. Drag reduction studies with microbubble injections utilizing wavelet techniques are promising and are needed to understand the drag reduction phenomena.

The relatively new method of using wavelets in well log analysis is a powerful tool for defining multiple superimposed scales of lithic trends and contacts. Interpreting depositional processes associated with different scales of vertical variation within well log responses allows prediction of the lateral extent of sands and the distribution of internal flow barriers important for development of oil field recovery strategies. Wavelet analysis of grain-size variations in a 2.1 km thick fluvial section including the fluvial Chinji and Nagri Formations, northern Pakistan, revealed three major wavelengths. Reliability of the wavelength values was tested and confirmed by multiple sectioning of the dataset. These dominant wavelengths are interpreted to reflect vertical variations within individual channels, the stacking of channel belts within overbank successions due to river avulsion, and larger-scale channel stacking patterns within this foreland basin that may reflect allocyclic influences. Wavelet analysis allows quantification of the scales of periodic vertical variations that may not be strictly cyclic in nature. Comparison of total wavelet energies over all scales for each depth to the grain size and sand percentages yielded good correlations with sand proportion curves. Although changes in the wavelet energy profile were much more distinct with respect to grain size, lithic boundaries' locations were not detected based solely on the total of the wavelet energies. The data were also analyzed using Fourier transforms. Although Fourier transforms of the data yielded the smallest scale cyclicities, the higher-order cyclicities were not defined. This comparison demonstrates the power of wavelet analysis in defining types of repetitive, but not strictly cyclic, variations that are commonly observed in the sedimentary record. Assessments of Milankovitch cyclicities were performed for the Chinji and the Nagri Formations using statistical and analytical analysis methods. A clear match between Milankovitch frequency ratios and vertical lithic variations was not observed, and thus distinct climatic control on cyclic lithological trends was not demonstrated. Analysis using wavelets to determine wavelet coefficients helps quantify characteristic scales of vertical variations, cyclicities, zone thicknesses, and locations of abrupt lithic boundaries. Wavelet analysis provides methods that could be used to help automate well log analysis.

Univ., Habil.-Schr.--Gießen. / Literaturverz. S. [127] - 133.