Automated Analysis of the Auditory Brainstem Response Using Derivative Estimation Wavelets

In this paper, we describe an algorithm that automatically detects and labels peaks I - VII of the normal, suprathreshold auditory brainstem response (ABR). The algorithm proceeds in three stages, with the option of a fourth: ( 1) all candidate peaks and troughs in the ABR waveform are identified using zero crossings of the first derivative, ( 2) peaks I - VII are identified from these candidate peaks based on their latency and morphology, ( 3) if required, peaks II and IV are identified as points of inflection using zero crossings of the second derivative and ( 4) interpeak troughs are identified before peak latencies and amplitudes are measured. The performance of the algorithm was estimated on a set of 240 normal ABR waveforms recorded using a stimulus intensity of 90 dBnHL. When compared to an expert audiologist, the algorithm correctly identified the major ABR peaks ( I, III and V) in 96 - 98% of the waveforms and the minor ABR peaks ( II, IV, VI and VII) in 45 - 83% of waveforms. Whilst peak II was correctly identified in only 83% and peak IV in 77% of waveforms, it was shown that 5% of the peak II identifications and 31% of the peak IV identifications came as a direct result of allowing these peaks to be found as points of inflection. Copyright (C) 2005 S. Karger AG, Basel.

Colour image coding with wavelets and matching pursuit

This thesis considers sparse approximation of still images as the basis of a lossy compression system. The Matching Pursuit (MP) algorithm is presented as a method particularly suited for application in lossy scalable image coding. Its multichannel extension, capable of exploiting inter-channel correlations, is found to be an efficient way to represent colour data in RGB colour space. Known problems with MP, high computational complexity of encoding and dictionary design, are tackled by finding an appropriate partitioning of an image. The idea of performing MP in the spatio-frequency domain after transform such as Discrete Wavelet Transform (DWT) is explored. The main challenge, though, is to encode the image representation obtained after MP into a bit-stream. Novel approaches for encoding the atomic decomposition of a signal and colour amplitudes quantisation are proposed and evaluated. The image codec that has been built is capable of competing with scalable coders such as JPEG 2000 and SPIHT in terms of compression ratio.

Optimization of Gabor Wavelets for Face Recognition

The article describes researches of a method of person recognition by face image based on Gabor wavelets. Scales of Gabor functions are determined at which the maximal percent of recognition for search of a person in a database and minimal percent of mistakes due to false alarm errors when solving an access control task is achieved. The carried out researches have shown a possibility of improvement of recognition system work parameters in the specified two modes when the volume of used data is reduced.

Inversion Formulas for the q-Riemann-Liouville and q-Weyl Transforms Using Wavelets

Mathematics Subject Classification: 42A38, 42C40, 33D15, 33D60

Estudo de famílias wavelets para aplicação na análise em DOAS

Trace gases are important to our environment even though their presence comes only by ‘traces’, but their concentrations must be monitored, so any necessary interventions can be done at the right time. There are some lower and upper boundaries which produce nice conditions for our lives and then monitoring trace gases comes as an essential task nowadays to be accomplished by many techniques. One of them is the differential optical absorption spectroscopy (DOAS), which consists mathematically on a regression - the classical method uses least-squares - to retrieve the trace gases concentrations. In order to achieve better results, many works have tried out different techniques instead of the classical approach. Some have tried to preprocess the signals to be analyzed by a denoising procedure - e.g. discrete wavelet transform (DWT). This work presents a semi-empirical study to find out the most suitable DWT family to be used in this denoising. The search seeks among many well-known families the one to better remove the noise, keeping the original signal’s main features, then by decreasing the noise, the residual left after the regression is done decreases too. The analysis take account the wavelet decomposition level, the threshold to be applied on the detail coefficients and how to apply them - hard or soft thresholding. The signals used come from an open and online data base which contains characteristic signals from some trace gases usually studied.

Estudo de famílias wavelets para aplicação na análise em DOAS

Trace gases are important to our environment even though their presence comes only by ‘traces’, but their concentrations must be monitored, so any necessary interventions can be done at the right time. There are some lower and upper boundaries which produce nice conditions for our lives and then monitoring trace gases comes as an essential task nowadays to be accomplished by many techniques. One of them is the differential optical absorption spectroscopy (DOAS), which consists mathematically on a regression - the classical method uses least-squares - to retrieve the trace gases concentrations. In order to achieve better results, many works have tried out different techniques instead of the classical approach. Some have tried to preprocess the signals to be analyzed by a denoising procedure - e.g. discrete wavelet transform (DWT). This work presents a semi-empirical study to find out the most suitable DWT family to be used in this denoising. The search seeks among many well-known families the one to better remove the noise, keeping the original signal’s main features, then by decreasing the noise, the residual left after the regression is done decreases too. The analysis take account the wavelet decomposition level, the threshold to be applied on the detail coefficients and how to apply them - hard or soft thresholding. The signals used come from an open and online data base which contains characteristic signals from some trace gases usually studied.

Implementación de un detector de coral utilizando filtros Gabor Wavelets y máquinas de aprendizaje

Este trabajo se enfoca en la implementación de un detector de arrecife de coral de desempeño rápido que se utiliza para un vehículo autónomo submarino (Autonomous Underwater Vehicle, AUV, por sus siglas en inglés). Una detección rápida de la presencia de coral asegura la estabilización del AUV frente al arrecife en el menor tiempo posible, evitando colisiones con el coral. La detección de coral se hace en una imagen que captura la escena que percibe la cámara del AUV. Se realiza una clasificación píxel por píxel entre dos clases: arrecife de coral y el plano de fondo que no es coral. A cada píxel de la imagen se le asigna un vector característico, el mismo que se genera mediante el uso de filtros Gabor Wavelets. Éstos son implementados en C++ y la librería OpenCV. Los vectores característicos son clasificados a través de nueve algoritmos de máquinas de aprendizaje. El desempeño de cada algoritmo se compara mediante la precisión y el tiempo de ejecución. El algoritmo de Árboles de Decisión resultó ser el más rápido y preciso de entre todos los algoritmos. Se creó una base de datos de 621 imágenes de corales de Belice (110 imágenes de entrenamiento y 511 imágenes de prueba).

Um modelo matemático baseado em wavelets para análise do método térmico de recuperação de óleo pesado aplicando irradiação eletromagnética

This work proposes a model to investigate the use of a cylindrical antenna used in the thermal method of recovering through electromagnetic radiation of high-viscosity oil. The antenna has a simple geometry, adapted dipole type, and it can be modelled by using Maxwell s equation. The wavelet transforms are used as basis functions and applied in conjunction with the method of moments to obtain the current distribution in the antenna. The electric field, power and temperature distribution are carefully calculated for the analysis of the antenna as electromagnetic heating. The energy performance is analyzed based on thermo-fluid dynamic simulations at field scale, and through the adaptation in the Steam Thermal and Advanced Processes Reservoir Simulator (STARS) by Computer Modelling Group (CMG). The model proposed and the numerical results obtained are stable and presented good agreement with the results reported in the specialized literature

Singularity and multifractal characterization of signals with wavelets. Application to clay soil images

In the field of multiscale analysis of signals, including images, the wavelet transform is one of the most attractive and powerful tool due to its ability to focus on signals structures at different scales. Wavelet Transform at different scales is successfully applied to image characterization (which can be applied to a watermarking scheme) and multiscale singularity detection and processing. In this work we show further research of computation of multifractals properties such as the multifractal spectrum (D(alpha)) applied to dye stained images of natural terrain. This can be useful for statically describing preferential flow path geometry.

Spatial analysis of urban violence based on emergency room data

OBJECTIVE: To estimate the spatial intensity of urban violence events using wavelet-based methods and emergency room data. METHODS: Information on victims attended at the emergency room of a public hospital in the city of São Paulo, Southeastern Brazil, from January 1, 2002 to January 11, 2003 were obtained from hospital records. The spatial distribution of 3,540 events was recorded and a uniform random procedure was used to allocate records with incomplete addresses. Point processes and wavelet analysis technique were used to estimate the spatial intensity, defined as the expected number of events by unit area. RESULTS: Of all georeferenced points, 59% were accidents and 40% were assaults. There is a non-homogeneous spatial distribution of the events with high concentration in two districts and three large avenues in the southern area of the city of São Paulo. CONCLUSIONS: Hospital records combined with methodological tools to estimate intensity of events are useful to study urban violence. The wavelet analysis is useful in the computation of the expected number of events and their respective confidence bands for any sub-region and, consequently, in the specification of risk estimates that could be used in decision-making processes for public policies.

Multifractality in plasma edge electrostatic turbulence

Plasma edge turbulence in Tokamak Chauffage Alfven Bresilien (TCABR) [R. M. O. Galvao et al., Plasma Phys. Contr. Fusion 43, 1181 (2001)] is investigated for multifractal properties of the fluctuating floating electrostatic potential measured by Langmuir probes. The multifractality in this signal is characterized by the full multifractal spectra determined by applying the wavelet transform modulus maxima. In this work, the dependence of the multifractal spectrum with the radial position is presented. The multifractality degree inside the plasma increases with the radial position reaching a maximum near the plasma edge and becoming almost constant in the scrape-off layer. Comparisons between these results with those obtained for random test time series with the same Hurst exponents and data length statistically confirm the reported multifractal behavior. Moreover, the persistence of these signals, characterized by their Hurst exponent, present radial profile similar to the deterministic component estimated from analysis based on dynamical recurrences. (C) 2008 American Institute of Physics.

Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

Multifractal regime transition in a modified minority game model

The search for more realistic modeling of financial time series reveals several stylized facts of real markets. In this work we focus on the multifractal properties found in price and index signals. Although the usual minority game (MG) models do not exhibit multifractality, we study here one of its variants that does. We show that the nonsynchronous MG models in the nonergodic phase is multifractal and in this sense, together with other stylized facts, constitute a better modeling tool. Using the structure function (SF) approach we detected the stationary and the scaling range of the time series generated by the MG model and, from the linear (non-linear) behavior of the SF we identified the fractal (multifractal) regimes. Finally, using the wavelet transform modulus maxima (WTMM) technique we obtained its multifractal spectrum width for different dynamical regimes. (C) 2009 Elsevier Ltd. All rights reserved.

Multifractality in the random parameter model for multivariate time series

The Random Parameter model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we explore the scaling properties of the model, as observed in the multifractal structure of the simulated time series. We use the Wavelet Transform Modulus Maxima technique to obtain the multifractal spectrum dependence with the parameters of the model. The model shows a scaling structure compatible with the stylized facts for a reasonable choice of the parameter values. (C) 2009 Elsevier B.V. All rights reserved.