The wavelet method as an alternative for reducing ionospheric effects from single-frequency GPS receivers

The ionospheric effect is one of the major errors in GPS data processing over long baselines. As a dispersive medium, it is possible to compute its influence on the GPS signal with the ionosphere-free linear combination of L1 and L2 observables, requiring dual-frequency receivers. In the case of single-frequency receivers, ionospheric effects are either neglected or reduced by using a model. In this paper, an alternative for single-frequency users is proposed. It involves multiresolution analysis (MRA) using a wavelet analysis of the double-difference observations to remove the short- and medium-scale ionosphere variations and disturbances, as well as some minor tropospheric effects. Experiments were carried out over three baseline lengths from 50 to 450 km, and the results provided by the proposed method were better than those from dual-frequency receivers. The horizontal root mean square was of about 0.28 m (1 sigma).

Análise das curvas de luz do CoroT usando diferentes processos comparativos: estimando períodos de rotação estelar

One of the main goals of CoRoT Natal Team is the determination of rotation period for thousand of stars, a fundamental parameter for the study of stellar evolutionary histories. In order to estimate the rotation period of stars and to understand the associated uncertainties resulting, for example, from discontinuities in the curves and (or) low signal-to-noise ratio, we have compared three different methods for light curves treatment. These methods were applied to many light curves with different characteristics. First, a Visual Analysis was undertaken for each light curve, giving a general perspective on the different phenomena reflected in the curves. The results obtained by this method regarding the rotation period of the star, the presence of spots, or the star nature (binary system or other) were then compared with those obtained by two accurate methods: the CLEANest method, based on the DCDFT (Date Compensated Discrete Fourier Transform), and the Wavelet method, based on the Wavelet Transform. Our results show that all three methods have similar levels of accuracy and can complement each other. Nevertheless, the Wavelet method gives more information about the star, from the wavelet map, showing the variations of frequencies over time in the signal. Finally, we discuss the limitations of these methods, the efficiency to give us informations about the star and the development of tools to integrate different methods into a single analysis

Análise sísmica usando transformada de Curvelet

Oil prospecting is one of most complex and important features of oil industry Direct prospecting methods like drilling well logs are very expensive, in consequence indirect methods are preferred. Among the indirect prospecting techniques the seismic imaging is a relevant method. Seismic method is based on artificial seismic waves that are generated, go through the geologic medium suffering diffraction and reflexion and return to the surface where they are recorded and analyzed to construct seismograms. However, the seismogram contains not only actual geologic information, but also noise, and one of the main components of the noise is the ground roll. Noise attenuation is essential for a good geologic interpretation of the seismogram. It is common to study seismograms by using time-frequency transformations that map the seismic signal into a frequency space where it is easier to remove or attenuate noise. After that, data is reconstructed in the original space in such a way that geologic structures are shown in more detail. In addition, the curvelet transform is a new and effective spectral transformation that have been used in the analysis of complex data. In this work, we employ the curvelet transform to represent geologic data using basis functions that are directional in space. This particular basis can represent more effectively two dimensional objects with contours and lines. The curvelet analysis maps real space into frequencies scales and angular sectors in such way that we can distinguish in detail the sub-spaces where is the noise and remove the coefficients corresponding to the undesired data. In this work we develop and apply the denoising analysis to remove the ground roll of seismograms. We apply this technique to a artificial seismogram and to a real one. In both cases we obtain a good noise attenuation

Representações espectrais de sistemas complexos: aplicações à síntese de superfícies brownianas fracionárias anisotrópicas, filtragem de sinais e identificação de correlações

In this thesis, we study the application of spectral representations to the solution of problems in seismic exploration, the synthesis of fractal surfaces and the identification of correlations between one-dimensional signals. We apply a new approach, called Wavelet Coherency, to the study of stratigraphic correlation in well log signals, as an attempt to identify layers from the same geological formation, showing that the representation in wavelet space, with introduction of scale domain, can facilitate the process of comparing patterns in geophysical signals. We have introduced a new model for the generation of anisotropic fractional brownian surfaces based on curvelet transform, a new multiscale tool which can be seen as a generalization of the wavelet transform to include the direction component in multidimensional spaces. We have tested our model with a modified version of the Directional Average Method (DAM) to evaluate the anisotropy of fractional brownian surfaces. We also used the directional behavior of the curvelets to attack an important problem in seismic exploration: the atenuation of the ground roll, present in seismograms as a result of surface Rayleigh waves. The techniques employed are effective, leading to sparse representation of the signals, and, consequently, to good resolutions

Mathematical tests about the existence and applications of PPS-wavelets in function approximation problems

Neural networks and wavelet transform have been recently seen as attractive tools for developing eficient solutions for many real world problems in function approximation. Function approximation is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. So, mathematical model is a very important tool to guarantee the development of the neural network area. In this article we will introduce one series of mathematical demonstrations that guarantee the wavelets properties for the PPS functions. As application, we will show the use of PPS-wavelets in pattern recognition problems of handwritten digit through function approximation techniques.

Comparative study between RBF and radial-PPS neural networks

The study of function approximation is motivated by the human limitation and inability to register and manipulate with exact precision the behavior variations of the physical nature of a phenomenon. These variations are referred to as signals or signal functions. Many real world problem can be formulated as function approximation problems and from the viewpoint of artificial neural networks these can be seen as the problem of searching for a mapping that establishes a relationship from an input space to an output space through a process of network learning. Several paradigms of artificial neural networks (ANN) exist. Here we will be investigated a comparative of the ANN study of RBF with radial Polynomial Power of Sigmoids (PPS) in function approximation problems. Radial PPS are functions generated by linear combination of powers of sigmoids functions. The main objective of this paper is to show the advantages of the use of the radial PPS functions in relationship traditional RBF, through adaptive training and ridge regression techniques.

IFTrace: Video segmentation of deformable objects using the Image Foresting Transform

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Multidimensional polynomial powers of sigmoid (PPS) Wavelet neural networks

Wavelet functions have been used as the activation function in feedforward neural networks. An abundance of R&D has been produced on wavelet neural network area. Some successful algorithms and applications in wavelet neural network have been developed and reported in the literature. However, most of the aforementioned reports impose many restrictions in the classical backpropagation algorithm, such as low dimensionality, tensor product of wavelets, parameters initialization, and, in general, the output is one dimensional, etc. In order to remove some of these restrictions, a family of polynomial wavelets generated from powers of sigmoid functions is presented. We described how a multidimensional wavelet neural networks based on these functions can be constructed, trained and applied in pattern recognition tasks. As an example of application for the method proposed, it is studied the exclusive-or (XOR) problem.

Robust fault diagnosis in power distribution systems based on fuzzy ARTMAP neural network-aided evidence theory

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Systematic analysis of the Fourier transform spectrum of (CH3OH)-C-13 between 400 and 950 cm(-1)

We have investigated a high-resolution Fourier transform (FT) absorption spectrum of the (CH3OH)-C-13 isotopomer of methanol from 400 to 950 cm(-1) with the Ritz program. We present the assignments of 7160 transitions, 3021 of which belong to Asymmetry, and 4139 to E-symmetry. These transitions occur between states labeled by K quantum numbers up to 14, and by torsional quantum numbers n up to 4. The Ritz program evaluated the energies of the 4684 involved levels with an accuracy of the order of 10(-4) cm(-1). All of the assigned lines correspond to transitions involving torsionally excited levels within the ground small-amplitude vibrational state. (c) 2005 Elsevier B.V. All rights reserved.

Estudo de Fractalidade e Evolução Dinâmica de Sistemas Complexos

In this work, the study of some complex systems is done with use of two distinct procedures. In the first part, we have studied the usage of Wavelet transform on analysis and characterization of (multi)fractal time series. We have test the reliability of Wavelet Transform Modulus Maxima method (WTMM) in respect to the multifractal formalism, trough the calculation of the singularity spectrum of time series whose fractality is well known a priori. Next, we have use the Wavelet Transform Modulus Maxima method to study the fractality of lungs crackles sounds, a biological time series. Since the crackles sounds are due to the opening of a pulmonary airway bronchi, bronchioles and alveoli which was initially closed, we can get information on the phenomenon of the airway opening cascade of the whole lung. Once this phenomenon is associated with the pulmonar tree architecture, which displays fractal geometry, the analysis and fractal characterization of this noise may provide us with important parameters for comparison between healthy lungs and those affected by disorders that affect the geometry of the tree lung, such as the obstructive and parenchymal degenerative diseases, which occurs, for example, in pulmonary emphysema. In the second part, we study a site percolation model for square lattices, where the percolating cluster grows governed by a control rule, corresponding to a method of automatic search. In this model of percolation, which have characteristics of self-organized criticality, the method does not use the automated search on Leaths algorithm. It uses the following control rule: pt+1 = pt + k(Rc − Rt), where p is the probability of percolation, k is a kinetic parameter where 0 < k < 1 and R is the fraction of percolating finite square lattices with side L, LxL. This rule provides a time series corresponding to the dynamical evolution of the system, in particular the likelihood of percolation p. We proceed an analysis of scaling of the signal obtained in this way. The model used here enables the study of the automatic search method used for site percolation in square lattices, evaluating the dynamics of their parameters when the system goes to the critical point. It shows that the scaling of , the time elapsed until the system reaches the critical point, and tcor, the time required for the system loses its correlations, are both inversely proportional to k, the kinetic parameter of the control rule. We verify yet that the system has two different time scales after: one in which the system shows noise of type 1 f , indicating to be strongly correlated. Another in which it shows white noise, indicating that the correlation is lost. For large intervals of time the dynamics of the system shows ergodicity

Application of wavelets to the evaluation of phantom images for mammography quality control

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Multifractal regime transition in a modified minority game model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Wavelet-Galerkin method for one-dimensional elastoplasticity and damage problems: Constitutive modeling and computational aspects

This work presents an analysis of the wavelet-Galerkin method for one-dimensional elastoplastic-damage problems. Time-stepping algorithm for non-linear dynamics is presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spacial discretization we can use wavelet-Galerkin method instead of standard finite element method. This approach allows to locate singularities. The discrete formulation developed can be applied to the simulation of one-dimensional problems for elastic-plastic-damage models. (C) 2007 Elsevier B.V. All rights reserved.

Feedforward neural networks based on PPS-wavelet activation functions

Function approximation is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. Neural networks and wavenets have been recently seen as attractive tools for developing efficient solutions for many real world problems in function approximation. In this paper, it is shown how feedforward neural networks can be built using a different type of activation function referred to as the PPS-wavelet. An algorithm is presented to generate a family of PPS-wavelets that can be used to efficiently construct feedforward networks for function approximation.