Contribución al análisis multiescala de señales. Aplicación a imágenes de suelos agrícolas y series financieras

En el campo del análisis multirresolución de señales, bien sean señales unidimensionales o imágenes, la transformada wavelet (u ondícula) es una de las herramientas más atractivas y potentes debido a su capacidad de análisis de las estructuras y singularidades presentes en una señal cuando esta es analizada en distintas escalas. Este trabajo parte de la investigación de cómo la modificación directa de los coeficientes wavelets permite añadir información en forma de marcas de agua a una imagen o también como con las mismas técnicas se pueden realizar esquemas relativamente sencillos de eliminación de ruido en imágenes. Estas aplicaciones son el primer paso para entender qué información capturan los coeficientes wavelet obtenidos mediante las distintas versiones existentes de transformada wavelet Siguiendo la relación entre el módulo de los coeficientes wavelets resultantes en distintas escalas llegamos a poder caracterizar las singularidades presentes en señales o imágenes con aplicaciones prácticas en campos como el análisis de imágenes mamográficas. Esta relación no es más que el primer paso para enlazar la teoría wavelet con el formalismo multifractal, relación definida en primera instancia a partir de la transforma wavelet de módulo máximo. El análisis entre señal, transformada wavelet de módulo máximo e información local de cada coeficiente wavelet da origen a la contribución principal de este trabajo de tesis que consiste en la estimación directa de distintos parámetros multifractales a partir del cálculo de coeficientes derivados de manera local para cada muestra de una señal o pixel de una imagen. La metodología propuesta se aplica en primer lugar a señales de una dimensión de gran complejidad o irregularidad como son las series financieras y específicamente los valores que componen el índice Dow Jones. El resultado permite la cuantificación de la volatilidad o riesgo asociado a cada uno de esas series. En segundo lugar y como principal aplicación de la metodología de análisis multiescala propuesta, el trabajo de investigación se centra en cómo calcular parámetros multifractales en imágenes que reflejan la estructura de suelos agrícolas. Estas imágenes son obtenidas bien aplicando un tinte especial o mediante modernas técnicas de tomografía axial computarizada. En ambos casos, el objetivo es completar la caracterización estadística de la geometría de los flujos preferenciales de agua y otras sustancias, aspectos claves para el correcto tratamiento de suelos agrícolas. Para validar e interpretar cada uno de los algoritmos desarrollados se utilizan señales multifractales sintetizadas y se comparan los resultados obtenidos en las distintas aplicaciones respecto de algoritmos ya consolidados en cada caso.

O EFEITO DO CONTROLE RESPIRATÓRIO EM VARIÁVEIS ELETROFISIOLÓGICAS DA ATENÇÃO

A prática do ioga tem se tornado cada vez mais popular, não apenas pelos benefícios físicos, mas principalmente pelo bem-estar psicológico trazido pela sua prática. Um dos componentes do ioga é o Prãnãyama, ou controle da respiração. A atenção e a respiração são dois mecanismos fisiológicos e involuntários requeridos para a execução do Prãnãyama. O principal objetivo desse estudo foi verificar se variáveis contínuas do EEG (potência de diferentes faixas que o compõem) seriam moduladas pelo controle respiratório, comparando-se separadamente as duas fases do ciclo respiratório (inspiração e expiração), na situação de respiração espontânea e controlada. Fizeram parte do estudo 19 sujeitos (7 homens/12 mulheres, idade média de 36,89 e DP = ± 14,46) que foram convidados a participar da pesquisa nas dependências da Faculdade de Saúde da Universidade Metodista de São Paulo. Para o registro do eletroencefalograma foi utilizado um sistema de posicionamento de cinco eletrodos Ag AgCl (FPz, Fz, Cz, Pz e Oz) fixados a uma touca de posicionamento rápido (Quick-Cap, Neuromedical Supplies®), em sistema 10-20. Foram obtidos valores de máxima amplitude de potência (espectro de potência no domínio da frequência) nas frequências teta, alfa e beta e delta e calculada a razão teta/beta nas diferentes fases do ciclo respiratório (inspiração e expiração), separadamente, nas condições de respiração espontânea e de controle respiratório. Para o registro do ciclo respiratório, foi utilizada uma cinta de esforço respiratório M01 (Pletismógrafo). Os resultados mostram diferenças significativas entre as condições de respiração espontânea e de controle com valores das médias da razão teta/beta menores na respiração controlada do que na respiração espontânea e valores de média da potência alfa sempre maiores no controle respiratório. Diferenças significativas foram encontradas na comparação entre inspiração e expiração da respiração controlada com diminuição dos valores das médias da razão teta/beta na inspiração e aumento nos valores das médias da potência alfa, sobretudo na expiração. Os achados deste estudo trazem evidências de que o controle respiratório modula variáveis eletrofisiológicas relativas à atenção refletindo um estado de alerta, porém mais relaxado do que na situação de respiração espontânea.

Tight frames of k-plane ridgelets and the problem of representing objects that are smooth away from d-dimensional singularities in Rn

For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L2 (Rn), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions that are smooth away from singularities along k-planes in Rn. We also develop tools to help decide whether k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tight frame on the X-ray bundle χn,k—the fiber bundle having the Grassman manifold Gn,k of k-planes in Rn for base space, and for fibers the orthocomplements of those planes. This wavelet-like tight frame is the pushout to χn,k, via the smooth local coordinates of Gn,k, of an orthonormal basis of tensor Meyer wavelets on Euclidean space Rk(n−k) × Rn−k. We then use the X-ray isometry [Solmon, D. C. (1976) J. Math. Anal. Appl. 56, 61–83] to map this tight frame isometrically to a tight frame for L2(Rn)—the k-plane ridgelets. This construction makes analysis of a function f ∈ L2(Rn) by k-plane ridgelets identical to the analysis of the k-plane X-ray transform of f by an appropriate wavelet-like system for χn,k. As wavelets are typically effective at representing point singularities, it may be expected that these new systems will be effective at representing objects whose k-plane X-ray transform has a point singularity. Objects with discontinuities across hyperplanes are of this form, for k = n − 1.

Aplicação e avaliação de desempenho de um sistema de otimização em tempo real em uma unidade de produção de propeno.

Com o objetivo de aumentar o lucro de plantas químicas, a Otimização em Tempo Real (RTO) é uma ferramenta que busca determinar as condições ótimas operacionais do processo em estado estacionário, respeitando as restrições operacionais estabelecidas. Neste trabalho foi realizada a implementação prática de um ciclo RTO em um processo de destilação por recompressão de vapor (VRD), propileno-propano, da Refinaria de Paulínia (Petrobras S.A.), a partir de dados históricos da planta. Foram consideradas as principais etapas de um ciclo clássico de RTO: identificação de estado estacionário, reconciliação de dados, estimação de parâmetros e otimização econômica. Essa unidade foi modelada, simulada e otimizada em EMSO (Environment for Modeling, Simulation and Optimization), um simulador de processos orientado a equações desenvolvido no Brasil. Foram analisados e comparados dois métodos de identificação de estado estacionário, um baseado no teste estatístico F e outro baseado em wavelets. Ambos os métodos tiveram resultados semelhantes e mostraram-se capazes de identificar os estados estacionários de forma satisfatória, embora seja necessário o ajuste de parâmetros na sua implementação. Foram identificados alguns pontos estacionários para serem submetidos ao ciclo RTO e foi possível verificar a importância de partir de um estado estacionário para a continuidade do ciclo, já que essa é uma premissa do método. A partir dos pontos analisados, os resultados deste estudo mostram que o RTO é capaz de aumentar o ganho econômico entre 2,5-24%, dependendo das condições iniciais consideradas, o que pode representar ganhos de até 18 milhões de dólares por ano. Além disso, para essa unidade, verificou-se que o compressor é um equipamento limitante no aumento de ganho econômico do processo.

Is the method of signal analysis and test selection important for measuring standing balance in subjects with persistent whiplash?

Dizziness and or unsteadiness, associated with episodes of loss of balance, are frequent complaints in those suffering from persistent problems following a whiplash injury. Research has been inconclusive with respect to possible aetiology, discriminative tests and analyses used. The aim of this pilot research was to identify the test conditions and the most appropriate method for the analysis of sway that may differentiate subjects with persistent whiplash associated disorders (WAD) from healthy controls. The six conditions of the Clinical Test for Sensory Interaction in Balance was performed in both comfortable and tandem stance in 20 subjects with persistent WAD compared to 20 control subjects. The analyses were carried out using a traditional method of measurement, total sway distance, to results obtained from the use of wavelet analysis. Subjects with WAD were significantly less able to complete the tandem stance tests on a firm surface than controls. In comfortable stance, using wavelet analysis, significant differences between subjects with WAD and the control group were evident in total energy of the trace for all test conditions apart from eyes open on the firm surface. In contrast, the results of the analysis using total sway distance revealed no significant differences between groups across all six conditions. Wavelet analysis may be more appropriate for detecting disturbances in balance in whiplash subjects because the technique allows separation of the noise from the underlying systematic effect of sway. These findings will be used to direct future studies on the aeitiology of balance disturbances in WAD. (c) 2004 Elsevier B.V. All rights reserved.

O EFEITO DO CONTROLE RESPIRATÓRIO EM VARIÁVEIS ELETROFISIOLÓGICAS DA ATENÇÃO

A prática do ioga tem se tornado cada vez mais popular, não apenas pelos benefícios físicos, mas principalmente pelo bem-estar psicológico trazido pela sua prática. Um dos componentes do ioga é o Prãnãyama, ou controle da respiração. A atenção e a respiração são dois mecanismos fisiológicos e involuntários requeridos para a execução do Prãnãyama. O principal objetivo desse estudo foi verificar se variáveis contínuas do EEG (potência de diferentes faixas que o compõem) seriam moduladas pelo controle respiratório, comparando-se separadamente as duas fases do ciclo respiratório (inspiração e expiração), na situação de respiração espontânea e controlada. Fizeram parte do estudo 19 sujeitos (7 homens/12 mulheres, idade média de 36,89 e DP = ± 14,46) que foram convidados a participar da pesquisa nas dependências da Faculdade de Saúde da Universidade Metodista de São Paulo. Para o registro do eletroencefalograma foi utilizado um sistema de posicionamento de cinco eletrodos Ag AgCl (FPz, Fz, Cz, Pz e Oz) fixados a uma touca de posicionamento rápido (Quick-Cap, Neuromedical Supplies®), em sistema 10-20. Foram obtidos valores de máxima amplitude de potência (espectro de potência no domínio da frequência) nas frequências teta, alfa e beta e delta e calculada a razão teta/beta nas diferentes fases do ciclo respiratório (inspiração e expiração), separadamente, nas condições de respiração espontânea e de controle respiratório. Para o registro do ciclo respiratório, foi utilizada uma cinta de esforço respiratório M01 (Pletismógrafo). Os resultados mostram diferenças significativas entre as condições de respiração espontânea e de controle com valores das médias da razão teta/beta menores na respiração controlada do que na respiração espontânea e valores de média da potência alfa sempre maiores no controle respiratório. Diferenças significativas foram encontradas na comparação entre inspiração e expiração da respiração controlada com diminuição dos valores das médias da razão teta/beta na inspiração e aumento nos valores das médias da potência alfa, sobretudo na expiração. Os achados deste estudo trazem evidências de que o controle respiratório modula variáveis eletrofisiológicas relativas à atenção refletindo um estado de alerta, porém mais relaxado do que na situação de respiração espontânea.

Grayscale and colour image Codec based on matching pursuit in the spatio-frequency domain

This report presents and evaluates a novel idea for scalable lossy colour image coding with Matching Pursuit (MP) performed in a transform domain. The benefits of the idea of MP performed in the transform domain are analysed in detail. The main contribution of this work is extending MP with wavelets to colour coding and proposing a coding method. We exploit correlations between image subbands after wavelet transformation in RGB colour space. Then, a new and simple quantisation and coding scheme of colour MP decomposition based on Run Length Encoding (RLE), inspired by the idea of coding indexes in relational databases, is applied. As a final coding step arithmetic coding is used assuming uniform distributions of MP atom parameters. The target application is compression at low and medium bit-rates. Coding performance is compared to JPEG 2000 showing the potential to outperform the latter with more sophisticated than uniform data models for arithmetic coder. The results are presented for grayscale and colour coding of 12 standard test images.

From cardinal spline wavelet bases to highly coherent dictionaries

Wavelet families arise by scaling and translations of a prototype function, called the mother wavelet. The construction of wavelet bases for cardinal spline spaces is generally carried out within the multi-resolution analysis scheme. Thus, the usual way of increasing the dimension of the multi-resolution subspaces is by augmenting the scaling factor. We show here that, when working on a compact interval, the identical effect can be achieved without changing the wavelet scale but reducing the translation parameter. By such a procedure we generate a redundant frame, called a dictionary, spanning the same spaces as a wavelet basis but with wavelets of broader support. We characterize the correlation of the dictionary elements by measuring their 'coherence' and produce examples illustrating the relevance of highly coherent dictionaries to problems of sparse signal representation.

Data Flow Analysis and the Linear Programming Model

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.be

Application of Wavelet Decomposition to Document Line Segmentation

ACM Computing Classification System (1998): I.7, I.7.5.

Principal component and second generation wavelet analysis of Treasury yield curve evolution

Prices of U.S. Treasury securities vary over time and across maturities. When the market in Treasurys is sufficiently complete and frictionless, these prices may be modeled by a function time and maturity. A cross-section of this function for time held fixed is called the yield curve; the aggregate of these sections is the evolution of the yield curve. This dissertation studies aspects of this evolution. ^ There are two complementary approaches to the study of yield curve evolution here. The first is principal components analysis; the second is wavelet analysis. In both approaches both the time and maturity variables are discretized. In principal components analysis the vectors of yield curve shifts are viewed as observations of a multivariate normal distribution. The resulting covariance matrix is diagonalized; the resulting eigenvalues and eigenvectors (the principal components) are used to draw inferences about the yield curve evolution. ^ In wavelet analysis, the vectors of shifts are resolved into hierarchies of localized fundamental shifts (wavelets) that leave specified global properties invariant (average change and duration change). The hierarchies relate to the degree of localization with movements restricted to a single maturity at the base and general movements at the apex. Second generation wavelet techniques allow better adaptation of the model to economic observables. Statistically, the wavelet approach is inherently nonparametric while the wavelets themselves are better adapted to describing a complete market. ^ Principal components analysis provides information on the dimension of the yield curve process. While there is no clear demarkation between operative factors and noise, the top six principal components pick up 99% of total interest rate variation 95% of the time. An economically justified basis of this process is hard to find; for example a simple linear model will not suffice for the first principal component and the shape of this component is nonstationary. ^ Wavelet analysis works more directly with yield curve observations than principal components analysis. In fact the complete process from bond data to multiresolution is presented, including the dedicated Perl programs and the details of the portfolio metrics and specially adapted wavelet construction. The result is more robust statistics which provide balance to the more fragile principal components analysis. ^

Digital signal processing implementation for near real-time wavelet transformation system for binary images

Communication has become an essential function in our civilization. With the increasing demand for communication channels, it is now necessary to find ways to optimize the use of their bandwidth. One way to achieve this is by transforming the information before it is transmitted. This transformation can be performed by several techniques. One of the newest of these techniques is the use of wavelets. Wavelet transformation refers to the act of breaking down a signal into components called details and trends by using small waveforms that have a zero average in the time domain. After this transformation the data can be compressed by discarding the details, transmitting the trends. In the receiving end, the trends are used to reconstruct the image. In this work, the wavelet used for the transformation of an image will be selected from a library of available bases. The accuracy of the reconstruction, after the details are discarded, is dependent on the wavelets chosen from the wavelet basis library. The system developed in this thesis takes a 2-D image and decomposes it using a wavelet bank. A digital signal processor is used to achieve near real-time performance in this transformation task. A contribution of this thesis project is the development of DSP-based test bed for the future development of new real-time wavelet transformation algorithms.

Proteção diferencial de transformadores de potência utilizando a transformada Wavelet

About 10% of faults involving the electrical system occurs in power transformers. Therefore, the protection applied to the power transformers is essential to ensure the continuous operation of this device and the efficiency of the electrical system. Among the protection functions applied to power transformers, the differential protection appears as one of the main schemes, presenting reliable discrimination between internal faults and external faults or inrush currents. However, when using the low frequency components of the differential currents flowing through the transformer, the main difficulty of the conventional methods of differential protection is the delay for detection of the events. However, internal faults, external faults and other disturbances related to the transformer operation present transient and can be appropriately detected by the wavelet transform. In this paper is proposed the development of a wavelet-based differential protection for detection and identification of external faults to the transformer, internal faults, and transformer energizing by using the wavelet coefficient energy of the differential currents. The obtained results reveal the advantages of using of the wavelet transform in the differential protection compared to conventional protection, since it provides reliability and speed in detection of these events.

Estimação de potência em tempo real utilizando a transformada wavelet

The goal of the power monitoring in electrical power systems is to promote the reliablility as well as the quality of electrical power.Therefore, this dissertation proposes a new theory of power based on wavelet transform for real-time estimation of RMS voltages and currents, and some power amounts, such as active power, reactive power, apparent power, and power factor. The appropriate estimation the of RMS and power values is important for many applications, such as: design and analysis of power systems, compensation devices for improving power quality, and instruments for energy measuring. Simulation and experimental results obtained through the proposed MaximalOverlap Discrete Wavelet Transform-based method were compared with the IEEE Standard 1459-2010 and the commercial oscilloscope, respectively, presenting equivalent results. The proposed method presented good performance for compact mother wavelet, which is in accordance with real-time applications.

Modeling the impact of large-scale solid mass transfers on the gravity field

The focus of this thesis is to explore and quantify the response of large-scale solid mass transfer events on satellite-based gravity observations. The gravity signature of large-scale solid mass transfers has not been deeply explored yet; mainly due to the lack of significant events during dedicated satellite gravity missions‘ lifespans. In light of the next generation of gravity missions, the feasibility of employing satellite gravity observations to detect submarine and surface mass transfers is of importance for geoscience (improves the understanding of geodynamic processes) and for geodesy (improves the understanding of the dynamic gravity field). The aim of this thesis is twofold and focuses on assessing the feasibility of using satellite gravity observations for detecting large-scale solid mass transfers and on modeling the impact on the gravity field caused by these events. A methodology that employs 3D forward modeling simulations and 2D wavelet multiresolution analysis is suggested to estimate the impact of solid mass transfers on satellite gravity observations. The gravity signature of various submarine and subaerial events that occurred in the past was estimated. Case studies were conducted to assess the sensitivity and resolvability required in order to observe gravity differences caused by solid mass transfers. Simulation studies were also employed in order to assess the expected contribution of the Next Generation of Gravity Missions for this application.