Multifractional splines: from seismic singularities to geological transitions

A matching pursuit technique in conjunction with an imaging method is used to obtain quantitative information on geological records from seismic data. The technique is based on a greedy, non-linear search algorithm decomposing data into atoms. These atoms are drawn from a redundant dictionary of seismic waveforms. Fractional splines are used to define this dictionary, whose elements are not only designed to match the observed waveforms but also to span the appropriate family of geological patterns. Consequently, the atom’s parameterization provides localized scale, order and direction information that reveals the stratigraphy and the type of geological transitions. Besides a localized scaling characterization, the atomic decomposition allows for an accurate denoised reconstruction of data with only a small number of atoms. Application of this approach to angles gathers allows us to track geological singularities from seismic data. Our characterization bridges the gap between the analysis of the main features within geologic processes, i.e. the geologic patterns, and the interpretation of their associated seismic response. A case study of Valhall data is presented.Massachusetts Institute of Technology. Earth Resources Laborator

On signal-noise decomposition of timeseries using the continuous wavelet transform: Application to sunspot index

We show that the continuous wavelet transform can provide a unique decomposition of a timeseries in to 'signal-like' and 'noise-like' components: From the overall wavelet spectrum two mutually independent skeleton spectra can be extracted, allowing the separate detection and monitoring in even non-stationary timeseries of the evolution of (a) both stable but also transient, evolving periodicities, such as the output of low dimensional dynamical systems and (b) scale-invariant structures, such as discontinuities, self-similar structures or noise. An indicative application to the monthly-averaged sunspot index reveals, apart from the well-known 11-year periodicity, 3 of its harmonics, the 2-year periodicity (quasi-biennial oscillation, QBO) and several more (some of which detected previously in various solar, earth-solar connection and climate indices), here proposed being just harmonics of the QBO, in all supporting the double-cycle solar magnetic dynamo model (Benevolenskaya, 1998, 2000). The scale maximal spectrum reveals the presence of 1/f fluctuations with timescales up to 1 year in the sunspot number, indicating that the solar magnetic configurations involved in the transient solar activity phenomena with those characteristic timescales are in a self-organized-critical state (SOC), as previously proposed for the solar flare occurence (Lu and Hamilton, 1991).Comment: 22 pages, 2 figure

Microsaccade characterization using the continuous wavelet transform and principal component analysis

During visual fixation on a target, humans perform miniature (or fixational) eye movements consisting of three components, i.e., tremor, drift, and microsaccades. Microsaccades are high velocity components with small amplitudes within fixational eye movements. However, microsaccade shapes and statistical properties vary between individual observers. Here we show that microsaccades can be formally represented with two significant shapes which we identfied using the mathematical definition of singularities for the detection of the former in real data with the continuous wavelet transform. For character-ization and model selection, we carried out a principal component analysis, which identified a step shape with an overshoot as first and a bump which regulates the overshoot as second component. We conclude that microsaccades are singular events with an overshoot component which can be detected by the continuous wavelet transform

Computational methods for hidden Markov tree models - An application to wavelet trees.

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1323262International audienceThe hidden Markov tree models were introduced by Crouse et al. in 1998 for modeling nonindependent, non-Gaussian wavelet transform coefficients. In their paper, they developed the equivalent of the forward-backward algorithm for hidden Markov tree models and called it the 'upward-downward algorithm'. This algorithm is subject to the same numerical limitations as the forward-backward algorithm for hidden Markov chains (HMCs). In this paper, adapting the ideas of Devijver from 1985, we propose a new 'upward-downward' algorithm, which is a true smoothing algorithm and is immune to numerical underflow. Furthermore, we propose a Viterbi-like algorithm for global restoration of the hidden state tree. The contribution of those algorithms as diagnosis tools is illustrated through the modeling of statistical dependencies between wavelet coefficients with a special emphasis on local regularity changes

Virtual Super Resolution of Scale Invariant Textured Images Using Multifractal Stochastic Processes

International audienceWe present a new method of magnification for textured images featuring scale invariance properties. This work is originally motivated by an application to astronomical images. One goal is to propose a method to quantitatively predict statistical and visual properties of images taken by a forthcoming higher resolution telescope from older images at lower resolution. This is done by performing a virtual super resolution using a family of scale invariant stochastic processes, namely compound Poisson cascades, and fractional integration. The procedure preserves the visual aspect as well as the statistical properties of the initial image. An augmentation of information is performed by locally adding random small scale details below the initial pixel size. This extrapolation procedure yields a potentially infinite number of magnified versions of an image. It allows for large magnification factors (virtually infinite) and is physically conservative: zooming out to the initial resolution yields the initial image back. The (virtually) super resolved images can be used to predict the quality of future observations as well as to develop and test compression or denoising techniques

Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters

Some spatial-domain and transform-domain digital image filtering algorithms have been developed in this thesis to suppress additive white Gaussian noise (AWGN). In many occasions, noise in digital images is found to be additive in nature with uniform power in the whole bandwidth and with Gaussian probability distribution. Such a noise is referred to as Additive White Gaussian Noise (AWGN). It is difficult to suppress AWGN since it corrupts almost all pixels in an image. The arithmetic mean filter, commonly known as Mean filter, can be employed to suppress AWGN but it introduces a blurring effect. Image denoising is usually required to be performed before display or further processing like segmentation, feature extraction, object recognition, texture analysis, etc. The purpose of denoising is to suppress the noise quite efficiently while retaining the edges and other detailed features as much as possible

Effectiveness of multifractal analysis for online signature verification

Orientador: Lee Luan LingDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: A verificação de identidades de forma confiável é cada vez mais necessária em nossa sociedade amplamente interconectada. Nesse contexto, a verificação biométrica é uma proposta alternativa, e mais segura, aos métodos tradicionalmente utilizados, como senhas e cartões. A análise multifractal, por sua vez, tem sido usada com sucesso em diversas aplicações de processamento de sinais, além disso, diversos estudos mostram a presença de características multifractais em processos naturais. Este trabalho tem como objetivo analisar os sinais referentes às assinaturas dinâmicas, provenientes de equipamentos como PDAs e tablet-pcs, sob o prisma da teoria multifractal. É estudada a capacidade de discriminação da característica multifractal na detecção de falsificações de assinaturas, tanto quando usadas isoladamente quanto em conjunto com características tradicionais, num contexto de fusão de informação, com resultados equivalentes ao estado da arte deste tema. Além disso, é realizada uma quantificação, através da teoria da informação, desta capacidade discriminatória. Por fim, é apresentada uma aplicação alternativa da informação multifractal no contexto da biometria: a análise de qualidade das amostrasAbstract: Reliable identity verification is an increasing necessity in our largely networked society. On this topic, biometric verification is a safer alternative to the traditional methods, such as passwords and ID cards. On the other hand, multifractal analysis has been successfully used in a wide range of signal processing applications; moreover, many works show the occurrence of multifractal traits on biological processes. This work aims at analyzing dynamic signature signals collected through devices such as PDAs and tablet-pcs, from a multifractal perspective. A study of the multifractal features discriminative capabilities on signature forgery detection is realized on two scenarios: when it is the unique feature used by the system, and in tandem with traditional features on an information fusion scheme; with results as good as those found in the state of the art of this area. Furthermore, an information theoretic quantification of the discrimination capability is realized. Finally, an alternative application for such features is presented: the evaluation of samples qualityMestradoTelecomunicações e TelemáticaMestre em Engenharia Elétric