On optimal wavelet bases for the realization of microcanonical cascade processes

International Journal of Wavelets, Multiresolution and Information ProcessingInternational audienceMultiplicative cascades are often used to represent the structure of turbulence. Under the action of a multiplicative cascade, the relevant variables of the system can be understood as the result of a successive transfer of information in cascade from large to small scales. However, to make this cascade transfer explicit (i.e, being able to decompose each variable as the product of larger scale contributions) is only achieved when signals are represented in an optimal wavelet basis. Finding such a basis is a data-demanding, highly-complex task. In this paper we propose a formalism that allows to find the optimal wavelet of a signal in an efficient, little data-demanding way. We confirm the appropriateness of this approach by analyzing the results on synthetic signals constructed with prescribed optimal bases. We show the validity of our approach constrained to given families of wavelets, though it can be generalized for a continuous unconstrained search scheme

Description, modeling and forecasting of data with optimal wavelets

Cascade processes have been used to model many different self-similar systems, as they are able to accurately describe most of their global statistical properties. The so-called optimal wavelet basis allows to achieve a geometrical representation of the cascade process-named microcanonical cascade- that describes the behavior of local quantities and thus it helps to reveal the underlying dynamics of the system. In this context, we study the benefits of using the optimal wavelet in contrast to other wavelets when used to define cascade variables, and we provide an optimality degree estimator that is appropriate to determine the closest-to-optimal wavelet in real data. Particularizing the analysis to stock market series, we show that they can be represented by microcanonical cascades in both the logarithm of the price and the volatility. Also, as a promising application in forecasting, we derive the distribution of the value of next point of the series conditioned to the knowledge of past points and the cascade structure, i.e., the stochastic kernel of the cascade process.

Microcanonical processing methodology for ECG and intracardial potential: application to atrial fibrillation

Cardiac diseases are the principal cause of human morbidity and mortality in the western world. The electric potential of the heart is a highly complex signal emerging as a result of nontrivial flow conduction, hierarchical structuring and multiple regulation mechanisms. Its proper accurate analysis becomes of crucial importance in order to detect and treat arrhythmias or other abnormal dynamics that could lead to life-threatening conditions. To achieve this, advanced nonlinear processing methods are needed: one example here is the case of recent advances in the Microcanonical Multiscale Formalism. The aim of the present paper is to recapitulate those advances and extend the analyses performed, specially looking at the case of atrial fibrillation. We show that both ECG and intracardial potential signals can be described in a model-free way as a fast dynamics combined with a slow dynamics. Sharp differences in the key parameters of the fast dynamics appear in different regimes of transition between atrial fibrillation and healthy cases. Therefore, this type of analysis could be used for automated early warning, also in the treatment of atrial fibrillation particularly to guide radiofrequency ablation procedures.Comment: Transactions on Mass-Data Analysis of Images and Signals 4, 1 (2012). Accepte

Characterizing Complexity of Atrial Arrhythmias through Effective Dynamics from Electric Potential Measures

International audienceThe cardiac electrical activity follows a complex dynamics whose accurate description is crucial to characterize arrythmias and classify their complexity. Rhythm reflects the connection topology of pacemaker cells at their source. Hence, characterizing the attractors as nonlinear, effective dynamics can capture the key parameters without imposing any particular model on the empirical signals. A dynamic phase-space reconstruction from appropriate embedding can be made robust and numerically stable with the presented method. \textbf{Methods:} Time series evolution is mapped to an object embedded in a phase space in abstract coordinates. $m$ independent observations construct an $m\mathrm{D}$ phase space, as per the ebmedding theorem. The dimension $m$ is the least one that embeds the dynamics (which is twice plus one the Minkowski dimension of its attractor set) and the time lag $\tau$ is the shortest for which the $m$ coordinates do not mutually interfere. With appropriate filtering, the method is robust and adapted to empirical signals. The result is a compact dynamical description that characterizes complexity degree and information distribution. \textbf{Results and Conclusion:} Nonlinear analysis provides appropriate tools to characterize cardiac dynamics. Singularity analysis and phase-space reconstruction are physically meaningful complexity measures with minimal assumptions on the underlying models. We validate our approach on ECG, endocavitary catheter measures and electrocardiographic maps. Key parameters vary infrequently and exhibit sharp transitions, which show where information concentrates and correspond to actual dynamical regime changes. In space domain, extreme values highlight arrhythmogenic areas whose ablation stopped the fibrillation. We observe a correspondence of time lag fluctuations of phase-space reconstructions with atrial fibrillation episodes in the same way as with the dynamical changes coming from singularity exponents. This opens the way for improved model-independent complexity descriptors to be used in non-invasive, automatic diagnosis support and ablation guide for electrical insulation therapy, in cases of arrhythmias such as atrial flutter and fibrillation

A Singularity-analysis Approach to characterize Epicardial Electric Potential

International audienceThe cardiac electrical activity conforms a complex sys- tem, for which nonlinear signal-processing is required to characterize it properly. In this context, an analysis in terms of singularity exponents is shown to provide compact and meaningful descriptors of the structure and dynam- ics. In particular, singularity components reconstruct the epicardial electric potential maps of human atria, inverse- mapped from surface potentials; such approach describe sinus-rhythm dynamics as well as atrial flutter and atrial fibrillation. We present several example cases in which the key descriptors in the form of fast-slow dynamics point at the arrhythmogenic areas in the atria

Novel multiscale methods for nonlinear speech analysis

Cette thèse présente une recherche exploratoire sur l'application du Formalisme Microcanonique Multiéchelles (FMM) à l'analyse de la parole. Dérivé de principes issus en physique statistique, le FMM permet une analyse géométrique précise de la dynamique non linéaire des signaux complexes. Il est fondé sur l'estimation des paramètres géométriques locaux (les exposants de singularité) qui quantifient le degré de prédictibilité à chaque point du signal. Si correctement définis est estimés, ils fournissent des informations précieuses sur la dynamique locale de signaux complexes. Nous démontrons le potentiel du FMM dans l'analyse de la parole en développant: un algorithme performant pour la segmentation phonétique, un nouveau codeur, un algorithme robuste pour la détection précise des instants de fermeture glottale, un algorithme rapide pour l analyse par prédiction linéaire parcimonieuse et une solution efficace pour l approximation multipulse du signal source d'excitation.This thesis presents an exploratory research on the application of a nonlinear multiscale formalism, called the Microcanonical Multiscale Formalism (the MMF), to the analysis of speech signals. Derived from principles in Statistical Physics, the MMF allows accurate analysis of the nonlinear dynamics of complex signals. It relies on the estimation of local geometrical parameters, the singularity exponents (SE), which quantify the degree of predictability at each point of the signal domain. When correctly defined and estimated, these exponents can provide valuable information about the local dynamics of complex signals and has been successfully used in many applications ranging from signal representation to inference and prediction.We show the relevance of the MMF to speech analysis and develop several applications to show the strength and potential of the formalism. Using the MMF, in this thesis we introduce: a novel and accurate text-independent phonetic segmentation algorithm, a novel waveform coder, a robust accurate algorithm for detection of the Glottal Closure Instants, a closed-form solution for the problem of sparse linear prediction analysis and finally, an efficient algorithm for estimation of the excitation source signal.BORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF