An optimized algorithm for the evaluation of local singularity exponents in digital signals

International audienceRecent works show that the determination of singularity exponents in images can be useful to assess their information content, and in some cases they can cast additional information about underlying physical processes. However, the concept of singularity exponent is associated to differential calculus and thus cannot be easily translated to a digital context, even using wavelets. In this work we show that a recently patented algorithm allows obtaining precise, meaningful values of singularity exponents at every point in the image by the use of a discretized combinatorial mask, which is an extension of a particular wavelet basis. This mask is defined under the hypothesis that singularity exponents are a measure not only of the degree of regularity of the image, but also of the reconstructibility of a signal from their points

Combining local regularity estimation and total variation optimization for scale-free texture segmentation

Texture segmentation constitutes a standard image processing task, crucial to many applications. The present contribution focuses on the particular subset of scale-free textures and its originality resides in the combination of three key ingredients: First, texture characterization relies on the concept of local regularity ; Second, estimation of local regularity is based on new multiscale quantities referred to as wavelet leaders ; Third, segmentation from local regularity faces a fundamental bias variance trade-off: In nature, local regularity estimation shows high variability that impairs the detection of changes, while a posteriori smoothing of regularity estimates precludes from locating correctly changes. Instead, the present contribution proposes several variational problem formulations based on total variation and proximal resolutions that effectively circumvent this trade-off. Estimation and segmentation performance for the proposed procedures are quantified and compared on synthetic as well as on real-world textures

Une nouvelle approche non-linéaire pour la segmentation phonétique

National audienceLe potentiel du Formalisme Multiéchelles Microcanonique (FMM) dans l'identification des frontières de transition du signal de parole a déjà été démontré dans nos travaux antérieurs, en développant une méthode originale de segmentation phonétique. Le FMM repose sur une évaluation précise des exposants de singularité (EdS). Dans ce papier, après avoir décrit en détail un algorithme pour l'estimation précise des EdS dans le cas d'un signal 1D, nous introduisons une nouvelle méthode qui utilise mieux les EdS pour améliorer la précision de la segmentation: d'abord le signal original et une version filtrée sont utilisés pour déterminer un ensemble de frontières candidates; ensuite un test d'hypothèse est effectué sur la distribution des EdS du signal d'origine pour sélectionner les frontières définitives. Nous évaluons la performance de ce nouvel algorithme sur la base TIMIT. Les résultats montrent qu'une amélioration considérable des performances de segmentation est réalisée

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

On mesoscale analysis and ASCAT ambiguity removal

45 pages, 17 figures, 7 tablesIn the so-called two-dimensional variational ambiguity removal (2DVAR) scheme [Vogelzanget al., 2010], the scatterometer observations and the model background (fromthe European Centre for Medium-range Weather Forecasts, ECMWF) are combined using a two-dimensional variational approach, similar to that used in meteorological data assimilation, to provide an analyzed wind field. Since scatterometers provide unique mesoscale information on the wind field, mesoscale analysis is a common challenge for 2DVAR and for mesoscale data assimilation in 4D-var or 3D-var, such as applied using the Integrated Forecasting System (IFS) at ECMWF, Meteo France or in the HIRLAM project (www.hirlam.org). This study elaborates on the common problem of specifying the observation and background error covariances in data assimilationThis documentation was developed within the context of the EUMETSAT Satellite Application Facility on Numerical Weather Prediction (NWP SAF), under the Cooperation Agreement dated 29 June 2011, between EUMETSAT and the Met Office, UK, by one or more partners within the NWP SAF. The partners in the NWP SAF are the Met Office, ECMWF, KNMI and Météo FrancePeer Reviewe

An optimized algorithm for the evaluation of local singularity exponents in digital signals

Recent works show that the determination of singularity exponents in images can be useful to assess their information content, and in some cases they can cast additional information about underlying physical processes. However, the concept of singularity exponent is associated to differential calculus and thus cannot be easily translated to a digital context, even using wavelets. In this work we show that a recently patented algorithm allows obtaining precise, meaningful values of singularity exponents at every point in the image by the use of a discretized combinatorial mask, which is an extension of a particular wavelet basis. This mask is defined under the hypothesis that singularity exponents are a measure not only of the degree of regularity of the image, but also of the reconstructibility of a signal from their pointsPeer Reviewe