Estimation de multiples différences de temps d'arrivée à l'aide d'une fonction d'intercorrélation sous contrainte

Dans cette communication, nous présentons une méthode permettant d'estimer les différences de temps d'arrivée dans le cas de plusieurs signaux bruités enregistrés simultanément à l'aide d'une grille de capteurs. L'approche proposée est basée sur l'estimation sous contrainte des fonctions d'intercorrélations entre tous les signaux, la contreinte imposant un respect des relations entre les différents décalages entre signaux. Cette méthode est tout d'abord présentée sur un exemple utilisant quatre signaux, puis elle est généralisée à un nombre quelconque de signaux. Enfin, nous appliquons cette nouvelle méthode à l'estimation des différences de temps d'arrivée de signaux de Potentiels d'Action cardiaque en vue du suivi de propagation du potentiel à la surface d'un tissu cardiaque

Comparaison de deux estimateurs de la variance relative à des fluctuations d'échelle de transitoires, en présence de bruit coloré

Lors de l'acquisition de certains signaux physiologiques répétitifs, le signal se répète d'une réalisation à l'autre avec une légère fluctuation aléatoire d'échelle . La présence de bruit peut alors empêcher l'estimation de chaque changement d'échelle. On montre dans cet article que l'on peut estimer directement la variance de ces fluctuations à partir de l'ensemble des réalisations en utilisant les résultats déjà obtenus lorsque le changement d'échelle est remplacé par un retard aléatoire. Les conditions d'acquisition font apparaître un bruit coloré ce qui nous conduit à utiliser un estimateur linéaire à biais nul et à variance mimimale. Nous proposons alors deux estimateurs non biaisés de la matrice de covariance du bruit (qui dans notre approche devient quadratique) dont nous calculons les variances respectives

Core Shape modelling of a set of curves

A new method for shape and time variability modelling of a set of curves is presented. Shape variability is captured via warping functions after time realignment of the curves. These warping functions relate normalized integrals but their meaning is different from those described in previously proposed methods for curve registration. For this purpose, a semi-parametric model, namely the Core Shape (CS) model, is proposed for shape variability characterization of a sample of curves. The curve variability is modelled as the composition of a polynomial term that accounts for time support variability and another term that accounts for intrinsic shape variability of the normalized integrals. This formalism provides specific statistical tools for shape dispersion analysis which are typically a mean shape curve, the Core Shape (CS) curve, and a shape distance, the so-called CS distance, according to the degree of specific polynomial time functions. These tools are invariant to time support variability and allow a direct access to intrinsic shape variability obtained at this polynomial degree. Also, a method for estimating shape parameters and functions of the model is presented and illustrated with simulated data. The influence of the polynomial choice is analyzed by simulation. Finally, usefulness of the proposed model for functional curve analysis is demonstrated through a real case study on Auditory Cortex Responses (ACR) analysis. A comparative study with a Curve Registration (CR) approach, namely the Self-Modelling Registration (SMR) method, is performed to better define differences in characterizing time and shape variability.

Corrected Integral Shape Averaging Applied to Obstructive Sleep Apnea Detection from the Electrocardiogram

We present a technique called corrected integral shape averaging (CISA) for quantifying shape and shape differences in a set of signals. CISA can be used to account for signal differences which are purely due to affine time warping (jitter and dilation/compression), and hence provide access to intrinsic shape fluctuations. CISA can also be used to define a distance between shapes which has useful mathematical properties; a mean shape signal for a set of signals can be defined, which minimizes the sum of squared shape distances of the set from the mean. The CISA procedure also allows joint estimation of the affine time parameters. Numerical simulations are presented to support the algorithm for obtaining the CISA mean and parameters. Since CISA provides a well-defined shape distance, it can be used in shape clustering applications based on distance measures such as -means. We present an application in which CISA shape clustering is applied to P-waves extracted from the electrocardiogram of subjects suffering from sleep apnea. The resulting shape clustering distinguishes ECG segments recorded during apnea from those recorded during normal breathing with a sensitivity of and specificity of .</p