Fast recursive detection-estimation of Bernouilli-Gaussian processes

This article deals with the problem of deconvolution of Bernoulli-Gaussian random processes observed through linear systems . This corresponds to situations that occur frequently in areas like geophysics, ultrasonic imaging or nondestructive inspection . Deconvolution of such signais is a detection-estimation problem which does not allow a purely linear data processing, and the nature of the difficulties greatly dépends on the type of representation chosen for the linear system . ARMA representations yield a non-standard state driving noise detection-estimation problem whose resolution is complex and requires great computational efforts . AR representations and the use of multi-pulse coding techniques cannot account for nonminimal phase systems and exhibit the disadvantages of output-error type methods . None of these approaches provide any on-line processing ability . In the method proposed here, a degenerate state-space representation is used, and a maximum a posteriori detection step is inserted in an estimation loop by Kalman filtering . This allows deconvolution of Bernoulli-Gaussian processes in a globally recursive manner . Furthermore, fast modified Chandrasekhar equations can be used for the implementation of this procedure and produce significant savings in computational requirements . Simulation results are satisfactory, and are obtained with less computations than other existing methods .Dans cet article, nous nous intéressons à la déconvolution d'un signal aléatoire du type Bernoulli-gaussien observé à travers un système linéaire, ce qui correspond à des problèmes rencontrés notamment en sismique, en échographie ultrasonore ou en contrôle non destructif. La déconvolution de tels signaux est un problème de détection-estimation, ce qui exclut un traitement purement linéaire des données . Les méthodes proposées jusqu'ici se distinguent essentiellement par la manière de représenter le système linéaire . Les formes ARMA conduisent a un problème non standard de détection-estimation d'un bruit d'état dont la résolution est complexe et coûteuse en temps calcul . Les formes AR et l'utilisation des techniques de codage multi-impulsionnel ne permettent pas de modéliser les systèmes à phase non minimale, et présentent les inconvénients des méthodes du type « erreur de sortie » . De plus, aucune de ces approches n'autorise un traitement en ligne des données . En modélisant le système par équations d'état dégénérées (forme MA), et en imbriquant une étape de détection par maximum a posteriori dans une boucle d'estimation par filtrage de Kalman, nous montrons qu'il est possible de déconvoluer un processus Bernoulli-gaussien de manière globalement récursive . De plus, cette procédure peut être mise en ceuvre sous forme rapide à l'aide d'équations de Chandrasekhar modifiées . Les résultats obtenus sur données synthétiques sont satisfaisants, et ne nécessitent qu'un volume de calcul très inférieur aux méthodes proposées jusqu'ici

Numerical approach for high precision 3-D relativistic star models

A multi-domain spectral method for computing very high precision 3-D stellar models is presented. The boundary of each domain is chosen in order to coincide with a physical discontinuity (e.g. the star's surface). In addition, a regularization procedure is introduced to deal with the infinite derivatives on the boundary that may appear in the density field when stiff equations of state are used. Consequently all the physical fields are smooth functions on each domain and the spectral method is absolutely free of any Gibbs phenomenon, which yields to a very high precision. The power of this method is demonstrated by direct comparison with analytical solutions such as MacLaurin spheroids and Roche ellipsoids. The relative numerical error reveals to be of the order of $10^{-10}$. This approach has been developed for the study of relativistic inspiralling binaries. It may be applied to a wider class of astrophysical problems such as the study of relativistic rotating stars too.Comment: Minor changes, Phys. Rev. D in pres

Use of a Priori Information for the Deconvolution of Ultrasonic Signals

The resolution of pulse-echo imaging technique is limited by the band-width of the transducer impulse response (IR). For flaws sizing or thickness measurement simple and accurate methods exist if the echoes do not overlap. These classical methods break if the echoes can not be separated in time domain

Improving the approximation ability of Volterra series identified with a cross-correlation method

This paper proposes an improvement in cross-correlation methods derived from the Lee–Schetzen method, in order to obtain a lower mean square error in the output for a wider range of the input variances. In particular, each Wiener kernel is identified with a different input variance and new formulas for conversion from Wiener to Volterra representation are presented

Magnetohydrodynamics in stationary and axisymmetric spacetimes: A fully covariant approach

Minor modifications (text only); published version (28 pages)This work was supported by JSPS Grant-in-Aid for Scientific Research(C) under Grant No. 20540275, MEXT Grant-in-Aid for Scientific Research on Innovative Area under Grant No. 20105004, NSF Grant No. PHY100155, and ANR Grant No. 06-2-134423 Me´thodes mathe´matiques pour la relativite´ ge´ne´ral

Rotating Stars in Relativity

Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information one could obtain about the equation of state of matter at extremely high densities and because they are considered to be promising sources of gravitational waves. The latest theoretical understanding of rotating stars in relativity is reviewed in this updated article. The sections on the equilibrium properties and on the nonaxisymmetric instabilities in f-modes and r-modes have been updated and several new sections have been added on analytic solutions for the exterior spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating stars in numerical relativity.Comment: 101 pages, 18 figures. The full online-readable version of this article, including several animations, will be published in Living Reviews in Relativity at http://www.livingreviews.org