24 research outputs found
Random sampling over lca groups and inversion of the radon transform
We consider the problem of reconstructing a measurable function over G from a countable subset ofsamples, taken accordingly to a Poisson random point process, when G is a locally compact abelian group. Thisresults are applied to the problem of approximating the inverse Radon Transform of a function.Fil: Porten, Erika. Universidad Nacional de San MartÃn; ArgentinaFil: Medina, Juan Miguel. Universidad de Buenos Aires. Facultad de IngenierÃa. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Morvidone, Marcela. Universidad Nacional de San MartÃn; ArgentinaVIII Congreso de Matemática Aplicada, Computacional e IndustrialLa PlataArgentinaAsociación Argentina de Matemática Aplicada Computacional e IndustrialUniversidad Nacional de Rio Cuarto. Facultad de Ciencias Exactas, FÃsico-QuÃmica y Naturale
Analytic inversion of a Radon transform on double circular arcs with applications in Compton Scattering Tomography
In this work we introduce a new Radon transform which arises from a new
modality of Compton Scattering Tomography (CST). This new system is made of a
single detector rotating around a fixed source. Unlike some previous CST, no
collimator is used at the detector. Such a system allows us to collect
scattered photons coming from two opposite sides of the source-detector
segment, hence the manifold of the associated Radon transform is a family of
double circular arcs. As first main theoretical result, an analytic inversion
formula is established for this new Radon transform. This is achieved through
the formulation of the transform in terms of circular harmonic expansion
satisfying the consistency conditions in Cormack's sense. Moreover, a fast and
efficient numerical implementation via an alternative formulation based on
Hilbert transform is carried out. Simulation results illustrate the theoretical
feasibility of the new system. From a practical point of view, an uncollimated
detector system considerably increases the amount of collected data, which is
particularly significant in a scatter imaging system.Comment: 14 pages, 5 figure
Algoritmo iterativo para la reconstrucción de una señal a partir de un muestreo aleatorio
En este artÃculo presentaremos un método iterativo para la reconstrucción de señales, no necesariamente de banda limitada, a partir de un muestreo irregular tomado de manera aleatoria por un proceso de Poisson.Fil: Porten, Erika Roxana. Universidad Nacional de San MartÃn. Escuela de Ciencia y TecnologÃa; ArgentinaFil: Medina, Juan Miguel. Universidad de Buenos Aires. Facultad de IngenierÃa. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Morvidone, Marcela Alejandra. Universidad Nacional de San MartÃn. Escuela de Ciencia y TecnologÃa; ArgentinaVII Congreso de Matemática Aplicada, Computacional e IndustrialRio CuartoArgentinasociación Argentina de Matemática Aplicada, Computacional e IndustrialUniversidad Nacional de RÃo Cuart
Time Scale Approach for Chirp Detection
International audienceTwo different approaches for joint detection and estimation of signals embedded in stationary random noise are considered and compared, for the subclass of amplitude and frequency modulated signals. Matched filter approaches are compared to time-frequency and time scale based approaches. Particular attention is paid to the case of the so-called " power-law chirps " , characterized by monomial and polynomial amplitude and frequency functions. As target application, the problem of gravitational waves at interferometric detectors is considered
Etude et comparaison d'algorithmes de détection optimale pour les signaux modulés en amplitude et en fréquence (applications aux ondes gravitationnelles)
Cette thèse est consacrée au problème de détection de signaux modulés en amplitude et en fréquence ("chirps") dans des situations où la forme du signal est connue, modulo quelques paramètres inconnus à estimer. Les données dont on dispose sont affectées par un bruit additif, modélisé comme un processus aléatoire faiblement stationnaire, centré. Le filtre adapté est la méthode classiquement utilisée pour résoudre ce type de problème ; un "banc de filtres" est construit à partir du signal de référence et de la densité spectrale du bruit. Cette technique optimale est toutefois assez peu robuste, et oblige à des discrétisations très fines, qui engendrent d'importants coûts de calcul. Il s'avère que les signaux de type chirp ont des caractéristiques qui justifient l'utilisation des méthodes temps-échelle (analyse par ondelettes) pour son étude. Ces transformations fournissent une représentation des chirps localisée sur des courbes (arêtes) dans l'espace bidimensionnel dans lequel elles sont définies. Nous développons une méthode de détection d'arêtes comme alternative au filtrage adapté. On montre que cette approche, sous-optimale en termes de détection, est toutefois plus robuste dans certains cas, et donc plus adaptée à des situations où le modèle de signal n'est connu qu'à un ordre d'approximation donné. Les performances des deux approches sont testées et comparées de façon systématique sur des signaux modèles (modèles d'ondes gravitationnelles, en approximations Newtonienne et post-Newtoniennes d'ordre deux).AIX-MARSEILLE1-BU Sci.St Charles (130552104) / SudocSudocFranceF
Variations on Hough-wavelet transforms for time-frequency chirp detection
International audienceSeveral different approaches for joint detection/estimation of amplitude and frequency modulated signals embedded in stationary random noise with prescribed spectral density are considered and compared. Matched filter approaches are compared to time-frequency and time scale based approaches, together with " reassigned " versions. Particular attention is paid to the case of the so-called " power-law chirps " , characterized by monomial and polynomial amplitude and frequency functions. As target application, the problem of gravitational waves at interferometric detectors is considered
Time-frequency and time-scale vector fields for deforming time-frequency and time-scale representations
International audienceWe study local deformations of time-frequency and timescale representations, in the framework of the so-called reassignment methods, which aim at " deblurring " time-frequency representations. We focus on deformations generated by appropriate vector fields defined on time-frequency or time scale plane, and constructed on the basis of geometric and group-theoretical arguments. Such vector fields may be used as such for signal analysis (as quantities generalizing instantaneous frequency or group delay) in the framework of reassignment algorithms