Time-dependent wave splitting and source separation

Starting from classical absorbing boundary conditions, we propose a method for the separation of time-dependent scattered wave fields due to multiple sources or obstacles. In contrast to previous techniques, our method is local in space and time, deterministic, and also avoids a priori assumptions on the frequency spectrum of the signal. Numerical examples in two space dimensions illustrate the usefulness of wave splitting for time-dependent scattering problems

Time reversed absorbing conditions

The aim of this paper is to introduce the time reversed absorbing conditions (TRAC) in time reversal methods. These new boundary conditions enable one to ``recreate the past'' without knowing the source which has emitted the signals that are back-propagated. This new method does not rely on any {\em a priori} knowledge of the physical properties of the inclusion. We prove an energy estimate for the resulting non-standard boundary value problem. Two applications to inverse problems are given

Low-rank representation of extended image volumes: Applications to imaging and velocity continuation

In this paper, we present a cost-effective low-rank factorized form of computing the full subsurface extended image volumes without explicitly calculating the receiver wavefields. The propose approach is computationally feasible, which exploits the low-rank structure of full subsurface extended image volumes organized as a matrix, thus avoiding the customary loop over sources. Using carefully selected stylized examples, we show how conventional migration images can be extracted from the low-rank factorized form. We also present a velocity continuation procedure that uses the same low-rank form and allows us to map the extended image for one velocity model to another velocity model without recomputing all the source wavefields

Whole-microwave system modeling for brain imaging

In this paper, we present the results of a whole-system modeling of a microwave measurement prototype for brain imaging, consisting of 160 ceramic-loaded antennas working around 1 GHz. The modelization has been performed using open source FreeFem++ solver. Quantitative comparisons were performed using commercial software Ansys-HFSS and measurements. Coupling effects between antennas are studied with the empty system (without phantom) and simulations have been carried out with a fine numerical brain phantom model issued from scanner and MRI data for determining the sensitivity of the system in realistic configurations

Time-dependent wave splitting and source separation

Non UBCUnreviewedAuthor affiliation: University of BaselPostdoctora

Reconstruction de signaux et identification d'objets par la méthode TRAC en retournement temporel

Compilé avec hyperrefWe introduce time reversed absorbing conditions (TRAC) in time reversal methods. They enable one to "recreate the past" without knowing the source which has emitted the signals that are back-propagated. We present two applications in inverse problems : the reduction of the size of the computational domain and the determination, from boundary measurements, of the location and volume of an unknown inclusion. The method does not rely on any a priori knowledge of the physical properties of the inclusion. Numerical tests with the wave equation illustrate the efficiency of the method. This technique is fairly insensitive with respect to noise in the data. In particular the TRAC method is applied to the differentiation between a single inclusion and a two close inclusion case.Nous présentons une méthode de retournement temporel avec conditions aux limites absorbantes (TRAC). Cette méthode permet de " recréer le passé " sans connaissance de la source qui a émis les signaux rétro-propagés. Nous proposons deux applications aux problèmes inverses : la réduction de la taille du domaine de calcul en redéfinissant une surface de référence virtuelle sur laquelle les récepteurs semblent positionnés, et la détermination de la localisation d'une inclusion inconnue à partir de mesures au bord. La méthode TRAC ne nécessite aucune connaissance a priori des propriétés physiques de l'inclusion. Des tests numériques effectués sur l'équation des ondes illustrent l'efficacité de cette méthode, qui se révèle être très robuste vis-à-vis du bruit sur les données. En particulier, nous appliquons la méthode TRAC à la discrimination entre une unique inclusion et deux inclusions proches

Reconstruction de signaux et identification d objets par la méthode TRAC en retournement temporel

Nous présentons une méthode de retournement temporel avec conditions aux limites absorbantes (TRAC). Cette méthode permet de recréer le passé sans connaissance de la source qui a émis les signaux rétro-propagés. Nous proposons deux applications aux problèmes inverses : la réduction de la taille du domaine de calcul en redéfinissant une surface de référence virtuelle sur laquelle les récepteurs semblent positionnés, et la détermination de la localisation d une inclusion inconnue à partir de mesures au bord. La méthode TRAC ne nécessite aucune connaissance a priori des propriétés physiques de l inclusion. Des tests numériques effectués sur l équation des ondes illustrent l efficacité de cette méthode, qui se révèle être très robuste vis-à-vis du bruit sur les données. En particulier, nous appliquons la méthode TRAC à la discrimination entre une unique inclusion et deux inclusions proches.We introduce time reversed absorbing conditions (TRAC) in time reversal methods. They enable one to recreate the past without knowing the source which has emitted the signals that are back-propagated. We present two applications in inverse problems : the reduction of the size of the computational domain and the determination, from boundary measurements, of the location and volume of an unknown inclusion. The method does not rely on any a priori knowledge of the physical properties of the inclusion. Numerical tests with the wave equation illustrate the efficiency of the method. This technique is fairly insensitive with respect to noise in the data. In particular the TRAC method is applied to the differentiation between a single inclusion and a two close inclusions case.PARIS-BIUSJ-Biologie recherche (751052107) / SudocPARIS-BIUSJ-Mathématiques rech (751052111) / SudocSudocFranceF

A new approach to solve the inverse scattering problem for waves: combining the TRAC and the Adaptive Inversion methods

The aim of this paper is to propose a new method to solve the inverse scattering problem. This method works directly in the time-dependent domain, using the wave equation and proceeds in two steps. The first step is the time-reversed absorbing condition (TRAC) method to reconstruct and regularize the signal and to reduce the computational domain. The second step is the adaptive inversion method to solve the inverse problem from the TRAC data, by using basis and mesh adaptation. This strategy allows us to recover the position, the shape and the properties of the scatterer in a precise and robust manner

Time Reversed Absorbing Condition in the Partial Aperture Case

International audienceThe time-reversed absorbing conditions (TRAC) method introduced enables one to ''recreate the past'' without knowing the source which has emitted the signals that are back-propagated. It has been applied to inverse problems for the reduction of the computational domain size and for the determination, from boundary measurements, of the location and volume of an unknown inclusion. The method does not rely on any a priori knowledge of the physical properties of the inclusion. The aim of this paper is to extend the {\em TRAC} method to the partial aperture configuration and to discrete receivers with various spacing. In particular the TRAC method is applied to the differentiation between a single inclusion and a two close inclusion case. The results are fairly insensitive to noise in the data