Results 1  10
of
428
A LevelSet Approach for Inverse Problems Involving Obstacles
, 1996
"... . An approach for solving inverse problems involving obstacles is proposed. The approach uses a levelset method which has been shown to be effective in treating problems of moving boundaries, particularly those that involve topological changes in the geometry. We develop two computational metho ..."
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Cited by 57 (2 self)
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. An approach for solving inverse problems involving obstacles is proposed. The approach uses a levelset method which has been shown to be effective in treating problems of moving boundaries, particularly those that involve topological changes in the geometry. We develop two computational methods based on this idea. One method results in a nonlinear timedependent partial differential equation for the levelset function whose evolution minimizes the residual in the data fit. The second method is an optimization that generates a sequence of levelset functions that reduces the residual. The methods are illustrated in two applications: a deconvolution problem and a diffraction screen reconstruction problem. Keywords: Inverse problems, levelset method, HamiltonJacobi equations, surface evolution, optimization, deconvolution, diffraction. 1. Inverse problems involving obstacles There is a host of inverse problems wherein the desired unknown is a region in IR 2 or IR 3 . ...
Adjoint Recovery of Superconvergent Functionals from Approximate Solutions of Partial Differential Equations
, 1998
"... Abstract. Motivated by applications in computational fluid dynamics, a method is presented for obtaining estimates of integral functionals, such as lift or drag, that have twice the order of accuracy of the computed flow solution on which they are based. This is achieved through error analysis that ..."
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Cited by 55 (9 self)
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Abstract. Motivated by applications in computational fluid dynamics, a method is presented for obtaining estimates of integral functionals, such as lift or drag, that have twice the order of accuracy of the computed flow solution on which they are based. This is achieved through error analysis that uses an adjoint PDE to relate the local errors in approximating the flow solution to the corresponding global errors in the functional of interest. Numerical evaluation of the local residual error together with an approximate solution to the adjoint equations may thus be combined to produce a correction for the computed functional value that yields the desired improvement in accuracy. Numerical results are presented for the Poisson equation in one and two dimensions and for the nonlinear quasionedimensional Euler equations. The theory is equally applicable to nonlinear equations in complex multidimensional domains and holds great promise for use in a range of engineering disciplines in which a few integral quantities are a key output of numerical approximations. Key words. PDEs, adjoint equations, error analysis, superconvergence AMS subject classifications. 65G99, 76N15 PII. S0036144598349423
A hybrid numericalasymptotic boundary integral method for highfrequency acoustic scattering
 NUMERISCHE MATHEMATIK
"... ..."
Fictitious Domain Methods For The Numerical Solution Of ThreeDimensional Acoustic Scattering Problems
 J. Comput. Phys
, 1999
"... . Efficient iterative methods for the numerical solution of threedimensional acoustic scattering problems are considered. The underlying exterior boundary value problem is approximated by truncating the unbounded domain and by imposing a nonreflecting boundary condition on the artificial boundary. ..."
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Cited by 25 (18 self)
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. Efficient iterative methods for the numerical solution of threedimensional acoustic scattering problems are considered. The underlying exterior boundary value problem is approximated by truncating the unbounded domain and by imposing a nonreflecting boundary condition on the artificial boundary. The finite element discretization of the approximate boundary value problem is performed using locally fitted meshes, and algebraic fictitious domain methods with separable preconditioners are applied to the solution of the arising mesh equations. These methods are based on imbedding the original domain into a larger one with a simple geometry (for example, a sphere or a parallelepiped). The iterative solution method is realized in a lowdimensional subspace, and partial solution methods are applied to the linear systems with the preconditioner. Results of numerical experiments demonstrate the efficiency and accuracy of the approach. Key words. Acoustic scattering, nonreflecting boundary ...
Spatial decomposition of MIMO wireless channels
 in The Seventh International Symposium on Signal Processing and its Applications
, 2003
"... In this paper a novel decomposition of spatial channels is developed to provide insight into spatial aspects of multiple antenna communication systems. The underlying physics of the free space propagation is used to model the channel in scatterer free regions around the transmitter and the receiver, ..."
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Cited by 25 (16 self)
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In this paper a novel decomposition of spatial channels is developed to provide insight into spatial aspects of multiple antenna communication systems. The underlying physics of the free space propagation is used to model the channel in scatterer free regions around the transmitter and the receiver, and the rest of the complex scattering media is represented by a parametric model. The channel matrix is separated into a product of known and random matrices where the known portion shows the effects of the physical configuration of antenna elements. We use the model to show the intrinsic degrees of freedom in a multiantenna system. Potential applications of the model are briefly discussed. 1.
Spatial Correlation for General Distributions of Scatterers
 IEEE Signal Processing Letters
, 2002
"... The wellknown results of the spatial correlation function for twodimensional and threedimensional diffuse fields of narrowband signals are generalized to the case of general distributions of scatterers. A method is presented that allows closedform expressions for the correlation function to be o ..."
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Cited by 24 (19 self)
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The wellknown results of the spatial correlation function for twodimensional and threedimensional diffuse fields of narrowband signals are generalized to the case of general distributions of scatterers. A method is presented that allows closedform expressions for the correlation function to be obtained for arbitrary scattering distribution functions. These closedform expressions are derived for a variety of commonly used scattering distribution functions.
The linear sampling method for anisotropic media
, 2002
"... We consider the inverse scattering problem of determining the support of an anisotropic inhomogeneous medium from a knowledge of the incident and scattered time harmonic acoustic wave at fixed frequency. To this end, we extend the linear sampling method from the isotropic case to the case of anisotr ..."
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Cited by 24 (16 self)
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We consider the inverse scattering problem of determining the support of an anisotropic inhomogeneous medium from a knowledge of the incident and scattered time harmonic acoustic wave at fixed frequency. To this end, we extend the linear sampling method from the isotropic case to the case of anisotropic medium. In the case when the coefficients are real we also show that the set of transmission eigenvalues forms a discrete set.
Solving timeharmonic scattering problems based on the pole condition: Convergence of the PML method
, 2001
"... In this paper we study the PML method for Helmholtztype scattering problems with radially symmetric potential. The PML method consists in surrounding the computational domain by a Perfectly Matched sponge Layer. We prove that the approximate solution obtained by the PML method converges exponential ..."
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Cited by 24 (4 self)
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In this paper we study the PML method for Helmholtztype scattering problems with radially symmetric potential. The PML method consists in surrounding the computational domain by a Perfectly Matched sponge Layer. We prove that the approximate solution obtained by the PML method converges exponentially fast to the true solution in the computational domain as the thickness of the sponge layer tends to infinity. This is a generalization of results by Lassas and Somersalo based on boundary integral equation techniques. Here we use techniques based on the pole condition instead. This makes it possible to treat problems without an explicitly known fundamental solution
Active speech source localization by a dual coarsetofine search
 in Proceedings IEEE International Conference on Acoustics, Speech, and Signal Processing
, 2001
"... Accurate and fast localization of multiple speech sound sources is asigni¿cant problem in videoconferencing systems. Based on the observation that the wavelengths of the sound from a speech source are comparable to the dimensions of the space being searched, and that the source is broadband, we deve ..."
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Cited by 23 (4 self)
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Accurate and fast localization of multiple speech sound sources is asigni¿cant problem in videoconferencing systems. Based on the observation that the wavelengths of the sound from a speech source are comparable to the dimensions of the space being searched, and that the source is broadband, we develop an ef¿cient search strategy that ¿nds the source(s) in a given space. The search is made ef¿cient by using coarseto¿ne strategies in both space and frequency. The algorithm is shown to be robust compared to typical delaybased estimators and fast enough for realtime implementation. Its performance can further be improved by using constraints from computer vision. 1.
Shape deformations in rough surface scattering: Cancellations, conditioning, and convergence
 J. Opt. Soc. Am. A
, 2004
"... We analyze the conditioning properties of classical shapeperturbation methods for the prediction of scattering returns from rough surfaces. A central observation relates to the identification of significant cancellations that are present in the recurrence relations satisfied by successive terms in ..."
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Cited by 23 (16 self)
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We analyze the conditioning properties of classical shapeperturbation methods for the prediction of scattering returns from rough surfaces. A central observation relates to the identification of significant cancellations that are present in the recurrence relations satisfied by successive terms in a perturbation series. We show that these cancellations are precisely responsible for the observed performance of shapedeformation methods, which typically deteriorates with decreasing regularity of the scattering surfaces. We further demonstrate that the cancellations preclude a straightforward recursive estimation of the size of the terms in the perturbation series, which, in turn, has historically prevented the derivation of a direct proof of its convergence. On the other hand, we also show that such a direct proof can be attained if a simple change of independent variables is effected in advance of the derivation of the perturbation series. Finally, we show that the relevance of these observations goes beyond the theoretical, as we explain how they provide definite guiding principles for the design of new, stabilized implementations of methods based on shape deformations. © 2004 Optical