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Inverse Obstacle Problem: Local Uniqueness for Rougher Obstacles and the
, 1995
"... In this paper, we study the determination of the shape of an obstacle with rough boundary (not necessary Lipschitz) from its scattering amplitude. Following the technique used in paper [6], we obtain an extension of the local uniqueness result for Lipschitz obstacles to rougher ones. We also give a ..."
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In this paper, we study the determination of the shape of an obstacle with rough boundary (not necessary Lipschitz) from its scattering amplitude. Following the technique used in paper [6], we obtain an extension of the local uniqueness result for Lipschitz obstacles to rougher ones. We also give a
LevenbergMarquardt Level Set Methods for Inverse Obstacle Problems
 Inverse Problems
, 2003
"... The aim of this paper is to construct LevenbergMarquardt level set methods for inverse obstacle problems, and to discuss their numerical realization. Based on a recently developed framework for the construction of level set methods, we can define LevenbergMarquardt level set methods in a general ..."
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Cited by 45 (1 self)
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The aim of this paper is to construct LevenbergMarquardt level set methods for inverse obstacle problems, and to discuss their numerical realization. Based on a recently developed framework for the construction of level set methods, we can define LevenbergMarquardt level set methods in a
Shape optimization methods for the Inverse Obstacle Problem with generalized impedance boundary conditions
, 2013
"... We aim to reconstruct an inclusion ω immersed in a perfect fluid flowing in a larger bounded domain Ω via boundary measurements on ∂Ω. The obstacle ω is assumed to have a thin layer and is then modeled using generalized boundary conditions (precisely Ventcel boundary conditions). We first obtain an ..."
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Cited by 1 (1 self)
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the existence of the shape derivatives with respect to the domain ω and characterize the gradient of this cost functional in order to make a numerical resolution. We also characterize the shape Hessian and prove that this inverse obstacle problem is unstable in the following sense: the functional is degenerated
THE “EXTERIOR APPROACH ” TO SOLVE THE INVERSE OBSTACLE PROBLEM FOR THE STOKES SYSTEM
"... Abstract. We apply an “exterior approach ” based on the coupling of a method of quasireversibility and of a level set method in order to recover a fixed obstacle immersed in a Stokes flow from boundary measurements. Concerning the method of quasireversibility, two new mixed formulations are intro ..."
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Cited by 1 (0 self)
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Abstract. We apply an “exterior approach ” based on the coupling of a method of quasireversibility and of a level set method in order to recover a fixed obstacle immersed in a Stokes flow from boundary measurements. Concerning the method of quasireversibility, two new mixed formulations
Inverse obstacle problem for the nonstationary wave equation with an unknown background
, 2011
"... Abstract. We consider boundary measurements for the wave equation on a bounded domain M ⊂ R2 or on a compact Riemannian surface, and introduce a method to locate a discontinuity in the wave speed. Assuming that the wave speed consist of an inclusion in a known smooth background, the method can dete ..."
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Cited by 4 (1 self)
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Abstract. We consider boundary measurements for the wave equation on a bounded domain M ⊂ R2 or on a compact Riemannian surface, and introduce a method to locate a discontinuity in the wave speed. Assuming that the wave speed consist of an inclusion in a known smooth background, the method can determine the distance from any boundary point to the inclusion. In the case of a known constant background wave speed, the method reconstructs a set contained in the convex hull of the inclusion and containing the inclusion. Even if the background wave speed is unknown, the method can reconstruct the distance from each boundary point to the inclusion assuming that the Riemannian metric tensor determined by the wave speed gives simple geometry in M. The method is based on reconstruction of volumes of domains of influence by solving a sequence of linear equations. For τ ∈ C(∂M) the domain of influence M(τ) is the set of those points on the manifold from which the distance to some boundary point x is less than τ(x).
SOLVING AN INVERSE OBSTACLE PROBLEM FOR THE WAVE EQUATION BY USING THE BOUNDARY CONTROL METHOD
"... Abstract. We introduced in [17] a method to locate discontinuities of a wave speed in dimension two from acoustic boundary measuments modelled by the hyperbolic NeumanntoDirichlet operator. Here we extend the method for sound hard obstacles in arbitrary dimension. We present numerical experiment ..."
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Abstract. We introduced in [17] a method to locate discontinuities of a wave speed in dimension two from acoustic boundary measuments modelled by the hyperbolic NeumanntoDirichlet operator. Here we extend the method for sound hard obstacles in arbitrary dimension. We present numerical
Integral Equation Methods for the Inverse Obstacle Problem with Generalized Impedance Boundary Condition
"... Abstract. Determining the shape of an inclusion within a conducting medium from voltage and current measurements on the accessible boundary of the medium can be modeled as an inverse boundary value problem for the Laplace equation. We present a solution method for such an inverse boundary value prob ..."
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Cited by 4 (0 self)
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Abstract. Determining the shape of an inclusion within a conducting medium from voltage and current measurements on the accessible boundary of the medium can be modeled as an inverse boundary value problem for the Laplace equation. We present a solution method for such an inverse boundary value
Inverse Acoustic and Electromagnetic Scattering Theory, Second Edition
, 1998
"... Abstract. This paper is a survey of the inverse scattering problem for timeharmonic acoustic and electromagnetic waves at fixed frequency. We begin by a discussion of “weak scattering ” and Newtontype methods for solving the inverse scattering problem for acoustic waves, including a brief discussi ..."
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Cited by 1072 (45 self)
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discussion of Tikhonov’s method for the numerical solution of illposed problems. We then proceed to prove a uniqueness theorem for the inverse obstacle problems for acoustic waves and the linear sampling method for reconstructing the shape of a scattering obstacle from far field data. Included in our
The Vector Field Histogram  Fast Obstacle Avoidance For Mobile Robots
 IEEE JOURNAL OF ROBOTICS AND AUTOMATION
, 1991
"... A new realtime obstacle avoidance method for mobile robots has been developed and implemented. This method, named the vector field histogram(VFH), permits the detection of unknown obstacles and avoids collisions while simultaneously steering the mobile robot toward the target. The VFH method uses a ..."
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Cited by 470 (23 self)
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A new realtime obstacle avoidance method for mobile robots has been developed and implemented. This method, named the vector field histogram(VFH), permits the detection of unknown obstacles and avoids collisions while simultaneously steering the mobile robot toward the target. The VFH method uses
Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems
 IEEE Journal of Selected Topics in Signal Processing
, 2007
"... Abstract—Many problems in signal processing and statistical inference involve finding sparse solutions to underdetermined, or illconditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared ℓ2) error term combined wi ..."
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Cited by 524 (15 self)
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Abstract—Many problems in signal processing and statistical inference involve finding sparse solutions to underdetermined, or illconditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared ℓ2) error term combined
Results 1  10
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