Inverse Obstacle Scattering Research Articles

Inverse Obstacle Scattering With Non-overdetermined Data

Inverse Obstacle Scattering With Non-overdetermined Data

Karp's Theorem in Inverse Obstacle Scattering Problems

In this work, we provide a proof of the so-called Karp's theorem in a different approach. We use the unique continuation principle together with the monotonicity of eigenvalues for the negative Laplace operator. This method is new and would be applicable to other types of inverse scattering problems.

Inverse Obstacle Scattering with Non-Over-Determined Scattering Data

Abstract The inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering 𝐴(𝛽;𝛼;𝑘), where 𝐴(𝛽;𝛼;𝑘) is the scattering amplitude, 𝛽;𝛼 𝜖 𝑆² is t...

Inverse Obstacle Scattering in an Unbounded Structure

Inverse Obstacle Scattering in an Unbounded Structure

Numerical Solution of an Inverse Obstacle Scattering Problem for Elastic Waves via the Helmholtz Decomposition

Numerical Solution of an Inverse Obstacle Scattering Problem for Elastic Waves via the Helmholtz Decomposition

Inverse Obstacle Scattering for Elastic Waves with Phased or Phaseless Far-Field Data

This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plan...

Inverse Obstacle Scattering in Two Dimensions with Multiple Frequency Data and Multiple Angles of Incidence

We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from one or more directions and at one or more frequencies. It is well known that this inverse scattering problem is both ill-posed and nonlinear. It is common practice to overcome the ill-posedness through the use of a penalty method or Tikhonov regularization. Here, we present a more physical regularization, based simply on restricting the unknown boundary to be band-limited in a suitable sense. To overcome the nonlinearity of the problem, we use a variant of Newton's method. When multiple frequency data is available, we supplement Newton's method with the recursive linearization approach due to Chen. During the course of solving the inverse problem, we need to compute the solution to a large number of forward scattering problems. For this, we use high-order accurate integral equation discretizations, coupled with fast direct solvers when the problem is sufficiently large.

Single Frequency Inverse Obstacle Scattering: A Sparsity Constrained Linear Sampling Method Approach

The linear sampling method (LSM) offers a qualitative image reconstruction approach, which is known as a viable alternative for obstacle support identification to the well-studied filtered backprojection (FBP), which depends on a linearized forward scattering model. Of practical interest is the imaging of obstacles from sparse aperture far-field data under a fixed single frequency mode of operation. Under this scenario, the Tikhonov regularization typically applied to LSM produces poor images that fail to capture the obstacle boundary. In this paper, we employ an alternative regularization strategy based on constraining the sparsity of the solution's spatial gradient. Two regularization approaches based on the spatial gradient are developed. A numerical comparison to the FBP demonstrates that the new method's ability to account for aspect-dependent scattering permits more accurate reconstruction of concave obstacles, whereas a comparison to Tikhonov-regularized LSM demonstrates that the proposed approach significantly improves obstacle recovery with sparse-aperture data.

Direct and Inverse Obstacle Scattering Problems in a Piecewise Homogeneous Medium

This paper is concerned with the problem of scattering of time-harmonic acoustic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation method, and then used, in conjunction with the representation in a combination of layer potentials of the solution, to prove a priori estimates of solutions on some part of the interface between the layered media. The inverse problem is also considered in this paper. A uniqueness result is obtained for the first time in determining both the penetrable interface and the impenetrable obstacle with its physical property from a knowledge of the far field pattern for incident plane waves. In doing so, an important role is played by the a priori estimates of the solution for the direct problem.

Fast Methods for Three-dimensional Inverse Obstacle Scattering Problems

We study the inverse problem to reconstruct the shape of a three– dimensional sound–soft obstacle from measurements of scattered acoustic waves. To solve the forward problem we use a wavelet based boundary element method and prove 4th order accuracy both for the evaluation of the forward solution operator and its Frechet derivative. Moreover, we discuss the characterization and implementation of the adjoint of the Frechet derivative. For the solution of the inverse problem we use a regularized Newton method. The boundaries are represented by a class of parametrizations, which include non star–shaped domains and which are not uniquely determined by the obstacle. To prevent degeneration of the parametrizations during the Newton iteration, we introduce an additional penalty term. Numerical examples illustrate the performance of our method.

A Numerical Algorithm for Solving 2D Inverse Obstacle Scattering

Article A Numerical Algorithm for Solving 2D Inverse Obstacle Scattering was published on December 1, 2003 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 4, issue 4).

The Numerical Solution of the Three Dimensional Inverse Obstacle Scattering Problem for Point Source Generated Wave Fields

This work is concerned with the inverse problem to retrieve the shape of a three dimensional obstacle from near-field measurements of the scattering of time-harmonic point source waves. A numerical method for solving the inverse obstacle scattering problem is presented, which is achieved by solving an ill-posed linear system and a well-posed minimization problem independently. Such a separate numerical treatment for the ill-posedness and nonlinearity of the inverse problem makes the numerical implementation of the proposed method very easy and fast since there involves only the solution of a small scale minimization problem with one unknown function in the nonlinear optimization step for reconstructing the shape of the obstacle. Another attractive feature of the scheme is that it needs only the knowledge of the near-field measurements of the scattered fields due to point source incident fields at a finite number of incidence and observation points distributed over a limited aperture. Some numerical examples based on synthetic near-field data are given, showing that this method produces reasonable reconstructions for low wavenumbers even when the incidence and observation aperture is as small as the possible ~ /4 solid angle.

A Numerical Method for Solving the Limited Aperture Problem in Three-Dimensional Inverse Obstacle Scattering

Article A Numerical Method for Solving the Limited Aperture Problem in Three-Dimensional Inverse Obstacle Scattering was published on March 1, 2001 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 2, issue 1).

Proceedings of the 9th Computational Techniques and Applications Conference

This Special Issue of the Journal of the Australian Mathematical Society, Series B (electronic) contains the refereed papers from the Ninth Biennial Computation Techniques and Applications Conference (CTAC99) held at the Australian National University, Canberra, during 20-22 September 1999. This proceedings is dedicated to Professor John Noye of the University of Adelaide as a mark of respect for his endeavours in support of the CTAC series of conferences over the past twenty years. He has been a prime mover not only as an organiser and editor of the proceedings, but also as a prolific contributor. The CTAC series of conferences is held under the auspices of the Computational Mathematics Group of the Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) division of the Australian Mathematics Society. They provide a forum for scientists, engineers, and mathematicians interested in the development of computational techniques and their application to problems of practical importance. Previous conferences in the CTAC series have been held at University of Sydney (1983), University of Melbourne (1985), University of Sydney (1987), Griffith University, Brisbane (1989), University of Adelaide (1991), Australian National University, Canberra (1993), Swinburne University of Technology, Melbourne (1995), University of Adelaide (1997). There were nearly 140 participants at the conference, six of whom gave keynote addresses as part of the general program for CTAC99-these speakers and the titles of their presentations were: Computational Challenges in Data Mining Markus Hegland, Australian National University; Numerical Methods in Inverse Obstacle Scattering Rainer Kress, University of Goettingen, Germany; How Many Matrices Does it Take to Keep a 777 Flying? John Lewis, Boeing Corp., U.S.A.; Computational Biology Terry Speed, University of California, Berkeley & University of Melbourne; Evolutionary Structural Optimisation Grant Steven, University of Sydney; Numerical Problems in Optimisation and Approximation Alistair Watson, University of Dundee, Scotland. CTAC99 also included a Public Lecture, delivered at the Australian Academy of Sciences: High Performance Computing and Trends Jack Dongarra, University of Tennessee & Oak Ridge National Laboratory, U.S.A. In addition to these seven invited presentations, another 100 contributed papers were presented at the conference. Of these 100 papers, 87 were submitted for consideration for the CTAC99 Proceedings, and 71 were accepted for publication after each was peer-reviewed by at least two referees. Following the convention established in previous CTAC proceedings, the papers appearing here have not been grouped by topic; the contributed papers appear in alphabetical order of the first author, preceded by invited papers. As this Proceedings has been dedicated to Professor John Noye, included as an introduction is a brief history of his considerable involvement in the CTAC series of conferences and the bibliography of his contributions - many coauthored with colleagues and students. As with previous CTAC Proceedings, the papers cover a wide variety of topics with the usual CTAC emphasis on both industrial applications and numerical techniques. A new feature is the relatively large number of papers addressing a contemporary field of interest, Data-Mining . This was the topic of one of the four full-day workshops which immediately followed the conference, the others being High Performance Computing, Advances in Differential Equations , and Scientific Visualisation and Virtual Environments . Participation levels in the workshops were substantial with each attacting 30-50 attendees. These workshop themes are reflected in many of the papers included in this Proceedings. The editors would like to thank the referees for their time and assistance with the refereeing process, and the Journal of the Australian Mathematics Society, Series B (electronic) for agreeing to publish the proceedings as a journal special issue. Also, we the (primary) editors wish to acknowledge the additional time and effort put in by the other members of the Editorial Committee: Bob Anderssen, Henry Gardner, Markus Hegland, Mike Osborne, and Steve Roberts. David Harrar II and Thanh Tran Centre for Mathematics and its Applications Australian National University June 2000 CTAC99 Organising Committee Director P ROFESSOR M IKE O SBORNE , Centre for Mathematics and its Applications, ANU Associate Director D R . B OB G INGOLD , ANU Supercomputer Facility, ANU Treasurer D R . S TEVE R OBERTS , School of Mathematical Sciences, ANU Secretary (Organisation) D R . D AVID H ARRAR II, Centre for Mathematics and its Applications, ANU Secretary (Administration) D R . T HANH T RAN , Centre for Mathematics and its Applications, ANU Committee D R . B OB A NDERSSEN , Centre for Mathematics and Information Sciences, CSIRO D R . H ENRY G ARDNER , Research School of Physical Sciences, ANU D R . M ARKUS H EGLAND , ACSys, Computer Sciences Laboratory, ANU D R . L UTZ G ROSZ , Centre for Mathematics and its Applications, ANU

Inverse Obstacle Scattering Using Reduced Data

The classical result of Schiffer in acoustic scattering is that a knowledge of the far field pattern for all observation directions and all incident directions at a fixed wave number k uniquely determines the sound-soft scattering obstacle D. This is widely believed to be far greater information than is required for uniqueness, and more recent results have been obtained that considerably weaken the amount of data needed, provided certain restrictions are placed on the scatterer. Most of this work has concentrated on reducing the number of incident waves required for a unique determination. This paper takes another approach and seeks to determine sufficient information to recover the obstacle from measurements of the far field at isolated points. Our approach will be constructive and some numerical reconstructions will be presented.