Inverse obstacle scattering in two dimensions with multiple frequency data and multiple angles of incidence

Carlos Borges, Leslie Greengard

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)280-298
Number of pages19
JournalSIAM Journal on Imaging Sciences
Volume8
Issue number1
DOIs
StatePublished - Jan 27 2015

Fingerprint

Newton-Raphson method
Incidence
Two Dimensions
Scattering
Forward scattering
Angle
Newton Methods
Inverse problems
Linearization
Integral equations
Far-field Pattern
Unknown
Forward Problem
Ill-posedness
Higher order equation
Inverse Scattering Problem
Penalty Method
Tikhonov Regularization
Acoustic waves
Scattering Problems

Keywords

  • Acoustics
  • Inverse scattering
  • Newton’s method
  • Recursive linearization
  • Regularization

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)

Cite this

Inverse obstacle scattering in two dimensions with multiple frequency data and multiple angles of incidence. / Borges, Carlos; Greengard, Leslie.

In: SIAM Journal on Imaging Sciences, Vol. 8, No. 1, 27.01.2015, p. 280-298.

Research output: Contribution to journalArticle

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