The point source method for inverse scattering in the time domain

Section: Introductionmentioning

confidence: 99%

Solving an inverse obstacle problem for the wave equation by using the boundary control method

Oksanen

2013

“…There are only a few works on qualitative methods using multiple frequency data. In [23], Luke and Potthast established conditions on the time-dependent waves that provided a correspondence between time-domain and frequency -domain inverse scattering via Fourier transforms. Then they applied the result to extend the point source method to scattering from the pulses.…”

Section: Introductionmentioning

confidence: 99%

An eigenvalue method using multiple frequency data for inverse scattering problems

Sun

2012

Dirichlet and transmission eigenvalues have important applications in qualitative methods in inverse scattering. Motivated by the fact that these eigenvalues can be obtained from scattering data, we propose a new eigenvalue method using multiple frequency data (EM 2 F). The method detects eigenvalues and builds indicator functions to reconstruct the support of the target. Numerical reconstruction is quite satisfactory. Dirichlet or transmission eigenvalues are estimated. Furthermore, reconstruction of D and estimation of eigenvalues can be combined together to distinguish between the sound-soft obstacle and nonabsorbing inhomogeneous medium.

“…In this chapter, we describe how to use the frequency-domain filter function g (α) ,x (•, k), k 0 to construct time-domain field splitting. The time-domain point source method has first been used in [8].…”

Section: Source Splitting For Time-domain Measurementsmentioning

confidence: 99%

“…Here, we will present a new and different approach based on the point source method introduced in 1996 for field reconstruction in acoustics, compare [12][13][14] or [2,8] for the time-domain case. The basic idea is to explicitly construct a filter for the reconstruction or particular sound components for each source region in space.…”

Section: Introductionmentioning

confidence: 99%

Source splitting via the point source method

Potthast¹,

Fazi²,

Nelson³

2010

Self Cite

We introduce a new algorithm for source identification and field splitting based on the point source method (Potthast 1998 A point-source method for inverse acoustic and electromagnetic obstacle scattering problems IMA J. Appl. Math. 61 119-40, Potthast R 1996 A fast new method to solve inverse scattering problems Inverse Problems 12 731-42). The task is to separate the sound fields u j , j = 1, . . . , n of n ∈ N sound sources supported in different bounded domains G 1 , . . . , G n in R 3 from measurements of the field on some microphone array-mathematically speaking from the knowledge of the sum of the fieldson some open subset of a plane. The main idea of the scheme is to calculate filter functions g 1 , . . . , g n , n ∈ N, to construct u for = 1, . . . , n from u| in the form u (x) = g ,x (y)u(y) ds(y), = 1, . . . , n.(1)We will provide the complete mathematical theory for the field splitting via the point source method. In particular, we describe uniqueness, solvability of the problem and convergence and stability of the algorithm. In the second part we describe the practical realization of the splitting for real data measurements carried out at the Institute for Sound and Vibration Research at Southampton, UK. A practical demonstration of the original recording and the splitting results for real data is available online.