276 research outputs found
On the robustness of inverse scattering for penetrable, homogeneous objects with complicated boundary
The acoustic inverse obstacle scattering problem consists of determining the
shape of a domain from measurements of the scattered far field due to some set
of incident fields (probes). For a penetrable object with known sound speed,
this can be accomplished by treating the boundary alone as an unknown curve.
Alternatively, one can treat the entire object as unknown and use a more
general volumetric representation, without making use of the known sound speed.
Both lead to strongly nonlinear and nonconvex optimization problems for which
recursive linearization provides a useful framework for numerical analysis.
After extending our shape optimization approach developed earlier for
impenetrable bodies, we carry out a systematic study of both methods and
compare their performance on a variety of examples. Our findings indicate that
the volumetric approach is more robust, even though the number of degrees of
freedom is significantly larger. We conclude with a discussion of this
phenomenon and potential directions for further research.Comment: 24 pages, 9 figure
Multipolar Acoustic Source Reconstruction from Sparse Far-Field Data using ALOHA
The reconstruction of multipolar acoustic or electromagnetic sources from
their far-field signature plays a crucial role in numerous applications. Most
of the existing techniques require dense multi-frequency data at the Nyquist
sampling rate. The availability of a sub-sampled grid contributes to the null
space of the inverse source-to-data operator, which causes significant imaging
artifacts. For this purpose, additional knowledge about the source or
regularization is required. In this letter, we propose a novel two-stage
strategy for multipolar source reconstruction from sub-sampled sparse data that
takes advantage of the sparsity of the sources in the physical domain. The data
at the Nyquist sampling rate is recovered from sub-sampled data and then a
conventional inversion algorithm is used to reconstruct sources. The data
recovery problem is linked to a spectrum recovery problem for the signal with
the \textit{finite rate of innovations} (FIR) that is solved using an
annihilating filter-based structured Hankel matrix completion approach (ALOHA).
For an accurate reconstruction, a Fourier inversion algorithm is used. The
suitability of the approach is supported by experiments.Comment: 11 pages, 2 figure
Detection of Buried Inhomogeneous Elliptic Cylinders by a Memetic Algorithm
The application of a global optimization procedure to the detection of buried inhomogeneities is studied in the present paper. The object inhomogeneities are schematized as multilayer infinite dielectric cylinders with elliptic cross sections. An efficient recursive analytical procedure is used for the forward scattering computation. A functional is constructed in which the field is expressed in series solution of Mathieu functions. Starting by the input scattered data, the iterative minimization of the functional is performed by a new optimization method called memetic algorithm. (c) 2003 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works
Stable determination of a scattered wave from its far-field pattern: the high frequency asymptotics
We deal with the stability issue for the determination of outgoing
time-harmonic acoustic waves from their far-field patterns. We are especially
interested in keeping as explicit as possible the dependence of our stability
estimates on the wavenumber of the corresponding Helmholtz equation and in
understanding the high wavenumber, that is frequency, asymptotics.
Applications include stability results for the determination from far-field
data of solutions of direct scattering problems with sound-soft obstacles and
an instability analysis for the corresponding inverse obstacle problem.
The key tool consists of establishing precise estimates on the behavior of
Hankel functions with large argument or order.Comment: 49 page
Inverse source problem of the biharmonic equation from multi-frequency phaseless data
This work deals with an inverse source problem for the biharmonic wave
equation. A two-stage numerical method is proposed to identify the unknown
source from the multi-frequency phaseless data. In the first stage, we
introduce some artificially auxiliary point sources to the inverse source
system and establish a phase retrieval formula. Theoretically, we point out
that the phase can be uniquely determined and estimate the stability of this
phase retrieval approach. Once the phase information is retrieved, the Fourier
method is adopted to reconstruct the source function from the phased
multi-frequency data. The proposed method is easy-to-implement and there is no
forward solver involved in the reconstruction. Numerical experiments are
conducted to verify the performance of the proposed method.Comment: 22 pages, 3 figures, 5 table
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