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The Factorization Method for Inverse Problems

Andreas Kirsch and Natalia Grinberg

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199213535
eISBN:
9780191707629
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213535.001.0001
Subject:
Mathematics, Applied Mathematics

This book is devoted to problems of shape identification in the context of (inverse) scattering problems and problems of impedance tomography. In contrast to traditional methods which are based on ... More


The mixed boundary value problem

Andreas Kirsch and Natalia Grinberg

in The Factorization Method for Inverse Problems

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199213535
eISBN:
9780191707629
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213535.003.0003
Subject:
Mathematics, Applied Mathematics

For the mixed boundary value problem, the scattering domain D consists of several components with different types of boundary conditions. The chapter begins by reviewing results on uniqueness and ... More


The MUSIC algorithm and scattering by an inhomogeneous medium

Andreas Kirsch and Natalia Grinberg

in The Factorization Method for Inverse Problems

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199213535
eISBN:
9780191707629
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213535.003.0004
Subject:
Mathematics, Applied Mathematics

This chapter examines the case of a penetrable scatterer with an index of refraction that can be space-dependent and is assumed to be different from the constant background index. The inverse ... More


The simplest cases: Dirichlet and Neumann boundary conditions

Andreas Kirsch and Natalia Grinberg

in The Factorization Method for Inverse Problems

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199213535
eISBN:
9780191707629
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213535.003.0001
Subject:
Mathematics, Applied Mathematics

After a short derivation of the Helmholtz equation in acoustics this chapter formulates the direct scattering problem and presents results on uniqueness and existence without proofs (but gives ... More


The factorization method for other types of inverse obstacle scattering problems

Andreas Kirsch and Natalia Grinberg

in The Factorization Method for Inverse Problems

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199213535
eISBN:
9780191707629
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213535.003.0002
Subject:
Mathematics, Applied Mathematics

This chapter studies some examples of inverse scattering problems in which the data operator fails to be normal. The impedance boundary condition, the reconstruction from limited-angle data, and the ... More


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