Publication Cover
Applicable Analysis
An International Journal
Volume 76, 2000 - Issue 3-4
94
Views
38
CrossRef citations to date
0
Altmetric
Original Articles

New characterizations of solutions in inverse scattering theory

Pages 319-350 | Received 01 May 2000, Published online: 10 May 2007

References

  • Albanese , R. , Medina , R.L. and Penn , J.W. 1994 . "Mathematics, Medicine and Microwaves" . Inverse Problems , 10 : 995 – 1007 .
  • Brühl M. Explicit Characterization of Inclusions in Electrical Impedance Tomography SIAM J. Appl. Math, to appear
  • Brühl M. Hanke M. Numerical Implemenation of two Non-lterative Methods for locating Inclusions by Impedance Tomography Inverse Problems, to appear
  • Colton D. Coyle J. Monk P. Recent Developments in inverse Acoustic Scattering Theory SIAM Rev., to appear
  • Colton D. Giebermann K. Monk P. A Regularized Sampling Method for Solving Three Dimensional Inverse Scattering Problems SIAM J. Sci. Comput., to appear
  • Colton , D. and Kirsch , A. 1996 . "A Simple Method for Solving Inverse Scattering Problems in the Resonance Region" . Inverse Problems , 12 : 383 – 393 .
  • Colton and Kress , R. 1983 . “ Integral Equation Methods in Scattering Theory ” . New York : Wiley .
  • Colton , D. and Kress , R. 1998 . “ Inverse Acoustic and Electromagnetic Scattering Theory ” . Springer, New York
  • Colton , D. and Monk , P. 1998 . A Linear Sampling Method for the Detection of Leukenna Using Microwaves . SIAM I Appl Math , 58 : 926 – 941 .
  • Colton , D. and Monk , P. 1999 . “ Mathematical Problems in Microwave Medical Imaging ” . In Computational Radiology and Imaging, Therapy and Diagnostics Edited by: Bergers , C. and Natterer , P. 137 – 156 . Springer Verlag, New York
  • Colton , D. , Monk , P. and Kirsch , A. “ The Linear Sampling Method in Inverse Scattering Theory ” . In Surveys on Solution Methods for Inverse Problems Edited by: Colton , D. , Engl , H.W. , Louis , A. , McLaughlin , J.R. and Rundell , W. Springer, Vienna, New York
  • Colton , D. and Piana , M. 1998 . The Simple Method for Solving the Electromagnetic Inverse Scattering Problem: The Case of TE Polarized Waves . Inverse Problems , 14 : 597 – 614 .
  • Colton , D. , Piana , M. and Potthast , R. 1997 . A Simple Method Using Morozov's Discrepancy Principle for Solving Inverse Scattering Problems . Inverse Problems , 13 : 1447 – 1493 .
  • Costabel , M. and Wendland , W. 1986 . Strong Ellipticity of Boundary Integral Operators . J. Reine Angew. Math , 372 : 34 – 63 .
  • Coté , M.G. 1992 . Automated Swept-Angle Bistatic Scattering Measurements Using Continuous Wave Radar . IEEE Trans. Instrum. Meas , 41 : 185 – 192 .
  • Gerlach , T. and Kress , R. 1996 . Uniqueness in Inverse Obstacle Scattering With Conductive Boundary Condition . Inverse Problems , 12 : 619 – 625 .
  • Gilbarg , D. and Trudinger , N.S. 1977 . Elliptic Partial Differential Equations of Second Order .
  • Kirsch , A. 1996 . An Introduction to the Mathematical Theory of Inverse Problems .
  • Kirsch , A. 1998 . Characterization of the Shape of the Scattering Obstacle by the Spectral Data of the Far Field Operator . Inverse Problem , 14 : 1489 – 1512 .
  • Kirsch , A. 1999 . Factorization of the Far Field Operator for the Inhomogeneous Medium Case And an Application in Inverse Scattering Theory . Inverse Problems , 15 : 413 – 429 .
  • Kirsch , A. and Kress , R. 1993 . Uniqueness in Inverse Obstacle Scattering . Inverse Problems , 9 : 285 – 299 .
  • Kirsch A. Ritter S. A Linear Sampling Method for Inverse Scattering From an Open Arc nverse Problems, to appear
  • Kleinman , R. and Van den Berg , P. 1992 . A Modified Gradient Method for Two Dimensional Problems in Tomography . J Comput. Appl. Math , 42 : 17 – 35 .
  • Kress , R. 1985 . Minimizing the Condition Number of Boundary Integral Operators in Acoustic and Electromagnetic Scattering . Quart. J. Mech. Appl. Math , 38 : 323 – 341 .
  • Langenberg , K.J. , Brandfass , M. , Klaholz , S. , Marklein , R. , Mayer , K. , Pitsch , A. and Schneider , R. 1997 . “ Applied inversion in nondestructive testing ” . In Inverse problems in medical imaging and nondestructive testing Edited by: Louis , A.K. , Engl , H.W. and Rundell , W. Springer, Wien
  • Maierhofer , Ch , Wiggenhauser , II , Brandfass , M. , Pitsch , A. and Langenberg , K.J. 1996 . Localisation of tendon ducts behind reinforcement in concrete using radar in combination with inverse scattering . Proc. 6th Int. Conf. on GPR , : 257 – 260 .
  • Nedelec , J.C. and Planchard , J. 1973 . Une Methode Variationelle d'Elements Finis pour la Resolution Numerique d'un Probleme Exterieur dans R3 . RAIRO R3 , 7 : 105 – 129 .
  • Sun , Z. and Uhlmann , G. 1993 . Recovery of Singularities for Formally Determined Inverse Problems . Comm. Math. Phys , 153 : 431 – 445 .
  • Werner , J. 1984 . Optimization, Theory and Applications , Braunschweig : Vieweg .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.