论文信息 - The scattering support

The scattering support

We discuss inverse problems for the Helmholtz equation at fixed energy, specifically the inverse source problem and the inverse scattering problem from a medium or an obstacle. We introduce the convex scattering support of a far field, a set which will be a subset of the convex hull of the support of any source which can produce it. We give several theorems which explain how to compute the convex scattering support and how to relate it to the actual support of a source, medium, or obstacle. © 2003 Wiley Periodicals, Inc.

Steven Kusiak | John Sylvester | J. Sylvester | S. Kusiak

[1] Peter Monk,et al. Recent Developments in Inverse Acoustic Scattering Theory , 2000, SIAM Rev..

[2] L. Hörmander. Analysis of Linear Partial Differential Operators II , 2005 .

[3] Masaru Ikehata,et al. Enclosing a polygonal cavity in a two-dimensional bounded domain from Cauchy data , 1999 .

[4] L. Hörmander. The analysis of linear partial differential operators , 1990 .

[5] Andreas Kirsch,et al. Factorization of the far-field operator for the inhomogeneous medium case and an application in inverse scattering theory , 1999 .

[6] Roland Potthast,et al. The No Response Test---A Sampling Method for Inverse Scattering Problems , 2003, SIAM J. Appl. Math..

[7] Brian Davies,et al. Partial Differential Equations II , 2002 .

[8] L. Hörmander,et al. The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis , 1983 .

[9] Michael E. Taylor,et al. Partial Differential Equations II: Qualitative Studies of Linear Equations , 1996 .

[10] R. Kress,et al. Inverse Acoustic and Electromagnetic Scattering Theory , 1992 .

[11] Roland Potthast,et al. A 'range test' for determining scatterers with unknown physical properties , 2003 .

[12] L. Hörmander,et al. The Analysis of Linear Partial Differential Operators II: Differential Operators with Constant Coefficients , 1983 .