Inverse medium scattering for the Helmholtz equation at fixed frequency Export

@article{citeulike:324645, abstract = {Consider a time-harmonic electromagnetic plane wave incident on a medium enclosed by a bounded domain in \bb{R}^2 . In this paper, existence and uniqueness of the variational problem for the direct scattering are established. An energy estimate for the scattered field is obtained on which the Born approximation is based. The Frechet differentiability of the scattering map is examined. A new continuation method for the inverse medium scattering, which reconstructs the scatterer of an inhomogeneous medium from the boundary measurements of the scattered waves, is developed. The algorithm requires only single-frequency scattering data. Using an initial guess from the Born approximation, each update is obtained via recursive linearization on the spatial frequency of a one-parameter family of plane waves by solving one forward and one adjoint problem of the Helmholtz equation.}, author = {Bao, Gang and Li, Peijun}, citeulike-article-id = {324645}, citeulike-linkout-0 = {http://dx.doi.org/10.1088/0266-5611/21/5/007}, citeulike-linkout-1 = {http://www.ingentaconnect.com/content/iop/ip/2005/00000021/00000005/art00007}, citeulike-linkout-2 = {http://stacks.iop.org/0266-5611/21/1621}, doi = {10.1088/0266-5611/21/5/007}, issn = {0266-5611}, journal = {Inverse Problems}, keywords = {helmholtz, near-field}, month = {October}, number = {5}, pages = {1621--1641}, posted-at = {2006-06-19 04:29:31}, priority = {2}, publisher = {Institute of Physics Publishing}, title = {Inverse medium scattering for the Helmholtz equation at fixed frequency}, url = {http://dx.doi.org/10.1088/0266-5611/21/5/007}, volume = {21}, year = {2005} }

TY - JOUR ID - citeulike:324645 L3 - citeulike-article-id:324645 N2 - Consider a time-harmonic electromagnetic plane wave incident on a medium enclosed by a bounded domain in \bb{R}^2 . In this paper, existence and uniqueness of the variational problem for the direct scattering are established. An energy estimate for the scattered field is obtained on which the Born approximation is based. The Frechet differentiability of the scattering map is examined. A new continuation method for the inverse medium scattering, which reconstructs the scatterer of an inhomogeneous medium from the boundary measurements of the scattered waves, is developed. The algorithm requires only single-frequency scattering data. Using an initial guess from the Born approximation, each update is obtained via recursive linearization on the spatial frequency of a one-parameter family of plane waves by solving one forward and one adjoint problem of the Helmholtz equation. IS - 5 JF - Inverse Problems SN - 0266-5611 EP - 1641 TI - Inverse medium scattering for the Helmholtz equation at fixed frequency PB - Institute of Physics Publishing VL - 21 SP - 1621 KW - helmholtz KW - near-field AU - Bao, Gang AU - Li, Peijun PY - 2005/10// UR - http://dx.doi.org/10.1088/0266-5611/21/5/007 ER -