417 research outputs found
Multi-frequency imaging of perfectly conducting cracks via boundary measurements
Imaging of perfectly conducting crack(s) in a 2-D homogeneous medium using
boundary data is studied. Based on the singular structure of the Multi-Static
Response (MSR) matrix whose elements are normalized by an adequate test
function at several frequencies, an imaging functional is introduced and
analyzed. A non-iterative imaging procedure is proposed. Numerical experiments
from noisy synthetic data show that acceptable images of single and multiple
cracks are obtained.Comment: 4 pages, 3 figure
Fast shape reconstruction of perfectly conducting cracks by using a multi-frequency topological derivative strategy
This paper concerns a fast, one-step iterative technique of imaging extended
perfectly conducting cracks with Dirichlet boundary condition. In order to
reconstruct the shape of cracks from scattered field data measured at the
boundary, we introduce a topological derivative-based electromagnetic imaging
function operated at several nonzero frequencies. The properties of the imaging
function are carefully analyzed for the configurations of both symmetric and
non-symmetric incident field directions. This analysis explains why the
application of incident fields with symmetric direction operated at multiple
frequencies guarantees a successful reconstruction. Various numerical
simulations with noise-corrupted data are conducted to assess the performance,
effectiveness, robustness, and limitations of the proposed technique.Comment: 17 pages, 27 figure
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