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We introduce a dispersive point target model based on scattering by a particle in the far-field. The synthetic aperture imaging problem is then expanded to identify these targets and recover their locations and frequency dependent reflectivities. We show that Kirchhoff migration (KM) is able to identify dispersive point targets in an imaging region. However, KM predicts target locations that are shifted in range from their true locations. We derive an estimate for this range shift for a single target. We also show that because of this range shift we cannot recover the complex-valued frequency dependent reflectivity, but we can recover its absolute value and hence the radar cross-section (RCS) of the target. Simulation results show that we can detect, recover the approximate location, and recover the RCS for dispersive point targets thereby opening opportunities to classifying important differences between multiple targets such as their sizes or material compositions.
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Quantitative signal subspace imaging
Abstract We develop and analyze a quantitative signal subspace imaging method for single-frequency array imaging. This method is an extension to multiple signal classification which uses (i) the noise subspace to determine the location and support of targets, and (ii) the signal subspace to recover quantitative information about the targets. For point targets, we are able to recover the complex reflectivity and for an extended target under the Born approximation, we are able to recover a scalar quantity that is related to the product of the volume and relative dielectric permittivity of the target. Our resolution analysis for a point target demonstrates this method is capable of achieving exact recovery of the complex reflectivity at subwavelength resolution. Additionally, this resolution analysis shows that noise in the data effectively acts as a regularization to the imaging functional resulting in a method that is surprisingly more robust and effective with noise than without noise.
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- Award ID(s):
- 1840265
- PAR ID:
- 10302824
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Inverse Problems
- Volume:
- 37
- Issue:
- 12
- ISSN:
- 0266-5611
- Page Range / eLocation ID:
- Article No. 125006
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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