2004
DOI: 10.1007/s00041-004-8008-0
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Microlocal Analysis of Synthetic Aperture Radar Imaging

Abstract: We consider Synthetic Aperture Radar (SAR) in which backscattered waves are measured from locations along a single flight path of an aircraft. Emphasis is on the case where it is not possible to form a beam with the radar. The article uses a scalar linearized mathematical model of scattering, based on the wave equation. This leads to a forward (scattering) operator, which maps singularities in the coefficient of the wave equation (viewed as a singular perturbation about a constant coefficient) to singularities… Show more

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Cited by 52 publications
(77 citation statements)
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“…We expected to have to make one-sided location assumption because in the case of the static radar this was a necessary assumption too [14].…”
Section: Proof Of Theorem 35mentioning
confidence: 99%
“…We expected to have to make one-sided location assumption because in the case of the static radar this was a necessary assumption too [14].…”
Section: Proof Of Theorem 35mentioning
confidence: 99%
“…Microlocal analysis can be used to understand what singularities are "visible" in limited data problems in X-ray tomography [58,15] and radar [56]. Singularity detection algorithms have been developed for the region of interest problem in planar X-ray CT [12,65] cone beam CT (e.g., [50,66]), as well as other modalities (e.g., [59]).…”
Section: Tomographymentioning
confidence: 99%
“…The model in single photon emission tomography [52] involves a Radon line transform with a measure that is not group invariant. Models in radar [56], sonar, and thermoacoustic tomography [1] involve circular, elliptical, or spherical mean transforms and their generalizations, and researchers use harmonic and microlocal analysis, PDEs, and group theory to develop reconstructions methods and properties. There is much elegant mathematics in these areas, but the details are beyond the scope of this review.…”
Section: Tomographymentioning
confidence: 99%
“…The antenna emits pulses of electromagnetic radiation, which scatter off the terrain and the scattered waves are detected with the same antenna. The received signals are then used to produce an image of the terrain (see [1], [5], [6], [7]). …”
Section: Introductionmentioning
confidence: 99%
“…Such operators map singular distributions to other singular distributions and the relationship between the input and the output singularities forms what is called a canonical relation. Canonical relations associated to FIOs are Lagrangian manifolds and have a rich geometric structure (see [3], [2], [7]). The authors study this in detail for the case when the antenna is flying perpendicularly to a perfectly reflective vertical wall.…”
Section: Introductionmentioning
confidence: 99%