A class of singular Fourier integral operators in Synthetic Aperture Radar imaging

Abstract

In this article, we analyze the microlocal properties of the linearized forward scattering operator F and the normal operator F * F (where F * is the L 2 adjoint of F ) which arises in Synthetic Aperture Radar imaging for the common midpoint acquisition geometry. When F * is applied to the scattered data, artifacts appear. We show that F * F can be decomposed as a sum of four operators, each belonging to a class of distributions associated to two cleanly intersecting Lagrangians, I p,l (Λ 0 , Λ 1 ), thereby explaining the latter artifacts.

Microlocal Analysis in Tomography

“…'/; a!. '/dx and this is exactly .x; dx/, and there is no other vector in T .R 2 / associated with 1 . In a similar way, one shows that the only vector in T .R 2 / associated with 2 is .x; dx/.…”

“…A detailed microlocal analysis of the forward operator (58) associated to T and R and the imaging operator P P was done in [1]. In contrast to the results in [19,54,70], here the canonical relation C associated to P is a 4-1 relation, and this is reflected in the fact the canonical left and right projections L and R drop rank on a union of two disjoint sets.…”

Microlocal analysis of Doppler synthetic aperture radar

“…In particular, in applications to inverse problems via the study of linearized forward maps, the singularities of π L and π R determine whether reconstruction via filtered backprojection (modulo smooth errors) is possible, and allows the characterization of artifacts cf. [15,16,25,26,9,11,13,1,10,27,12,2].…”

Singular FIOs in SAR Imaging, II: Transmitter and Receiver at Different Speeds

“…We study the normal operator F * F and the artifacts which appear by using this method. The current article is a continuation of our prior work [2], where, motivated by certain multiple scattering scenarios, we considered the case when the transmitter and receiver move at equal speeds away from a common midpoint along a straight line. The main result of that article made precise the added singularities and their strengths (in comparison to the true singularities) when reconstruction is done using the backprojection method mentioned above.…”

“…The microlocal analysis of linearized SAR imaging operators (both monostatic and bistatic) was done in [30,40,10,2,36]. Bistatic SAR imaging problems, due to the fact that the transmitter and receiver are spatially separated, naturally lead to the study of elliptical Radon transforms, which are also of independent interest.…”