A class of singular Fourier integral operators in synthetic aperture radar imaging

TL;DR

This paper investigates the microlocal properties of the forward scattering operator in synthetic aperture radar imaging, revealing how artifacts arise and can be explained through a decomposition into specific classes of Fourier integral operators.

Contribution

It introduces a novel analysis of the normal operator in SAR imaging, decomposing it into a sum of operators associated with intersecting Lagrangians to explain imaging artifacts.

Findings

Decomposition of the normal operator into four Fourier integral operators.

Explanation of artifacts as arising from intersecting Lagrangian distributions.

Enhanced understanding of the microlocal structure of SAR imaging operators.

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, $I^{p,l} (\Lambda_0, \Lambda_1)$, thereby explaining the latter artifacts.