Is a curved flight path in SAR better than a straight one?

TL;DR

This paper investigates the effectiveness of curved versus straight flight paths in SAR and related imaging modalities, analyzing wave front set recovery and artifact resolution under different geometric conditions.

Contribution

It provides new insights into wave front set recovery from circular integrals, especially highlighting the benefits of known singularity locations and the use of backpropagation.

Findings

Artifacts cannot be resolved when singularities hit the curve once.

Recovery of wave front set is possible if singularities are in a known compact set.

Explicit recovery method using backpropagation is proposed.

Abstract

In the plane, we study the transform $R_\gamma f$ of integrating a unknown function $f$ over circles centered at a given curve $\gamma$. This is a simplified model of SAR, when the radar is not directed but has other applications, like thermoacoustic tomography, for example. We study the problem of recovering the wave front set $\WF(f)$. If the visible singularities of $f$ hit $\gamma$ once, we show that the "artifacts" cannot be resolved. If $\gamma$ is a closed curve, we show that this is still true. On the other hand, if $f$ is known a priori to have singularities in a compact set, then we show that one can recover $\WF(f)$, and moreover, this can be done in a simple explicit way, using backpropagation for the wave equation.