Microlocal analysis of an ultrasound transform with circular source and receiver trajectories

TL;DR

This paper analyzes the microlocal properties of a generalized Radon transform in ultrasound reflection tomography with circular source and receiver trajectories, showing that it allows for the recovery of singularities of certain distributions.

Contribution

It provides a microlocal analysis of the ultrasound transform with circular trajectories, demonstrating that the associated operator is elliptic and enables singularity recovery.

Findings

$R^*R$ is an elliptic pseudodifferential operator of order -1

Singularities of distributions inside the circle can be recovered

The analysis advances understanding of ultrasound reflection tomography

Abstract

In this article, we consider a generalized Radon transform that comes up in ultrasound reflection tomography. In our model, the ultrasound emitter and receiver move at a constant distance apart along a circle. We analyze the microlocal properties of the transform $R$ that arises from this model. As a consequence, we show that for distributions with support sufficiently inside the circle, $R^*R$ is an elliptic pseudodifferential operator of order $-1$ and hence all the singularities of such distributions can be recovered.