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

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, $R^{\ast }R$ is an elliptic pseudodifferential operator of order $-1$ and hence all the singularities of such distributions can be recovered.