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

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

2011-10-19

arxiv.org/abs/1110.4339v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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