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| The talk discusses a generalized Radon transform that appears in ultrasound reflection tomography. In our model, the ultrasound emitter and receiver move along a circle with a fixed distance between them. The measured data corresponds to the integrals of the unknown image function along ellipses with foci at the emitter and receiver locations.
We analyze the microlocal properties of the transform $R$ that arises from this model. As a consequence, we show that, for distributions with support contained in a disc $D_b$ sufficiently inside the circle, $R^*R$ is an elliptic pseudo-differential operator. We provide a local filtered back projection algorithm $L =R^*DR$, where $D$ is a well-chosen differential operator. Finally, we discuss an extension with some modifications of our result outside of $D_b$. |
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