2011/10/19 by Gaik Ambartsoumian, Ambartsoumian, Gaik, Venky Krishnan +3 · 1 citation
Mathematics · Computer Science · #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #Image and Signal Denoising Methods
paper · pdf · doi:10.48550/arxiv.1110.4339
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.