2015/07/22 by Sunghwan Moon, Moon, Sunghwan, Joonghyeok Heo +1
Earth and Planetary Sciences · Engineering · Computer Science · #Seismic Imaging and Inversion Techniques #Geophysical Methods and Applications #Image and Object Detection Techniques
paper · pdf · doi:10.48550/arxiv.1507.06031
In recent years, many types of elliptical Radon transforms that integrate functions over various sets of ellipses/ellipsoids have been considered, relating to studies in bistatic synthetic aperture radar, ultrasound reflection tomography, radio tomography, and migration imaging. In this article, we consider the transform that integrates a given function in \mathbf Rn over a set of ellipses (when n=2) or ellipsoids of rotation (when n≥ 3) with foci restricted to a hyperplane. We show a relation between this elliptical Radon transform and the regular Radon transform, and provide the inversion formula for the elliptical Radon transform using this relation. Numerical simulations are performed to demonstrate the suggested algorithms in two dimensions, and these simulations are also provided in this article.