Matias Courdurier
University of Washington
Date: May 10, 2006
In two and three dimensions a formula to invert the finite Hilbert transform has been used in [1] and [2] to recover the density function in some region by knowledge of the X-Ray transform on a reduced set of lines only. This differs from the traditional inversion formula which requires the X-Ray transform over all the lines. In the class we will discuss the ideas presented in the papers of how to obtain the Hilbert transform from the X-Ray transform data and how to recover the density function by means of an inversion formula of the finite Hilbert transform.