Applied Math Seminar: X-ray transforms and applications
Speaker: Francois Monard (University of California Santa Cruz)
Abstract: In integral geometry, X-ray transforms are examples of linear and non-linear operators which encode families of integrals of a given (geometric) quantity along distinguished families of curves. The problem of recovering a quantity from its X-ray transform naturally appears in several applied fields such as medical imaging (X-ray CT), seismology (linearized travel-time tomography, tensor tomography) and the imaging of magnetic fields in materials (Polarimetric Neutron Tomography).
Depending on the problem and the underlying geometry of propagation, the transform considered can be inverted with varying degrees of explicitness, by means of either explicit formulas, or statistical tools (e.g. Markov Chain Monte Carlo). The validity of these inversions (or lack thereof, in 'bad' cases) is typically captured using analytic toolboxes such as PDE methods, microlocal analysis, and mathematical statistics.
In this talk, we will discuss some examples of X-ray transforms, their applications, as well as recent progress on these topics by the author and his collaborators.
Thursday, May 13 at 3:30pm to 4:30pm