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SUMMARY:Energy methods for the geodesic X-ray transform - Mikko Salo (Univ
 ersity of Jyväskylä)
DTSTART:20170518T140000Z
DTEND:20170518T150000Z
UID:TALK72581@talks.cam.ac.uk
CONTACT:Rachel Furner
DESCRIPTION:The Euclidean X-ray transform\, which encodes the integrals of
  a function over straight lines\, is a classical topic (going back to J. R
 adon in 1917)\nand forms the basis of imaging methods such as X-ray comput
 ed tomography and PET. The geodesic X-ray transform encodes the integrals 
 of a function over more general families of curves\, such as the geodesics
  of a sound speed or Riemannian metric. It arises in seismic imaging and t
 ransmission ultrasound imaging as the linearization of the travel time tom
 ography problem\, in Electrical Impedance Tomography (the Calderon problem
 )\, and in inverse spectral problems.\n\nThere has been considerable recen
 t progress in understanding the mathematical properties of the geodesic X-
 ray transform\, based on several\ndifferent methods. In this talk we will 
 discuss results related to energy methods for the underlying transport PDE
 \, partly based on joint works with G. Paternain (Cambridge) and G. Uhlman
 n (Washington).
LOCATION:MR9 Centre for Mathematical Sciences
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