Inverse Problems Course Notes

Here is an index to the course notes I have taken for Gunther Uhlmann’s Inverse Problems class in the Math Department at the University of Washington, Autumn 2009.  In the early notes, I tried to stay faithful to exactly what I heard in the lecture.  Later on, I add quite a bit of my own commentary — mostly  because it helps me learn the material.  Comments and corrections are welcome!

  1. Introduction and Overview
  2. The Radon Transform and its Inversion Formula
  3. Radon Inversion
  4. Extending the Domain of R to Distributions
  5. Sobolev Spaces
  6. Stability of Radon Inversion
  7. More About Stability
  8. The Range of the Radon Transform
  9. Motivating the Range Characterization of the Radon Transform
  10. A Proof of the Helgason-Ludwig Characterization of R‘s Range
  11. The Support Theorem for the Radon Transform
  12. The Paley-Wiener Theorem
  13. The X-Ray Transform
  14. An Alternative Development of the X-Ray Transform
  15. The X-Ray Transform for Distributions
  16. Stability Estimates for the X-Ray Transform
  17. The Range of the X-Ray Transform, John’s Equations
  18. There is more to come…
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5 thoughts on “Inverse Problems Course Notes

  1. Pingback: Inverse Problems Course Notes — Introduction and Overview « Rolfe's Lecture Notes

  2. Pingback: Inverse Problems Course Notes — An Alternative Development of the X-Ray Transform « Rolfe's Lecture Notes

  3. Pingback: Inverse Problems Course Notes — The X-Ray Transform for Distributions « Rolfe's Lecture Notes

  4. Pingback: Inverse Problems Course Notes — The Range of the X-Ray Transform « Rolfe's Lecture Notes

  5. Pingback: Inverse Problems Course Notes — Numerical Methods for X-Ray Transform Reconstruction « Rolfe's Lecture Notes

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