Thematic Program on Inverse Problems and Imaging
and Short Courses held at the Fields Institute
January 9July 31,2012
All courses will be held at the Fields Institute, Room 230
unless otherwise noted.
January 9 April
|1. Mathematics of Medical Imaging
Instructor: Adrian Nachman, University of Toronto.
Tuesdays and Thursdays 1:30-3:00, Room 230, Fields Institute
Topics to be covered:
i) Magnetic Resonance Imaging: the Bloch Equation.
ii) Introduction to Compressed Sensing.
iii) Inverse boundary value problems: Electric Impedance
iv) Inverse problems with interior data: Current Density
v) Inverse scattering methods: progress on quantitative
vi) Open problems.
|2. Inverse Transport Theory and
Instructor: Alex Tamasan, University of Central Florida
Tuesdays and Thursdays 3:30-5:00, Stewart Library, Fields
Topics to be covered:
i) The transport model through an attenuating and scattering
- The Forward Problem
- The Albedo operator and its kernel
- An inverse boundary value problem.
ii) The non- attenuated and non-scattering case
- The X-ray Transform and the Radon Transform
- Inversion formulae
- The Helgason-Ludwig Range Conditions
- Stability questions
- Finitely many measurements: non-uniqueness examples
- The filtered Back Projection Algorithm.
iii) The attenuated X-Ray transform
- Novikovs approach: the Riemann-Hilbert Problem
- Other Inversion Formulae (Natterer, Oleg-Stromberg)
- Bukhgeims approach: the theory of A-analytic maps
- Other applications of Bukhgeims approach: the Doppler
iv) The attenuating and scattering case
- Isotropic attenuation and weak scattering: an iterative
- Anisotropic attenuation. Non-uniqueness and gauge equivalence.
v) Open problems
March 26 April
Program on Geometry in Inverse Problems
April 30 May 31, 2012
Program on Variational Methods and Compressive Sensing in Imaging
July August 2012
Summer Thematic Program on the Mathematics of Medical Imaging
Graduate Course on Medical Image
Jan Modersitzki, University of Lübeck
Research in Mathematical Image Processing
Todd Wittman, UCLA
Variational Regularization Methods
for Image Analysis and Inverse Problems
Otmar Scherzer, University of Vienna
1 July 3-6
1. Frontiers in Rapid
MRI, from Parallel Imaging to Compressed Sensing and Back
Michael Lustig, UC Berkeley
2. Sparse and Redundant Representation
Modeling of Images
Michael Elad, Technion
3. MRI for Mathematicians.
Numerical Methods for Maxwell's Equations
Charles Epstein, University of Pennsylvania.
4. Numerical Methods for Distributed
Eldad Haber, University of British Columbia
5. Microlocal Methods
in Inverse Problems
Gunther Uhlmann, University of Washington
6. Microlocal Analysis of Thermoacoustic
Plamen Stefanov, Purdue University
Junior Collaborative Research
Taking the Institute's Courses for
As graduate students at any of the Institute's University Partners,
you may discuss the possibility of obtaining a credit for one
or more courses in this lecture series with your home university
graduate officer and the course instructor. Assigned reading
and related projects may be arranged for the benefit of students
requiring these courses for credit.