January 30, 2015
January-August 2012
Thematic Program on Inverse Problems and Imaging
Graduate and Short Courses held at the Fields Institute
January 9–July 31,2012

All courses will be held at the Fields Institute, Room 230 unless otherwise noted.

January 9– April 6, 2012

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 Tomography.

iv) Inverse problems with interior data: Current Density Impedance Imaging.

v) Inverse scattering methods: progress on quantitative Ultrasound imaging.

vi) Open problems.

2. Inverse Transport Theory and Tomography
Instructor: Alex Tamasan, University of Central Florida

Tuesdays and Thursdays 3:30-5:00, Stewart Library, Fields Institute

Topics to be covered:
i) The transport model through an attenuating and scattering medium
- 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
- Novikov’s approach: the Riemann-Hilbert Problem
- Other Inversion Formulae (Natterer, Oleg-Stromberg)
- Bukhgeim’s approach: the theory of A-analytic maps
- Other applications of Bukhgeim’s approach: the Doppler Transform.

iv) The attenuating and scattering case
- Isotropic attenuation and weak scattering: an iterative reconstruction method.
- Anisotropic attenuation. Non-uniqueness and gauge equivalence.

v) Open problems

March 26 – April 27, 2012
Program on Geometry in Inverse Problems

Short Courses

April 30 – May 31, 2012
Program on Variational Methods and Compressive Sensing in Imaging
Short Courses

July –August 2012
Summer Thematic Program on the Mathematics of Medical Imaging

Graduate Courses

Graduate Course on Medical Image Registration
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

Short Courses

Week 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

Week 2 July 9-13
3. MRI for Mathematicians. Numerical Methods for Maxwell's Equations
Charles Epstein, University of Pennsylvania.

4. Numerical Methods for Distributed Parameter Identification
Eldad Haber, University of British Columbia
Partner: Mitacs

Week 3 July 16-20
5. Microlocal Methods in Inverse Problems
Gunther Uhlmann, University of Washington

6. Microlocal Analysis of Thermoacoustic Tomography
Plamen Stefanov, Purdue University

Week 4 July 23-27
Junior Collaborative Research Workshop

Taking the Institute's Courses for Credit
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.