THEMATIC PROGRAMS

January-August 2012 Thematic Program on Inverse Problems and Imaging at the Fields Institute, Toronto Organizers: Tony Chan (Hong Kong University of Science and Technology), Charles Epstein (Pennsylvania), Allan Greenleaf (Rochester), Yaroslav Kurylev (University College London), Jan Modersitzki (Lübeck), Adrian Nachman (Toronto), Gunther Uhlmann (Washington), Luminita Vese (UCLA)

Mailing List : To receive updates on the program please subscribe to our mailing list at www.fields.utoronto.ca/maillist

Outline of Scientific Activities (program poster)

The proposed program will take place in conjunction with the Mitacs Focus Period on the Mathematics of Medical Imaging (FP-MMI). A Mitacs International Focus Period consists of a series of scientific events on diverse topics - all centered on a common theme that addresses key socio-economic issues of high provincial and federal priority. June 2011 to August 2012 is the MITACS International Focus Period on The Mathematics of Medical Imaging.

The Fields Thematic Program on Inverse Problems and Imaging aims to focus in depth on selected active areas of recent mathematical research in Inverse Problems and Image Analysis. There will be emphasis on longer events that encourage collaborations on important new directions of investigation. The main components will be:

1.A month-long program on Geometry in Inverse Problems.
2.A month-long program on Variational Methods and Compressive Sensing in Imaging
3.A two-month Summer Thematic Program on "Mathematics of Medical Imaging.

January 9– April 6, 2012
Graduate Courses

1. . Mathematics of Medical Imaging
Tuesdays and Thursdays 1:30-3:00, Room 230, Fields Institute
Instructor: Adrian Nachman, University of Toronto

2. Inverse Transport Theory and Tomography
Tuesdays and Thursdays 3:30-5:00, Stewart Library, Fields Institute
Instructor: Alex Tamasan, University of Central Florida

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

Organizers:
Yaroslav Kurylev, University College London
Adrian Nachman, University of Toronto

Description of the Program
This will be a research-intensive program aimed at close collaboration between the participants. The focus will be on five main topics:
i) The boundary rigidity problem.
ii) Anisotropic inverse problems, geometric convergence and spectral geometry.
iii) Index theory and inverse problems; reconstruction of topological or geometric invariants.
iv) Inverse problems on Lorentzian manifolds.
v) The geometric Whitney problem.

There will be a number of short courses aimed at attracting graduate students and postdoctoral fellows and at helping define the research questions to be investigated during the program.
We plan to have regularly scheduled seminars and informal working groups organized around the main themes of the program.

Short Courses

1. Boundary Rigidity, Volume Minimality, and Minimal Surfaces in L^\infinity
Dmitri Burago, Pennsylvania State University (to be confirmed).

2. Inverse Spectral Problems on Riemannian Manifolds
Matti Lassas, University of Helsinki

3. Carleman Estimates and Anisotropic Inverse Problems
Miko Salo, University of Helsinki

4. Whitney's Extension Problem
Charles Fefferman, Princeton University

5. Inverse Problems for Connections
Gabriel Paternain, Cambridge University

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April 30 – May 31, 2012
Theme Period on Variational Methods and Compressive Sensing in Imaging

Organizers:
Tony Chan, Hong Kong University of Science and Technology
Adrian Nachman, University of Toronto
Luminita Vese, UCLA

Description of the Program
This program is intended to foster research, learning and collaboration between distinguished researchers in the various areas of Image Analysis. There will be a number of short courses devoted to various topics in Image Analysis and Compressed Sensing. These courses are aimed at attracting graduate students and postdoctoral fellows and at helping define the research questions to be investigated during the program.

In addition, there will be research talks by the participants in the program.
Preliminary topics for the program:

1. L1 minimization and applications (including Total Variation minimization).
2. Compressed Sensing by variational regularization methods.
3. Proximal point methods and iterative methods for solving ill-posed inverse problems (including iterative Bregman methods, hierarchical decompositions, surrogate functionals).
4. Geometric processing (denoising of surfaces, non-rigid shape processing and analysis).
5. Optimal Transportation and Wasserstein Distance methods for registration and segmentation.
6. PDE methods for image processing.
7. Nonlocal methods (nonlocal means, nonlocal total variation, bilateral filtering).

Distinguished Lecture Series

May 7- 9, 2012
Emmanuel Candes, Professor of Mathematics and of Statistics, Professor of Electrical Engineering (by courtesy),Stanford University

Short Courses

1.Sparse Signal Processing and Compressive Sensing
Richard Baraniuk, Rice University.

2.Geodesic Methods in Image Analysis
Laurent Cohen, Université Paris-Dauphine

3.Partial Differential Equation Methods in Image Processing
Selim Esedoglu, University of Michigan

4.Numerical Methods for Sparse Recovery
Massimo Fornasier, Johann Radon Institute

5.Numerical Geometry of Images
Ron Kimmel, Technion

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July–August 2012
Summer Theme Period on the Mathematics of Medical Imaging

Organizers: Charles Epstein, University of Pennsylvania Allan Greenleaf, University of Rochester Jan Modersitzki, University of Lübeck

Adrian Nachman, University of Toronto Gunther Uhlmann, University of Washington Hongmei Zhu, York University

Applications for support to the July 3-31, 2012 Summer Research School on the Mathematics of Medical Imaging

Applicants: 1) please fill out the funding application here 2) have your advisor submit a letter of recommendation to thematic<at>fields.utoronto.ca 3) send us your CV and include your thesis subject and current projects to thematic<at>fields.utoronto.ca A number of students/fellows will be awarded support to stay for July 2- August 24 to continue work on their research projects and participate in all all the Summer's activities. Please indicate on the application form is you wish to be considered for support for an extended stay July 2-August 24. The extended activities include: July 3-31, 2012 Summer Research School on the Mathematics of Medical Imaging August 13-17, 2012 Workshop on Microlocal Methods in Medical Imaging August 20-24, 2012 Industrial Problem-Solving Workshop on Medical Imaging

Coxeter Lecture Series
to be announced

July 3-31, 2012
Summer Research School on the Mathematics of Medical Imaging
Organizers:
Guillaume Bal, Columbia University
Allan Greenleaf, University of Rochester
Stephen McDowall, Western Washington University
Adrian Nachman, University of Toronto
Todd Wittman, UCLA
Luminita Vese, UCLA

The program will open to applications and about 40 participants will be selected. They will be organized into small teams of up to 5 graduate students and postdocs, based on the project they choose. Some of these will be alumni of the AMS MRC 2009 conference on "Inverse Problems". The groups will work on a range of research problems.
For the first three weeks a number of graduate courses and short courses will be offered. In addition, there will be lectures by senior researchers to be invited around the week's theme.

Graduate Courses

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

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

Short Courses 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

Short Courses 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

Short Courses Week 4 July 23-27

Junior Collaborative Research Workshop

August 13-17, 2012
Workshop on Microlocal Methods in Medical Imaging
Organizers:
Peter Gibson,York University
Allan Greenleaf, University of Rochester
Luigi Rodino, Universita di Torino
M. W. Wong, York University
Hongmei Zhu, York University

This 5-day workshop aims to bring together experts from microlocal analysis with medical imaging practitioners. The focus will be on the following topics:
i) Microlocal Analysis in Tomography, Thermoacoustic Tomography, Electron Tomography.
ii) Numerical Methods of Pseudodifferential Operators.
iii) Stockwell and Wavelet Transforms in Medical Imaging.
iv) Wavelets and curvelets in Medical Imaging.
v) Microlocal Analysis of the Geometric Separation Problem in imaging.

August 20-24, 2012
Industrial Problem-Solving Workshop on Medical Imaging
Organizers: Sean Bohun (UOIT), Michael Lynch (MITACS), Huaxiong Huang (York), Nilima Nigam (SFU), Mary Pugh (Toronto), Hongmei Zhu (York)
Partner: Mitacs

This 5-day workshop will follow the very successful format of previous Fields-MITACS Industrial Problem-Solving Workshops. Some of the problems to be discussed will be ones generated during the Connector Events at the Inaugural Conference and at the Workshop on Brain Imaging. Participants will include between 36-50 academic experts (including mathematicians), and experts from industry. On the first day, the industrial sponsors will present their problem statements. The academic experts will divide into teams of 6-10 people each, with one team assigned to each problem. The teams spend the next 3 days collaborating on solutions to their problem, and present their solution on the final day of the workshop.

Postdoctoral Fellows

The Thematic Program on Inverse Problems and Imaging is pleased to welcome the following Postdoctoral Fellows to the Program:

Fields Ontario Postdoctoral Fellows

Prashant Athavale, PhD (University of Maryland, College Park, 2009)

Program Visitors

We will support a number of visitors to the program, including visiting Ph.D. students

All scientific events are open to the mathematical sciences community. Visitors who are interested in office space or funding are requested to apply by filling out the application form (open shortly) . Fields scientific programs are devoted to research in the mathematical sciences, and enhanced graduate and post-doctoral training opportunities. Part of the mandate of the Institute is to broaden and enlarge the community, and to encourage the participation of women and members of visible minority groups in our scientific programs.

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