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IMA Newsletter #347

September 2005

2005-2006 Program

Imaging

See http://www.ima.umn.edu/2005-2006 for a full description of the 2005-2006 program on Imaging.

News and Notes

The IMA in the News

On August 31, IMA Director Doug Arnold was interviewed on World Talk Radio's Science and Society. He discussed the IMA and the impact of interdisciplinary mathematical research. (Listen to the archived broadcast.) Arnold also recently appeared on a KARE 11 TV News feature on the mathematical puzzle craze Sudoku.

The Air Force Research Laboratory joins the IMA

The Air Force Research Laboratory has joined the IMA as a Participating Institution. Greg Arnold serves as the AFRL's representative to the Industrial Advisory Board. Industrial postdoc Kai Medville will be working with the AFRL.

IMA Events

IMA Tutorial

Radar and Optical Imaging

September 19-23, 2005

http://www.ima.umn.edu/2005-2006/T9.19-23.05

The 2005-2006 IMA thematic program Imaging begins with a week-long tutorial consisting of two lecture series providing background on imaging techniques that are appropriate for two different regions of the electromagnetic spectrum, namely the microwave and optical regions. The microwave region will be considered by Margaret Cheney (RPI) in a tutorial on radar imaging, whereas the optical region will be considered by David Brady (Duke University), whose tutorial will focus on the impact of electronic recording processes. The lectures will provide background on radar imaging, computational optical imaging, and spectroscopy.
Schedule

Monday, September 5

Labor Day —IMA closed.

Wednesday, September 7

10:15a-11:00aStart of the Year ReceptionLind Hall 400
11:00a-12:00pStart of the Year OrientationLind Hall 409

Tuesday, September 13

9:30a-11:45aPostdoc Show and TellEE/CS 3-180
11:45a-1:30pPostdoc posters, with lunchLind Hall 400
1:30p-2:15pPostdoc Show and Tell (continued)EE/CS 3-180

Monday, September 19

9:00a-9:30aCoffee and RegistrationEE/CS 3-180 T9.19-23.05
9:30a-10:20aIntroduction to Radar Imaging Margaret Cheney (Rensselaer Polytechnic Institute)EE/CS 3-180 T9.19-23.05
10:20a-10:30aDiscussionEE/CS 3-180 T9.19-23.05
10:30a-11:00a CoffeeEE/CS 3-176 T9.19-23.05
11:00a-11:50aComputational Optical Imaging and SpectroscopyDavid Brady (Duke University) T9.19-23.05
11:50a-12:00pDiscussionEE/CS 3-180 T9.19-23.05
12:00p-1:30p Lunch T9.19-23.05
1:30p-2:20pIntroduction to Radar Imaging (continued)Margaret Cheney (Rensselaer Polytechnic Institute)EE/CS 3-180 T9.19-23.05
2:20p-2:30p DiscussionEE/CS 3-180 T9.19-23.05
2:30p-3:00p CoffeeEE/CS 3-176 T9.19-23.05
3:00p-3:50pComputational Optical Imaging and Spectroscopy (continued)David Brady (Duke University)EE/CS 3-180 T9.19-23.05
3:50p-4:00pDiscussionEE/CS 3-180 T9.19-23.05
4:00p-5:00pReceptionLind Hall 400 T9.19-23.05

Tuesday, September 20

9:00a-9:30aCoffee and RegistrationEE/CS 3-176 T9.19-23.05
9:30a-10:20aIntroduction to Radar ImagingMargaret Cheney (Rensselaer Polytechnic Institute)EE/CS 3-180 T9.19-23.05
10:20a-10:30aDiscussionEE/CS 3-180 T9.19-23.05
10:30a-11:00aCoffeeEE/CS 3-176 T9.19-23.05
11:00a-11:50aComputational Optical Imaging and SpectroscopyDavid Brady (Duke University)EE/CS 3-180 T9.19-23.05
11:50a-12:00pDiscussionEE/CS 3-180 T9.19-23.05
12:00p-1:30pLunch T9.19-23.05
1:30p-2:20pIntroduction to Radar Imaging (continued)Margaret Cheney (Rensselaer Polytechnic Institute)EE/CS 3-180 T9.19-23.05
2:20p-2:30pDiscussionEE/CS 3-180 T9.19-23.05
2:30p-3:00pCoffeeEE/CS 3-176 T9.19-23.05
3:00p-3:50pComputational Optical Imaging and Spectroscopy (continued)David Brady (Duke University)EE/CS 3-180 T9.19-23.05
3:50p-4:00pDiscussionEE/CS 3-180 T9.19-23.05

Wednesday, September 21

9:00a-9:30aCoffee and RegistrationEE/CS 3-176 T9.19-23.05
9:30a-10:20aIntroduction to Radar ImagingMargaret Cheney (Rensselaer Polytechnic Institute)EE/CS 3-180 T9.19-23.05
10:20a-10:30aDiscussionEE/CS 3-180 T9.19-23.05
10:30a-11:00aCoffeeEE/CS 3-176 T9.19-23.05
11:00a-11:50aComputational Optical Imaging and SpectroscopyDavid Brady (Duke University)EE/CS 3-176 T9.19-23.05
11:50a-12:00pDiscussionEE/CS 3-180 T9.19-23.05
12:00p-1:30pLunch T9.19-23.05
1:30p-2:20pIntroduction to Radar Imaging (continued)Margaret Cheney (Rensselaer Polytechnic Institute)EE/CS 3-180 T9.19-23.05
2:20p-2:30pDiscussionEE/CS 3-176 T9.19-23.05
2:30p-3:00pCoffeeEE/CS 3-176 T9.19-23.05
3:00p-3:50pComputational Optical Imaging and Spectroscopy (continued)David Brady (Duke University)EE/CS 3-180 T9.19-23.05
3:50p-4:00pDiscussionEE/CS 3-180 T9.19-23.05

Thursday, September 22

9:00a-9:30aCoffee and Registration T9.19-23.05
9:30a-10:20aIntroduction to Radar ImagingMargaret Cheney (Rensselaer Polytechnic Institute)EE/CS 3-180 T9.19-23.05
10:20a-10:30aDiscussionEE/CS 3-180 T9.19-23.05
10:30a-11:00aCoffeeEE/CS 3-176 T9.19-23.05
11:00a-11:50aComputational Optical Imaging and SpectroscopyDavid Brady (Duke University)EE/CS 3-180 T9.19-23.05
11:50a-12:00pDiscussionEE/CS 3-176 T9.19-23.05
12:00p-1:30pLunch T9.19-23.05
1:30p-2:20pIntroduction to Radar Imaging (continued)Margaret Cheney (Rensselaer Polytechnic Institute)EE/CS 3-180 T9.19-23.05
2:20p-2:30pDiscussionEE/CS 3-180 T9.19-23.05
2:30p-3:00pCoffeeEE/CS 3-176 T9.19-23.05
3:00p-3:50pComputational Optical Imaging and Spectroscopy (continued)David Brady (Duke University)EE/CS 3-180 T9.19-23.05
3:50p-4:00pDiscussionEE/CS 3-180 T9.19-23.05

Friday, September 23

9:00a-9:30aCoffee and RegistrationEE/CS 3-180 T9.19-23.05
9:30a-10:20aIntroduction to Radar ImagingMargaret Cheney (Rensselaer Polytechnic Institute)EE/CS 3-180 T9.19-23.05
10:20a-10:30aDiscussionEE/CS 3-180 T9.19-23.05
10:30a-11:00aCoffeeEE/CS 3-176 T9.19-23.05
11:00a-11:50aComputational Optical Imaging and SpectroscopyDavid Brady (Duke University)EE/CS 3-180 T9.19-23.05
11:50a-12:00pDiscussionEE/CS 3-180 T9.19-23.05
12:00p-1:30pLunch T9.19-23.05
1:30p-2:20pIntroduction to Radar Imaging (continued)Margaret Cheney (Rensselaer Polytechnic Institute)EE/CS 3-180 T9.19-23.05
2:20p-2:30pDiscussionEE/CS 3-180 T9.19-23.05
2:30p-3:00pCoffeeEE/CS 3-176 T9.19-23.05
3:00p-3:50pComputational Optical Imaging and Spectroscopy (continued)David Brady (Duke University)EE/CS 3-180 T9.19-23.05
3:50p-4:00pDiscussionEE/CS 3-180 T9.19-23.05

Event Legend:

T9.19-23.05Radar and Optical Imaging
Abstracts
Start of the Year Orientation
Abstract: A short orientation to the IMA and the 2005-6 Imaging program for postdocs, long-term visitors, and participating University of Minnesota faculty.
Postdoc Show and Tell
Abstract: To facilitate the matching of post-docs with mentors, we will hold our annual "Show and Tell" on Tuesday September 13. Each postdoc will give a 10-minute introduction to their background and scientific interests. The talks will be supplemented by posters which will be on view during the lunch break. All members of the U of M and IMA imaging community are invited to attend.
David Brady (Duke University) Computational Optical Imaging and Spectroscopy

Biography: David J. Brady is the Addy Family Professor of Electrical and Computer Engineering in the Pratt School of Engineering at Duke University. Brady's research focuses on computational optical sensors. He leads the DISP group (www.disp.duke.edu), which is pursing projects in biometric sensor networks, spectroscopic telescopy, multimodal spectroscopy for biomedical and compressive sampling for digital imaging. DISP is supported by grants from the Defense Advanced Research Projects Agency, the Air Force Office of Scientific Research, the Army Research Office, the National Institute on Alcohol Abuse and Alcoholism and the National Science Foudation. Brady holds a B.A. in physics and mathematics from Macalester College and M.S. and Ph.D. degrees in applied physics from the California Institute of Technology. He was on the faculty of electrical and computer engineering at the University of Illinois in Urbana-Champaign from 1990 until joining the Duke faculty in 2001. He was a David and Lucile Packard Foundation Fellow from 1990 until 1995.

Abstract: The history of artificial optical sensing is punctuated by three major innovations. The first innovation was the development, beginning approximately 700 years ago, of optical elements. These include lenses, prisms, gratings and mirrors. Optical elements enabled humans to see things that could not otherwise be seen. The second innovation was the development, beginning approximately 200 years ago, of photochemical recording processes. Photochemistry enabled humans to capture and store information produced by optical elements. The third innovation is the development, beginning approximately 50 years ago, of electronic recording processes and digital data analysis.

Just as 50-100 years passed between the first observations of photochemical behavior and its widespread use in photography, the implications of the electronic imaging remain unclear and in rapid development. From a mathematical perspective the most fundamental difference between electronic and photochemical photography lies in the association between the focal plane image and the display image. The photochemical display image is directly derived, through chemical processing, from the recorded focal plane image. The electronic image is created from recorded data by digital processing and need not be isomorphic in any sense to the focal plane field distribution.

As part of the disassociation of the focal plane distribution and the reconstructed image, discrete analysis plays a much greater role in digital imaging than in conventional systems. In view of this, the mathematical language of imaging is slowly evolving away from continuous transformations and toward discrete and multiscale analysis. While the instructor is not a professional mathematician, this tutorial will attempt to explain for a mathematical audience the current issues in the sampling theory of digital imaging and spectroscopy systems. In anticipation of an IMA workshop later in the fall on integrated sensing and processing, the tutorial will focus on integrated computational imaging system design, meaning joint analysis of physical layer filtering and processing and digital analysis and reconstruction algorithms.

Outline:

  1. Geometric analysis of optical fields
    • Simple imaging systems
    • Coded aperture imaging
    • Tomography
    • Reference structure tomography
  2. Wave analysis of optical fields
    • Fourier analysis of imaging and filtering
    • Coded wavefront imaging
    • Sampling and representation of wave fields
  3. Correlation fields and interferometric imaging
    • The van Cittert Zernike theorem
    • Coherence and spectra
  4. Compressive sampling and components of modern digital imaging systems
  5. Spectroscopy and imaging
    • multiplex sensing in spectroscopy and imaging
    • Coded transformations in spectroscopy and imaging

Margaret Cheney (Rensselaer Polytechnic Institute) Introduction to Radar Imaging

Biography: Margaret Cheney is a Professor of Mathematics at Rensselaer Polytechnic Institute. Her Ph.D. in mathematics is from Indiana University; after a postdoc at Stanford University, she spent 3 years as assistant professor at Duke University before moving to RPI. She has held visiting appointments at NYU's Courant Institute (1987-1988) at the Minnesota Institue for Mathematics and Its Applications (1994-1995 and 1997), the Berkeley Mathematical Sciences Research Institute (2001), the Naval Air Warfare Center Weapons Division (2002), and the UCLA Institute for Pure and Applied Mathematics (2003). Most of her work has been on the inverse problems that arise in quantum mechanics, acoustics, and electromagnetic theory. Cheney has received several awards, including the Office of Naval Research Young Investigator Award in 1986, a National Science Foundation Faculty Award for Women in Science and Engineering in 1990, and the Lise Meitner Visiting Professorship at Lund Institute of Technology in 2000. She was a member of the Rensselaer Impedance Imaging team that received the 1993 ComputerWorld Smithsonian award in the Medicine category. She is a member of the SIAM board of Trustees, of the Electromagnetics Academy, and is a Fellow of the Institute of Physics. From 1994 to 2003, she served on the editorial board for the SIAM Journal of Applied Mathematics and was Editor-in-Chief 1995-97. She currently serves on the editorial board of Inverse Problems. She has 4 patents and roughly 90 publications, and she has given over 100 research lectures in the U.S. and Europe.

Abstract: Radar imaging is a technology that has been developed, very successfully, within the engineering community during the last 50 years. The key component that makes radar imaging possible, however, is mathematics, and many of the open problems are mathematical ones.

This tutorial will explain, in terms suitable for a mathematical audience, the basics of radar and the mathematics involved in producing high-resolution radar images.

This tutorial will help prepare participants for the upcoming workshop, and will provide them with a foundation that will enable them to read some of the theoretical engineering literature and begin research in the area.

Outline:

  1. Nonimaging radar
      radar system architecture
      waveforms, correlation receiver, ambiguity function

  2. Introduction to scattering
      Lippmann-Schwinger equation, Born approximation
  3. Introduction to antennas
      electromagnetic vector potentials
      radiation from a current distribution
      far-field form of electric field
      examples: sinc pattern, phased arrays

  4. Synthetic-aperture radar imaging
      model for the received signal
      interpretation as a Fourier Integral Operator
      approximate inversion
      point spread function and resolution

  5. Properties of the image (time permitting)
      introduction to microlocal analysis
      microlocal analysis of the imaging operator

Recommended prerequisites are knowledge of vector calculus and the Fourier transform. Some familiarity with the wave equation would be helpful but not strictly necessary. The approach will be similar to that of the paper "A mathematical tutorial on Synthetic Aperture Radar", SIAM Review 43 (2001) 301-312.

Visitors in Residence
Tuncay Aktosun Mississippi State University 9/18/2005 - 9/24/2005
Jung-Ha An University of Minnesota 9/1/2005 - 8/31/2007
Fredrik Andersson Lund University 9/17/2005 - 11/14/2005
Kartik B. Ariyur Honeywell 9/19/2005 - 9/23/2005
Douglas N. Arnold University of Minnesota 7/15/2001 - 8/31/2006
Donald G. Aronson University of Minnesota 9/1/2002 - 8/31/2006
Evgeniy Bart University of Minnesota 9/1/2005 - 8/31/2007
Nicholas Bennett Schlumberger-Doll Research 9/18/2005 - 9/23/2005
Francisco Blanco-Silva Purdue University 9/1/2005 - 6/30/2006
David Brady Duke University 9/18/2005 - 12/10/2005
Robert Burridge Massachusetts Institute of Technology 9/1/2005 - 12/31/2005
Qianyong Chen University of Minnesota 9/1/2004 - 8/31/2006
Margaret Cheney Rensselaer Polytechnic Institute 9/6/2005 - 12/31/2005
Giulio Ciraolo University degli Studi de Firenze 9/5/2005 - 12/23/2005
Dana Clahane University of California - Riverside 9/18/2005 - 11/18/2005
Steven Benjamin Damelin Georgia Southern University 8/9/2005 - 6/30/2006
Anthony J. Devaney Northeastern University 9/5/2005 - 12/30/2005
Brian DiDonna University of Minnesota 9/1/2004 - 8/31/2006
Grant Erdmann University of Minnesota 9/18/2005 - 9/23/2005
Ali Eydgahi Unversity of Maryland Eastern Shore 9/18/2005 - 9/24/2005
Yi Fang Rensselaer Polytechnic Institute 9/12/2005 - 12/20/2005
Adel Faridani Oregon State University 9/18/2005 - 10/21/2005
Anne Gelb Arizona State University 9/1/2005 - 9/30/2005
Jeff P. Grossman InnerVision Medical Technologies Inc. 9/18/2005 - 9/24/2005
Changfeng Gui University of Connecticut 9/12/2005 - 6/30/2006
Robert Gulliver University of Minnesota 9/19/2005 - 9/30/2005
Jooyoung Hahn KAIST 8/26/2005 - 7/31/2006
Gloria Haro Ortega University of Minnesota 9/1/2005 - 8/31/2007
Chandanie Hetti Entegra Power Group 9/19/2005 - 9/23/2005
Xiang Huang University of Connecticut 9/1/2005 - 6/30/2006
Sookyung Joo University of Minnesota 9/1/2004 - 8/31/2006
Chiu Yen Kao University of Minnesota 9/1/2004 - 8/31/2006
Taufiquar Khan Clemson University 9/1/2005 - 12/31/2005
Richard Kowar University of Innsbruck 9/17/2005 - 9/24/2005
Matthias Kurzke University of Minnesota 9/1/2004 - 8/31/2006
Kiwoon Kwon Rensselaer Polytechnic Institute 9/18/2005 - 9/24/2005
Song-Hwa Kwon University of Minnesota 8/30/2005 - 8/31/2007
Chang-Ock Lee KAIST 8/1/2005 - 7/31/2006
Richard Leiderman Boston University 9/18/2005 - 9/24/2005
Debra Lewis University of Minnesota 7/15/2004 - 8/31/2006
Hstau Liao University of Minnesota 9/2/2005 - 8/31/2007
Bradley J. Lucier Purdue University 8/15/2005 - 6/30/2006
Russell Luke University of Delaware 9/6/2005 - 12/31/2005
Peter Maass University of Bremen 9/27/2005 - 10/12/2005
Alison Malcolm University of Minnesota 9/1/2005 - 8/31/2007
Stephen McDowall Western Washington University 9/18/2005 - 9/24/2005
Kai Medville University of Minnesota 9/1/2005 - 8/31/2007
Steen Moeller University of Minnesota 9/19/2005 - 9/23/2005
Frank Natterer Universitaet Muenster 9/26/2005 - 10/22/2005
Mahdi Nezafat University of Minnesota 9/19/2005 - 9/23/2005
Peter J. Olver University of Minnesota 9/1/2005 - 6/30/2006
Winston Ou Purdue University 9/1/2005 - 1/13/2006
Peter Philip University of Minnesota 8/22/2004 - 8/31/2006
Gregory J. Randall Universidad de la Republica 8/18/2005 - 7/31/2006
Walter Richardson University of Texas - San Antonio 9/1/2005 - 6/30/2006
Thomas Roberts Air Force Research Laboratory 9/18/2005 - 9/23/2005
Fadil Santosa University of Minnesota 9/1/2005 - 6/30/2006
Guillermo R. Sapiro University of Minnesota 9/1/2005 - 6/30/2006
Arnd Scheel University of Minnesota 7/15/2004 - 8/31/2006
Tom L. Scofield Calvin College 9/1/2005 - 12/31/2005
Shaun Sellers Washington University - St. Louis 9/19/2005 - 10/22/2005
Shagi-Di Shih University of Wyoming 9/19/2005 - 10/21/2005
Tatiana Soleski University of Minnesota 9/1/2005 - 8/31/2007
Vladimir Sverak University of Minnesota 9/1/2005 - 6/30/2006
Alain B. Tchagang University of Minnesota 9/19/2005 - 9/23/2005
Alan Thomas Clemson University 9/4/2005 - 12/17/2005
Carl Toews University of Minnesota 9/1/2005 - 8/31/2007
Jingyue Wang Purdue University 9/1/2005 - 6/30/2006
Xiaoqiang Wang University of Minnesota 9/1/2005 - 8/31/2007
Michael Werman The Hebrew University 9/18/2005 - 9/25/2005
Rebecca Willett Duke University 9/19/2005 - 9/23/2005
Jeong-Rock Yoon Clemson University 9/6/2005 - 12/23/2005
Ofer Zeitouni University of Minnesota 9/1/2005 - 6/30/2006
Legend: Postdoc or Industrial Postdoc Long-term Visitor

Participating Institutions: Air Force Research Laboratory, Carnegie Mellon University, Consiglio Nazionale delle Ricerche (CNR), Georgia Institute of Technology, Indiana University, Iowa State University, Kent State University, Lawrence Livermore National Laboratories, Los Alamos National Laboratory, Michigan State University, Mississippi State University, Northern Illinois University, Ohio State University, Pennsylvania State University, Purdue University, Rice University, Rutgers University, Sandia National Laboratories, Seoul National University (BK21), Seoul National University (SRCCS), Texas A & M University, University of Chicago, University of Cincinnati, University of Delaware, University of Houston, University of Illinois - Urbana-Champaign, University of Iowa, University of Kentucky, University of Maryland, University of Michigan, University of Minnesota, University of Notre Dame, University of Pittsburgh, University of Texas - Austin, University of Wisconsin - Madison, University of Wyoming, Wayne State University
Participating Corporations: 3M, Boeing, Corning, ExxonMobil, Ford Motor Company, General Electric, General Motors, Honeywell, IBM Corporation, Johnson & Johnson, Lockheed Martin, Medtronic, Inc., Motorola, Schlumberger-Doll Research, Siemens, Telcordia Technologies