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Workshop

Inverse problems and Applications November 05, 2001 - November 16, 2001
Registration Deadline: November 16, 2001 about 17 years ago
To apply for Funding you must register by: August 05, 2001 over 17 years ago
Parent Program:
Organizers Joyce McLaughlin, Adrian Nachman, William Symes, Gunther Uhlmann (chair) and Michael Vogelius
Speaker(s)

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Description
Workshop Schedule Inverse problems arise in practical situations such as medical imaging, exploration geophysics, and non-destructive evaluation where measurements made in the exterior of a body are used to deduce properties of the hidden interior. In the last couple of decades there have been substantial developments in the mathematical theory of inverse problems. The purpose of the workshop will be to bring together people working on different aspects of inverse problems, to appraise the current status of development of the field, and to encourage interaction between mathematicians and scientists and engineers working directly with the applications. Some of the more specific topics of the workhops will include: 1) The advances in engineering and image processing mathematics which have allowed for significant enhancement of widely used imaging techniques like X-ray tomography, magnetic resonance imaging, single photon emission tomography, positron emission tomography, ultrasound etc. 2) The new emerging areas in inverse boundary problems of Optical Tomography and Diffuse Tomography, which are based on boundary measurements of near-infrared light transmitted through a body, and Electrical Impedance Tomography which uses low-frequency electrical currents to probe a body. 3) The recent progress in understanding migration problems for elastic waves in an anisotropic medium. 4) New numerical inversion algorithms, particularly in the inverse scattering problem by an obstacle. 5) Time reversal imaging. 6) Elasticity imaging of biological tissue. The following is a partial list of invited speakers: S. Arridge, G. Bao, C. Bardos, R. Brown, E. Candes, M. Cheney, D. Colton, M. de Hoop, D. Dobson, O. Dorn, H. Engl, G. Eskin, D. Finch, J. Greenleaf, F.A. Grunbaum, G. Hermann, D. Isaacson, M. Klibanov, M. Lassas, J. McLaughlin, A. Melin, A. Nachman, F. Natterer, C. Nolan, V. Palomodov, S. Patch, R. Potthast, W. Rundell, F. Santosa, J. Schotland, J.A. Sethian, P. Stefanov, W. Symes, D. Tataru, A. Vasy, V. Venugopalan, R. Weder and M. Zworski. On November 13, there will be a concentration on optical tomography. On November 15 and 16 there will be a concentration on imaging and time reversal in random media. The invited speakers will include G. Bal, J. Berryman, L. Borcea, L. Carin, D. Chambers, J.P. Fouque, M. Fink, A. Larraza, G. Papanicolaou, L. Ryzhik, K. Solna, C. Tsogka and H. Zhao. Group photo of participants
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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A block of rooms has been reserved at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability.

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Schedule, Notes/Handouts & Videos
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Nov 05, 2001
Monday
08:00 AM - 05:00 PM
  Ultrasound imaging using eigenfunctions of the scattering operator
Adrian I. Nachman
08:00 AM - 05:00 PM
  Inversion and range of the attenuated Radon transform
Frank Natterer
08:00 AM - 05:00 PM
  Time reversed acoustics
Mathias Fink
08:00 AM - 05:00 PM
  Long-range transmission of nonlinear waves in random media
Josselin Garnier
08:00 AM - 05:00 PM
  Time reversal in solids
Chrysoula Tsogka (University of Crete)
08:00 AM - 05:00 PM
  Shear modulus imaging of tissues with transient elastography
Mathias Fink
08:00 AM - 05:00 PM
  Tank-scale experiments on applications to time-reversal acoustics
Andres Larraza
08:00 AM - 05:00 PM
  Refocusing for classical waves in complicated media
Leonid Ryzhik
10:45 AM - 11:50 AM
  Nonlinear problems in seismic inverse scattering
William Symes (Rice University)
11:50 AM - 02:00 PM
  Aharonov-Bohm effect and time-dependent inverse scattering theory
Ricardo Weder (UNAM - Universidad Nacional Autonoma de Mexico)
02:00 PM - 03:00 PM
  Local uniqueness theorems in inverse obstacle scattering and associated reconstruction methods
William Rundell
Nov 06, 2001
Tuesday
09:30 AM - 11:00 AM
  The linear sampling method for anisotropic media
David Colton (University of Delaware)
11:00 AM - 02:00 PM
  An inverse scattering problem for the 2D transport equation
Plamen Stefanov
02:00 PM - 03:30 PM
  Identification of parameters in polymer crystallization, semiconductor models and elasticity via iterative regularization methods
Heinz Engl
03:30 PM - 04:00 PM
  Geometric singularities in tomography
David Finch
04:00 PM - 05:00 PM
  A direct regularized reconstruction method for EIT
Nov 07, 2001
Wednesday
09:30 AM - 11:00 AM
  Microlocal analysis of seismic inversion: Characteristic strips, generalized Radon transform, and differential semblance optimization
Maarten de Hoop (Purdue University)
11:00 AM - 02:00 PM
  Birkhoff normal forms in semi-classical inverse problems
Maciej Zworski (University of California, Berkeley)
02:00 PM - 03:30 PM
  Microlocal aspects of synthetic aperture imagery
Clifford Nolan
03:30 PM - 04:30 PM
  Phase space analysis of stability of inverse problems
Victor Palamodov
Nov 08, 2001
Thursday
09:30 AM - 11:00 AM
  Inverse and optimization problems involving eigenvalues and eigenfunctions
Fadil Santosa
11:00 AM - 02:00 PM
  Inverse problems in many-body scattering
Andras Vasy (Stanford University)
02:00 PM - 03:30 PM
  Inverse problem for Maxwell equation in time-domain
Matti Lassas
03:30 PM - 04:30 PM
  Ultrasound-modulated optical imaging of biological tissue
David Dobson
Nov 09, 2001
Friday
09:00 AM - 10:30 AM
  Electrical impedance imaging
David Isaacson
10:30 AM - 11:35 AM
  Unique continuation problems for parabolic equations
Daniel Tataru (University of California, Berkeley)
11:35 AM - 02:00 PM
  Deterministic mathematical analysis of the time reversal mirror
Claude Bardos
02:00 PM - 03:00 PM
  Global uniqueness in the inverse scattering problem for the Schrödinger with external Yang-Mills potentials
Gregory Eskin
Nov 12, 2001
Monday
09:30 AM - 11:00 AM
  TBA
Adrian Nachman (University of Toronto)
11:00 AM - 02:00 PM
  Recent studies of an inverse medium problem
Gang Bao
02:00 PM - 03:30 PM
  TBA
Frank Natterer
03:30 PM - 04:00 PM
  Convexification of multi-extremal cost functionals for inverse problems via Carleman weight functions (joint with A. Timonov)
Michael Klibanov
04:00 PM - 04:30 PM
  Reconstruction of a current distribution from its magnetic field
Roland Potthast
04:30 PM - 05:30 PM
  L2 estimates for a scattering transform in two dimensions
Russell Brown (University of Kentucky)
Nov 13, 2001
Tuesday
09:30 AM - 11:00 AM
  Reconstruction methods in optical tomography
Simon Arridge
11:00 AM - 02:00 PM
  Near-field optical tomography
John Schotland
02:00 PM - 03:30 PM
  Application of photon migration to sub-millimeter length scales and highly absorbing tissues
Vasan Venugopalan
03:30 PM - 04:00 PM
  An nonlinear inverse problem for a Markov chain: Recovering the one step transition probability matrix from boundary measurements
F. Alberto Grünbaum (University of California, Berkeley)
04:00 PM - 05:00 PM
  F. John’s ultrahyperbolic equation and 3D computed tomography
Sarah Patch
Nov 14, 2001
Wednesday
09:30 AM - 11:00 AM
  TBA
Joyce McLaughlin
11:00 AM - 02:00 PM
  Curvelets and linear inverse problems
Emmanuel Candes (Stanford University)
02:00 PM - 03:30 PM
  Intertwining operators, nonlinear Radon transforms and inverse backscattering
Anders Melin
03:30 PM - 04:30 PM
  Three dimensional reconstruction of two dimensional crystals
Gabor Herman
Nov 15, 2001
Thursday
09:00 AM - 10:30 AM
  TBA
Mathias Fink
10:30 AM - 11:30 AM
  Imaging and time reversal in random media
George Papanicolaou (Stanford University)
11:30 AM - 01:30 PM
  Scaling relations with time reversed refocusing
Knut Solna
01:30 PM - 02:00 PM
  Inverse scattering for elastic targets in a shallow water channel
Lawrence Carin (Duke University)
02:00 PM - 02:30 PM
  TBA
Josselin Garnier
02:30 PM - 03:30 PM
  TBA
Chrysoula Tsogka (University of Crete)
03:30 PM - 04:00 PM
  Imaging in random media
Liliana Borcea (Rice University)
04:00 PM - 04:30 PM
  Time reversal and the adjoint method
Oliver Dorn
04:30 PM - 05:00 PM
  Spectrum of the time reversal operator
David Chambers
05:00 PM - 05:30 PM
  Some recent results in time reversal and imaging in random media.
Peter Blomgren
Nov 16, 2001
Friday
09:00 AM - 10:30 AM
  TBA
Mathias Fink
10:30 AM - 11:40 AM
  Ultrasound stimulated vibro-acoustography
James Greenleaf
11:40 AM - 02:00 PM
  Application of time-reversal methods to ocean acoustics
William Kuperman
02:00 PM - 02:30 PM
  Time-reversal acoustics for multiple targets
James Berryman
02:30 PM - 03:00 PM
  Can we hear the size of the target?
Hong-Kai Zhao (University of California, Irvine)
03:00 PM - 04:00 PM
  TBA
Andres Larraza
04:00 PM - 04:30 PM
  Radiative transport limit for the random Schrödinger equation
Leonid Ryzhik
04:30 PM - 05:00 PM
  Time reversal for classical waves in random media and the abstract
Guillaume Bal (University of Chicago)
05:00 PM - 06:00 PM
  Separation of scales asymptotics for waves in random media
Jean-Pierre Fouque