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Spring 2008 Seminars

Thursday, February 14, 2008
Inverse Problems Seminar
Speaker: Maria Cameron, Courant Institute, New York University
Title: Seismic Velocity Estimation from Time Migration
Location: Amos Eaton Rm 402
Time: 4:00PM-5:00PM

We address the problem of the estimation of the sound speed inside the Earth from time migration. The velocities chosen in the process of time migration, known as time migration velocities, are used as the input. We have derived theoretical relationships between the time migration velocities and the true seismic velocities in 2D and 3D. We have developed PDE's which allow us to reconstruct the seismic velocities from the time migration velocities. These PDE's are elliptic, while the physical setting allows us to pose only a Cauchy problem which is well-known to be ill-posed. Nonetheless we have developed some inversion techniques, tested them on a collection of synthetic examples in 2D and 3D and applied to field data with severe lateral inhomogeniety. The theoretical components of the work are based on the seismic ray tracing theory. The numerical components include Dijkstra-like solvers, level set methods, finite difference methods with stabilizing error terms and techniques for data smoothing.

Thursday, March 27, 2008
Inverse Problems Seminar
Speaker: Professor Brett Borden, Graduate School of Engineering and Applied Sciences, Monterrey, California
Title: EM Scattering Approximations: Radar Imaging and ad hoc Patches
Location: Amos Eaton 402
Time: 4:00 PM- 5:00 PM
Host: Margaret Cheney

Radar imaging is, of course, based on Maxwell's equations which lead to vector wave/Helmholtz equations. In cartesian coordinates, the vector Helmholtz equation reduces to three scalar equations and this, perhaps, is a reason why many radar imaging practitioners start with a scalar scattering model. More careful treatments result in formidable vector solutions which, in many practical situations, are intractable and must be reduced using various other approximations. We will discuss these approximations and the associated limitations --- especially in the context of solving several important open problems in radar imaging.

Thursday, April 10, 2008
Inverse Problems Seminar
Professor George Biros
Penn Engineering, Mechanical Engineering and Applied Mechanics
Title: Cardiac motion estimation from cine-MR images
Location: Amos Eaton 402
Time: 4:00PM -5:00 PM
Host: Assad Oberai

Cine Magnetic Resonance Imaging is routinely used for diagnosing cardiovascular disorders. Clinical interpretation of MR images requires semi-automatic image processing by certified technicians. Image processing is necessary to recover global and localized measures of the motion of the myocardium but it has significant intra- and inter-rater variability. Along with collaborators at the Hospital of the University of Pennsylvania, we are developing novel technologies for cardiac motion estimation. The key feature of our approach is an optimization formulation that is constrained by partial differential equations. The optimality conditions for this problem result in a nonlinear four-dimensional, boundary value problem. I will briefly review the related work in cardiac motion estimation, discuss the formulation, and algorithmic issues related to discretization and solution. I will conclude with a discussion on numerical results on synthetic and clinical datasets.

Thursday, April 24, 2008
Inverse Problems Seminar
Dr. Allison Malcolm
Massachusetts Institute of Technology
Title: A series approach to multiply scattered waves in inverse problems
Location: Amos Eaton 402
Time: 4:00PM -5:00 PM
Host: Margaret Cheney

In many wave problems, it is assumed that waves propagate away from the source, reflect once in the region of interest and continue directly to the receiver.  This assumption is known as the single scattering assumption and it is ubiquitous because it linearizes the inverse problem.  In many situations, however, multiply scattered waves make up a non-negligible portion of the recorded signal. Treating these waves as singly scattered waves results in artifacts in the final image.   We have studied a series approach to modeling specifically seismic reflection data in which multiply scattered waves are identified through higher-order terms in the series.  By understanding both modeling and imaging in this framework we are able to predict these artifacts.  The same series, when modified to account for illumination effects allows for image improvements, using the information contained in multiply scattered waves, by solving a sequence of linear inverse problems.


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