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Spring 2008 Seminars Thursday, February 14, 2008
Thursday, March 27, 2008 Abstract: 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 Abstract: 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 Abstract: 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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