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Spring 2009 Seminars

Friday, February 13, 2009
Inverse Problems Seminar
Speaker: Edwin Marengo,
Department of Electrical and Computer Engineering, Northeastern University,
Main current areas are compressive sensing, signal subspace-based imaging, and electromagnetic theory.
Title: A New Theory of the Generalized Optical Theorem: Scalar, Vector
and Dyadic Field Systems
Location: Amos Eaton Rm 402
Time: 3:00-4:00 PM

New derivations and interpretations of the generalized optical cross-section theorem and of its particular manifestation, the ordinary optical theorem, are developed that are applicable to a variety of scalar, vector and dyadic source-field systems of interest in electromagnetic, optical and acoustic direct and inverse problems. The generalized optical theorem is discussed in a general theoretical framework that applies in general inhomogeneous propagating media, to arbitrary
excitation fields, and in general representational domains (Green function representation, plane wave expansion, multipole expansion, and so on). The derived technique is conceptually simple
and relies mostly on cross flux concepts and Greens function theory. Unlike the most familiar derivations of the optical theorem, it does not make use of the stationary phase method (Jones' lemma). Connections of the present new results to past known results on the optical theorem and its applications, and related areas in direct and inverse problems are indicated. This includes connection to and generalization to the full vector and dyadic regime of the so-called Porter-Bojarski integral equation which plays an important role in the theories of the inverse source problem and holography.

Edwin A. Marengo's online biography

Thursday, April 23rd
Inverse Problems Seminar
Speaker: Professor Assad Oberai
Department of Mechanical, Aerospace, and Nuclear Engineering
Title:Krylov subspace methods in focusing and imaging
Location: Amos Eaton Rm 402
Time: 4:00 PM

We consider the application of iterative methods based on computing the Krylov sub-
space of an operator in acoustic, or any other type of wave-based, focusing and imaging.
We treat the medium as an analog computer, and describe how it may be used to construct
the Krylov subspace of a desired operator. We consider two applications of this idea. The
first involves the use of Lanczos iterations in developing a new, iterative time-reversal algo-
rithm with optimal focusing properties. The second involves the use of Lanczos iterations
in developing a new, dynamic imaging algorithm based on multiple signal classification
(MUSIC) that requires fewer acoustic excitations and provides a new updated image with
each measurement.
This work has been done in collaboration with Prof. Paul Barbone at Boston University
and Dr. Gonzalo Feijoo at the Woods Hole Oceanographic Institute.


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