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[PAST EVENT] Colloquium: Fast and Accurate Tomography
April 12, 2013
3pm - 4pm
In tomography, we send signals through a medium, say human tissue, and based on measurements on the boundary we try to reconstruct important properties of the medium, say whether there is a tumor or not and where. This is a hard problem as the solution, the reconstruction of the medium, is generally not unique and does not depend continuously on the data. Moreover, as the measurements contain noise, an exact solution typically does not exist and a (nearly) exact solution would be spoiled by noise. We need to regularize the problem, and we need to take many measurements to obtain meaningful solutions.
To compute solutions, we derive a model of the system to simulate how a signal propagates through the medium depending on its properties and what the detectors should measure (the forward problem). Next we can optimize over the space of parameters that describe the medium to find the parameter set that best matches our measurements (the inverse problem). However, the objective function of this optimization problem involves the (expensive) simulation of the signal propagation for possibly thousands of signals. Hence an accurate reconstruction becomes very expensive. After an introduction to some of the complications of tomography, we describe some recent approaches to solve these problems much faster.
Bio: Eric de Sturler received his Ph.D. in 1994 at Delft University of Technology under the supervision of Henk van der Vorst. From 1993, he spent 5 years at ETH Zurich as (senior) research scientist at the Interdisciplinary Project Center for Supercomputing and the Swiss Center for Scientific Computing. He was a Leslie Fox prizewinner in 1997, and he spent the summer of 1997 visiting Stanford University at the invitation of Prof. Gene Golub. In 1998, he joined the faculty of the Department of Computer Science at the University of Illinois at Urbana-Champaign. He has been on faculty of the Mathematics Department at Virginia Tech since 2006. He was the Program Director of the SIAM Activity Group on Supercomputing from 2003 to 2006; he co-chaired the third SIAM Conference on Computational Science and Engineering in 2005; he was a general co-chair of the 13th IEEE International Conference on Computational Science and Engineering in 2010; and recently he was on the organizing committee of the SIAM Conference on Applied Linear Algebra in 2012. He has served as an editor for multiple journals, among others, for Applied Numerical Mathematics since 2005 and for SIAM Journal on Numerical Analysis from 2003 to 2009. He has given numerous invited addresses at conferences and institutes, among others at several Householder symposia, and he will be a plenary speaker at the 2013 international preconditioning conference at Oxford University.
To compute solutions, we derive a model of the system to simulate how a signal propagates through the medium depending on its properties and what the detectors should measure (the forward problem). Next we can optimize over the space of parameters that describe the medium to find the parameter set that best matches our measurements (the inverse problem). However, the objective function of this optimization problem involves the (expensive) simulation of the signal propagation for possibly thousands of signals. Hence an accurate reconstruction becomes very expensive. After an introduction to some of the complications of tomography, we describe some recent approaches to solve these problems much faster.
Bio: Eric de Sturler received his Ph.D. in 1994 at Delft University of Technology under the supervision of Henk van der Vorst. From 1993, he spent 5 years at ETH Zurich as (senior) research scientist at the Interdisciplinary Project Center for Supercomputing and the Swiss Center for Scientific Computing. He was a Leslie Fox prizewinner in 1997, and he spent the summer of 1997 visiting Stanford University at the invitation of Prof. Gene Golub. In 1998, he joined the faculty of the Department of Computer Science at the University of Illinois at Urbana-Champaign. He has been on faculty of the Mathematics Department at Virginia Tech since 2006. He was the Program Director of the SIAM Activity Group on Supercomputing from 2003 to 2006; he co-chaired the third SIAM Conference on Computational Science and Engineering in 2005; he was a general co-chair of the 13th IEEE International Conference on Computational Science and Engineering in 2010; and recently he was on the organizing committee of the SIAM Conference on Applied Linear Algebra in 2012. He has served as an editor for multiple journals, among others, for Applied Numerical Mathematics since 2005 and for SIAM Journal on Numerical Analysis from 2003 to 2009. He has given numerous invited addresses at conferences and institutes, among others at several Householder symposia, and he will be a plenary speaker at the 2013 international preconditioning conference at Oxford University.
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