Parallel Multigrid Algorithms for Inverse Problems
Speaker: George Biros, Georgia Tech
Location: Warren Weaver Hall 1302
Date: March 11, 2011, 11:30 a.m.
Host: Denis Zorin
I will present algorithms for inverse problems governed by partial differential equations (PDEs). In practice, one is rarely content with performing a simulation of a physical or engineered system; sensitivity analysis, parameter estimation, and optimization are required for a complete analysis. For such problems, efficient algorithms are of paramount importance as every optimization iterations typically involves the solution of a PDE problem.
In the first part of my talk, I will describe one class of motivating applications: assimilation of biophysical models with Magnetic Resonance (MR) images. MR images can be used to drive least-squares problems to estimate unknown parameters in elastically deforming tissues. Similarly, biophysical models can be used as priors for statistical inference on images. Examples include analysis of brain images of patients with primary brain tumors and cardiac motion estimation using Cine-MR. In the second part of my talk, I will discuss fast parallel algorithms for the solution of these inverse problems. The main algorithmic ingredients are (1) multigrid schemes for nearly compact operators, and (2) parallel octree multiresolution representations. I will present results that demonstrate the excellent algorithmic and parallel scalability of these methods.
George Biros holds Associate Professor appointments with the Schools of Computational Science and Engineering at Georgia Tech and The Wallace H. Coulter Department of Biomedical Engineering at Georgia Tech and Emory University. Prior to joining Georgia Tech, he was an assistant professor in Mechanical Engineering and Applied Mechanics, Bioengineering and Computer and Information Science at the University of Pennsylvania. He received his BS in Mechanical Engineering from Aristotle University Greece (1995), his MS in Biomedical Engineering from Carnegie Mellon (1996), and his PhD in Computational Science and Engineering also from Carnegie Mellon (2000). He was a postdoctoral associate at the Courant Institute from 2000 to 2003.
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