New algorithms for iterative regularization and low rank matrix approximation with applications to large scale problems in geotomography and imaging
Sergey Voronin, Ph.D.
University of Colorado Boulder
Department of Applied Mathematics
Tuesday – March 29, 2016
10:00a.m. – 11:30a.m.
S&E II, Rm. 302
View candidate's talk live here.
Inverse problems in geotomography and imaging applications present two distinct challenges: the need for effective algorithms and penalization strategies to resolve multi-scale model features and overcome the effects of ill-conditioning; and the need to be able to apply these algorithms to very large data sets. To address these two challenges, we will first discuss novel iterative regularization algorithms using different penalization schemes, which are applicable to sparse wavelet-based model representations, useful for multi-scale data recovery. We will then present novel randomized algorithms for rapidly constructing various low rank approximations to a matrix, without prior knowledge of its rate of singular value decay. Finally, we will go on to discuss the application of low rank approximations to the construction of approximate but accurate regularized solutions and to imaging applications and describe the ongoing development of high performance numerical libraries for the new algorithms.
Sergey Voronin obtained his Ph.D. degree from the Program in Applied and Computational Mathematics at Princeton University, under the supervision of Prof. Ingrid Daubechies. Dr. Voronin was a CNRS postdoctoral fellow at Geoazur, University of Nice, working with Prof. Guust Nolet and is currently an instructor and research associate in the Department of Applied Mathematics, University of Colorado Boulder, working with Prof. Gunnar Martinsson.
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