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SUMMARY:Advancements in Hybrid Iterative Methods for Inverse Problems - Ju
 lianne Chung (Virginia Polytechnic Institute and State University)
DTSTART:20171031T163000Z
DTEND:20171031T172000Z
UID:TALK94126@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Hybrid iterative methods are increasingly being used to solve 
 large\, ill-posed inverse problems\, due to their desirable properties of 
 (1) avoiding semi-convergence\, whereby later reconstructions are no longe
 r dominated by noise\, and (2) enabling adaptive and automatic regularizat
 ion parameter selection.  In this talk\, we describe some recent advanceme
 nts in hybrid iterative methods for computing solutions to large-scale inv
 erse problems. First\, we consider a hybrid approach based on the generali
 zed Golub-Kahan bidiagonalization for computing Tikhonov regularized solut
 ions to problems where explicit computation of the square root and inverse
  of the covariance kernel for the prior covariance matrix is not feasible.
  This is useful for large-scale problems where covariance kernels are defi
 ned on irregular grids or are only available via matrix-vector multiplicat
 ion\, e.g.\, those from the Matern class. Second\, we describe flexible hy
 brid methods for solving l_p regularized inverse problems\, where we appro
 ximate the p-norm penalization term as a sequence of 2-norm penalization t
 erms using adaptive regularization matrices\, and we exploit flexible prec
 onditioning techniques to efficiently incorporate the weight updates.  We 
 introduce a flexible Golub-Kahan approach within a Krylov-Tikhonov hybrid 
 framework\, such that our approaches extend to general (non-square) l_p re
 gularized problems. Numerical examples from dynamic photoacoustic tomograp
 hy and space-time deblurring demonstrate the range of applicability and ef
 fectiveness of these approaches.   This is joint work with Arvind Saibaba\
 , North Carolina State University\, and Silvia Gazzola\, University of Bat
 h.
LOCATION:Seminar Room 1\, Newton Institute
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