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SUMMARY:A priorconditioned LSQR algorithm for linear ill-posed problems wi
 th edge-preserving regularization - Betcke\, M (University College London)
DTSTART:20140207T114500Z
DTEND:20140207T121500Z
UID:TALK50708@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-authors: Simon Arridge (University College London)\, Lauri 
 Harhanen (Aalto University) \n\nIn this talk we present a method for solvi
 ng large-scale linear inverse problems regularized with a nonlinear\, edge
 -preserving penalty term such as e.g. total variation or PeronaMalik. In t
 he proposed scheme\, the nonlinearity is handled with lagged diffusivity f
 ixed point iteration which involves solving a large-scale linear least squ
 ares problem in each iteration. The size of the linear problem calls for i
 terative methods e.g. Krylov methods which are matrix-free i.e. the forwar
 d map can be defined through its action on a vector. Because the convergen
 ce of Krylov methods for problems with discontinuities is notoriously slow
 \, we propose to accelerate it by means of priorconditioning. Priorconditi
 oning is a technique which embeds the information contained in the prior (
 expressed as a regularizer in Bayesian framework) directly into the forwar
 d operator and hence into the solution space. We derive a factorization-fr
 ee priorconditioned LSQR algorithm\, allowing implicit ap plication of the
  preconditioner through efficient schemes such as multigrid. We demonstrat
 e the effectiveness of the proposed scheme on a three-dimensional problem 
 in fluorescence diffuse optical tomography using algebraic multigrid preco
 nditioner.\n
LOCATION:Seminar Room 1\, Newton Institute
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