skip to content

A priorconditioned LSQR algorithm for linear ill-posed problems with edge-preserving regularization

Presented by: 
M Betcke University College London
Friday 7th February 2014 - 11:45 to 12:15
INI Seminar Room 1
Co-authors: Simon Arridge (University College London), Lauri Harhanen (Aalto University)

In this talk we present a method for solving large-scale linear inverse problems regularized with a nonlinear, edge-preserving penalty term such as e.g. total variation or Perona–Malik. In the proposed scheme, the nonlinearity is handled with lagged diffusivity fixed point iteration which involves solving a large-scale linear least squares problem in each iteration. The size of the linear problem calls for iterative methods e.g. Krylov methods which are matrix-free i.e. the forward map can be defined through its action on a vector. Because the convergence of Krylov methods for problems with discontinuities is notoriously slow, we propose to accelerate it by means of priorconditioning. Priorconditioning is a technique which embeds the information contained in the prior (expressed as a regularizer in Bayesian framework) directly into the forward operator and hence into the solution space. We derive a factorization-free priorconditioned LSQR algorithm, allowing implicit ap plication of the preconditioner through efficient schemes such as multigrid. We demonstrate the effectiveness of the proposed scheme on a three-dimensional problem in fluorescence diffuse optical tomography using algebraic multigrid preconditioner.

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons