  This article presents a method for solving large-scale linear inverse
problems regular- ized with a nonlinear, edge-preserving penalty term such as
the 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. 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
application of the preconditioner through efficient schemes such as multigrid.
The resulting method is matrix-free i.e. the forward map can be defined through
its action on a vector. We demonstrate the effectiveness of the proposed scheme
on a three-dimensional problem in fluorescence diffuse optical tomography using
algebraic multigrid preconditioner.
