Regularization by inexact Krylov methods with applications to blind deblurring

This paper is concerned with the regularization of large-scale discrete inverse problems by means of inexact Krylov methods. Specifically, we derive two new inexact Krylov methods that can be efficiently applied to unregularized or Tikhonov-regularized least squares problems, and we study their theoretical properties, including links with their exact counterparts and strategies to monitor the amount of inexactness. We then apply the new methods to separable nonlinear inverse problems arising in blind deblurring, where both the sharp image and the parameters defining the blur are unkown. When employing a variable projection method jointly with the new inexact solvers in this setting, the latter can naturally handle varying inexact blurring parameters while solving the linear deblurring subproblems, allowing for a much reduced number of total iterations and substantial computational savings with respect to their exact counterparts.


Read More: https://epubs.siam.org/doi/abs/10.1137/21M1402066