Interplay between preconditioning and regularization for linear ill-posed problems solved by conjugate gradient. Application to optical flow estimation

This paper investigates the possibilities offered by combining regularization and preconditioning by the same symmetric positive semi-definite operator when solving ill-posed problems. We study the question of the stopping criterion, and the possibility offered by Ritz eigenelements for the a posteriori filtering of the solution and the tuning of Tikhonov's weight. The method is applied as the linear solver for an optical flow estimator and it is coupled with a subspace recycling strategy.