REGULARIZATION OF ILL-POSED PROBLEMS BY ENVELOPE GUIDED CONJUGATE GRADIENTS

We propose a new way to iteratively solve large scale ill-posed proble ms by exploiting the relation between Tikhonov regularization and mult iobjective optimization to obtain, iteratively, approximations to the Tikhonov L-curve and its corner. Monitoring the change of the approxim ate L-curves allows us to adjust the regularization parameter adaptive ly during a preconditioned conjugate gradient iteration, so that the d esired solution can be reconstructed with a low number of iterations. We apply the technique to an idealized image reconstruction problem in positron emission tomography.