Title: A new class of iterative regularization methods for inverse problems with non-negativity constraint
Speaker: Associate Professor Ye Zhang, Shenzhen MSU-BIT University
Abstract: In order to obtain a stable non-negative approximate solution, I will develop two novel non-negativity preserving iterative regularization methods.
In contrast to the projected Landweber iteration, which has only weak convergence w.r.t. noise for the regularized solution,
the newly introduced regularization methods exhibit the strong convergence. The convergence result for the imperfect forward model, as well as the convergence rates, are discussed.
Two new discrepancy principles are developed for a posteriori stopping of our iterative regularization algorithms.
As an application of new approaches, we consider a biosensor problem, which is modelled as a two dimensional Fredholm integral equation of the first kind.