Non-negativity preserving iterative regularization algorithms for ill-posed problems

Events

Presentation Name：	Non-negativity preserving iterative regularization algorithms for ill-posed problems
Presenter：	Ye Zhang
Date：	2019-11-22
Location：	光华东主楼1801
Abstract：	Many inverse problems are concerned with the estimation of non-negative parameters. In this talk, in order to obtain a stable non-negative approximate solution, we 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 our new approaches, we consider a biosensor problem, which is modelled as a two dimensional Fredholm integral equation of the first kind. Several numerical examples, as well as a comparison with the projected Landweber method, are given to show the accuracy and the acceleration effect of our new methods. For a real data problem, the developed methods can produce a meaningful featured regularization solution. 海报
Annual Speech Directory：	No.247

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