Two new non-negativity preserving iterative regularization methods for ill-posed inverse problems

Many inverse problems are concerned with the estimation of non-negative parameter functions. In this paper, in order to obtain stable approximate solutions ill-posed linear operator equations a Hilbert space setting, we develop two novel non-negativity preserving iterative regularization methods. They based on fixed point iterations combination preconditioning ideas. contrast projected Landweber iteration, for which only weak convergence can be shown regularized solution when noise level tends zero, introduced methods exhibit strong convergence. There presented results, even noisy right-hand side and imperfect forward operators, one approaches there also rates results. Specifically adapted discrepancy principles used as posteriori stopping rules established algorithms. For an application suggested new approaches, consider biosensor problem, is modelled dimensional Fredholm integral equation first kind. Several numerical examples, well comparison method, show accuracy acceleration effect Case studies real data problem indicate that developed produce meaningful featured solutions.