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