  We present and analyse an approach to image reconstruction problems with
imperfect forward models based on partially ordered spaces - Banach lattices.
In this approach, errors in the data and in the forward models are described
using order intervals. The method can be characterised as the lattice analogue
of the residual method, where the feasible set is defined by linear inequality
constraints. The study of this feasible set is the main contribution of this
paper. Convexity of this feasible set is examined in several settings and
modifications for introducing additional information about the forward operator
are considered. Numerical examples demonstrate the performance of the method in
deblurring with errors in the blurring kernel.
