  One important property of imaging modalities and related applications is the
resolution of image reconstructions which relies on various factors such as
instrumentation or data processing. Restrictions in resolution can have
manifold origins, e.g., limited resolution of available data, noise level in
the data, and/or inexact model operators. In this work we investigate a novel
data processing approach suited for inexact model operators. Here, two
different information sources, high-dimensional model information and
high-quality measurement on a lower resolution, are comprised in a hybrid
approach. The joint reconstruction of a high resolution image and parameters of
the imaging operator are obtained by minimizing a Tikhonov-type functional. The
hybrid approach is analyzed for bilinear operator equations with respect to
stability, convergence, and convergence rates. We further derive an algorithmic
solution exploiting an algebraic reconstruction technique. The study is
complemented by numerical results ranging from an academic test case to image
reconstruction in magnetic particle imaging.
