Abstract 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.