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One important property of imaging modalities and related applications is theresolution of image reconstructions which relies on various factors such asinstrumentation or data processing. Restrictions in resolution can havemanifold origins, e.g., limited resolution of available data, noise level inthe data, and/or inexact model operators. In this work we investigate a noveldata processing approach suited for inexact model operators. Here, twodifferent information sources, high-dimensional model information andhigh-quality measurement on a lower resolution, are comprised in a hybridapproach. The joint reconstruction of a high resolution image and parameters ofthe imaging operator are obtained by minimizing a Tikhonov-type functional. Thehybrid approach is analyzed for bilinear operator equations with respect tostability, convergence, and convergence rates. We further derive an algorithmicsolution exploiting an algebraic reconstruction technique. The study iscomplemented by numerical results ranging from an academic test case to imagereconstruction in magnetic particle imaging.

inverse problems

Joint super-resolution image reconstruction and parameter identification  in imaging operator: Analysis of bilinear operator equations, numerical  solution, and application to magnetic particle imaging