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Multi-modality (or multi-channel) imaging is becoming increasingly important and more widely available, e.g. hyperspectral imaging in remote sensing, spectral CT in material sciences as well as multi-contrast MRI and PET-MR in medicine. Research in the last decades resulted in a plethora of mathematical methods to combine data from several modalities. State-of-the-art methods, often formulated as variational regularization, have shown to significantly improve image reconstruction both quantitatively and qualitatively. Almost all of these models rely on the assumption that the modalities are perfectly registered, which is not the case in most real world applications. We propose a variational framework which jointly performs reconstruction and registration, thereby overcoming this hurdle. Our approach is the first to achieve this for different modalities and outranks established approaches in terms of accuracy of both …