Multi-modality imaging with structure-promoting regularisers

Imaging with multiple modalities or multiple channels is becoming increasingly important for our modern society. A key tool for understanding and early diagnosis of cancer and dementia is PET-MR, a combined positron emission tomography and magnetic resonance imaging scanner which can simultaneously acquire functional and anatomical data. Similarly in remote sensing, while hyperspectral sensors may allow to characterise and distinguish materials, digital cameras offer high spatial resolution to delineate objects. In both of these examples, the imaging modalities can be considered individually or jointly. In this chapter we discuss mathematical approaches which allow to combine information from several imaging modalities so that multi-modality imaging can be more than just the sum of its components.