compressed sensing and matrix completion

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Nowadays we frequently encounter sensors generating high-dimensional data that make sampling by traditional ways difficult or even entirely impossible. Compressed sensing and matrixcompletion are techniques where data is acquired at the data information rate rather than what would be expected by its ambient dimension.The main goal of the project is to extend these techniques to higher dimensions and heterogeneous data.The first part of the project is concerned with sparse plus low rank models applied to hyperspectral imaging. Correlations in the hyperspectral images will be used to under-sample the tensor and then reconstruct it by optimising over the space of low tensor rank plus sparse innovations. We will consider a specific type of subsampling based on the use of mosaic filters. The aim is to understand what filter/image combination allow successful reconstruction, which couldpotentially lead to practical methods for compressive multispectral imaging, which is also of interest to Selex ES.The second part of the project will extend the aforementioned models to heterogeneous data types where disparate data of a common object is combined for reconstruction and/or classification.This project falls within the EPSRC Numerical Analysis research area.