Beyond its theoretical contribution, this work also has signicant practical impact. It provides new and important insight into how to adapt and optimize the performance of compressed sensing in practical applications. It introduces a new generation of sampling strategies based on multilevel random sampling which are both theoretically optimal and outperform previous state-of-the-art approaches in practice. It has led to new approaches in MRI, NMR, uorescence microscopy and helium atom scattering which offer signicant performance gains.
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