On the Absence of Uniform Recovery in Many Real-World Applications of Compressed Sensing and the Restricted Isometry Property and Nullspace Property in Levels
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The purpose of this paper is twofold. The first is to point out that the property of uniform recovery, meaning that all sparse vectors are recovered, does not hold in many applications where compressed sensing is successfully used. This includes fields like magnetic resonance imaging (MRI), nuclear magnetic resonance computerized tomography, electron tomography, radio interferometry, helium atom scattering, and fluorescence microscopy. We demonstrate that for natural compressed sensing matrices involving a level based reconstruction basis (e.g., wavelets), the number of measurements required to recover all
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Engineering and Physical Sciences Research Council (EP/H023348/1)
Engineering and Physical Sciences Research Council (EP/N014588/1)