The Importance of Phase in Complex Compressive Sensing

@article{Jacques2021TheIO,
  title={The Importance of Phase in Complex Compressive Sensing},
  author={Laurent Jacques and Thomas Feuillen},
  journal={IEEE Transactions on Information Theory},
  year={2021},
  volume={67},
  pages={4150-4161}
}
We consider the question of estimating a real low-complexity signal (such as a sparse vector or a low-rank matrix) from the phase of complex random measurements. We show that in this phase-only compressive sensing (PO-CS) scenario, we can perfectly recover such a signal with high probability and up to global unknown amplitude if the sensing matrix is a complex Gaussian random matrix and the number of measurements is large compared to the complexity level of the signal space. Our approach… 

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