ROP inception: signal estimation with quadratic random sketching

@article{Delogne2022ROPIS,
  title={ROP inception: signal estimation with quadratic random sketching},
  author={R'emi Delogne and Vincent Schellekens and Laurent Jacques},
  journal={ArXiv},
  year={2022},
  volume={abs/2205.08225}
}
Rank-one projections (ROP) of matrices and quadratic random sketching of signals support several data processing and machine learning methods, as well as recent imaging applications, such as phase retrieval or optical processing units. In this paper, we demonstrate how signal estimation can be operated directly through such quadratic sketches--equivalent to the ROPs of the"lifted signal"obtained as its outer product with itself--without explicitly reconstructing that signal. Our analysis relies… 
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