($\ell _1,\ell _2$)-RIP and Projected Back-Projection Reconstruction for Phase-Only Measurements

  title={(\$\ell \_1,\ell \_2\$)-RIP and Projected Back-Projection Reconstruction for Phase-Only Measurements},
  author={Thomas Feuillen and Mike E. Davies and Luc Vandendorpe and Laurent Jacques},
  journal={IEEE Signal Processing Letters},
This letter analyzes the performances of a simple reconstruction method, namely the Projected Back-Projection (PBP), for estimating the direction of a sparse signal from its phase-only (or amplitude-less) complex Gaussian random measurements, i.e., an extension of one-bit compressive sensing to the complex field. To study the performances of this algorithm, we show that complex Gaussian random matrices respect, with high probability, a variant of the Restricted Isometry Property (RIP) relating… 

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