(l_1,l_2)-RIP and Projected Back-Projection Reconstruction for Phase-Only Measurements
(2020) IEEE Signal Processing Letters — Vol. 27, n° 27, p. 396-400 (2020)
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- Authors
Feuillen, Thomas 
Davies, Mike E.
- Abstract
- 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 to the L1 -norm of the sparse signal measurements to their L2-norm. This property allows us to upper-bound the reconstruction error of PBP in the presence of phase noise. Monte Carlo simulations are performed to highlight the performance of our approach in this phase-only acquisition model when compared to error achieved by PBP in classical compressive sensing.
- Affiliations
Citations
Feuillen, T., Davies, M. E., Vandendorpe, L., & Jacques, L. (2020). (l_1,l_2)-RIP and Projected Back-Projection Reconstruction for Phase-Only Measurements. IEEE Signal Processing Letters, 27(27), 396-400. https://doi.org/10.1109/lsp.2020.2973506 (Original work published 2020)