Invertibility and Robustness of Phaseless Reconstruction
arXiv:1308.4718
Abstract
This paper is concerned with the question of reconstructing a vector in a finite-dimensional real Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We analyze various Lipschitz bounds of the nonlinear analysis map and we establish theoretical performance bounds of any reconstruction algorithm. We show that robust and stable reconstruction requires additional redundancy than the critical threshold.
19 pages
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- Reconstruction of Signals from Magnitudes of Redundant Representations: The Complex Case
- On Lipschitz Analysis and Lipschitz Synthesis for the Phase Retrieval Problem
- Phase Retrieval using Lipschitz Continuous Maps