Stable phase retrieval with low-redundancy frames
arXiv:1302.5487
Abstract
We investigate the recovery of vectors from magnitudes of frame coefficients when the frames have a low redundancy, meaning a small number of frame vectors compared to the dimension of the Hilbert space. We first show that for vectors in d dimensions, 4d-4 suitably chosen frame vectors are sufficient to uniquely determine each signal, up to an overall unimodular constant, from the magnitudes of its frame coefficients. Then we discuss the effect of noise and show that 8d-4 frame vectors provide a stable recovery if part of the frame coefficients is bounded away from zero. In this regime, perturbing the magnitudes of the frame coefficients by noise that is sufficiently small results in a recovery error that is at most proportional to the noise level.
12 pages AMSLaTeX, 1 figure
References in corpus (5)
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- On Lipschitz Analysis and Lipschitz Synthesis for the Phase Retrieval Problem
- Phase Retrieval using Lipschitz Continuous Maps
- Phase retrieval for the Cauchy wavelet transform