Stability of Frames Which Give Phase Retrieval

Abstract

In this paper we study the property of phase retrievability by redundant sysems of vectors under perturbations of the frame set. Specifically we show that if a set F of m vectors in the complex Hilbert space of dimension n allows for vector reconstruction from magnitudes of its coefficients, then there is a perturbation bound ρ so that any frame set within ρ from F has the same property. In particular this proves a recent construction for the case m = 4n− 4 is stable under perturbations. Additionally we provide estimates of the stability radius.

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Cite this paper

@inproceedings{Balan2015StabilityOF, title={Stability of Frames Which Give Phase Retrieval}, author={Radu V. Balan}, year={2015} }