Stability of Phase Retrievable Frames
This addresses stability issues in phase retrieval for signal processing and imaging applications, but appears incremental as it builds on prior conjectures and constructions.
The paper tackles the problem of phase retrievability in redundant vector systems under perturbations, showing that if a frame set allows vector reconstruction from coefficient magnitudes, there exists a perturbation bound ensuring the same property for nearby frames, thereby proving stability for a recent construction.
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 $\fc$ 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 $\fc$ has the same property. In particular this proves the recent construction in \cite{BH13} is stable under perturbations. By the same token we reduce the critical cardinality conjectured in \cite{BCMN13a} to proving a stability result for non phase-retrievable frames.