In this paper we study the property of phase retrievability by redundant systems 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 the recent construction in¹⁵ is stable under perturbations. By the same token we reduce the critical cardinality conjectured in¹¹ to proving a stability result for non phase-retrievable frames.

Date Published: 26 September 2013
PDF: 10 pages
Proc. SPIE 8858, Wavelets and Sparsity XV, 88580H (26 September 2013); doi: 10.1117/12.2026135

Published in SPIE Proceedings Vol. 8858:
Wavelets and Sparsity XV
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)