Stability of phase retrievable frames

Radu Balan

doi:10.1117/12.2026135

26 September 2013 Stability of phase retrievable frames

Radu Balan

Proceedings Volume 8858, Wavelets and Sparsity XV; 88580H (2013) https://doi.org/10.1117/12.2026135
Event: SPIE Optical Engineering + Applications, 2013, San Diego, California, United States

Abstract

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.

Citation Download Citation

Radu Balan "Stability of phase retrievable frames", Proc. SPIE 8858, Wavelets and Sparsity XV, 88580H (26 September 2013); https://doi.org/10.1117/12.2026135

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