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  1. ; ; ; ; (, Proceedings of the American Mathematical Society, Series B)
    Dilworth, Stephen (Ed.)
    A frame ( x j ) j ∈<#comment/> J (x_j)_{j\in J} for a Hilbert space H H is said to do phase retrieval if for all distinct vectors x , y ∈<#comment/> H x,y\in H the magnitudes of the frame coefficients ( | ⟨<#comment/> x , x j ⟩<#comment/> | ) j ∈<#comment/> J (|\langle x, x_j\rangle |)_{j\in J} and ( | ⟨<#comment/> y , x j ⟩<#comment/> | ) j ∈<#comment/> J (|\langle y, x_j\rangle |)_{j\in J} distinguish x x from y y (up to a unimodular scalar). A frame which does phase retrieval is said to do C C -stable phase retrieval if the recovery of any vector x ∈<#comment/> H x\in H from the magnitude of the frame coefficients is C C -Lipschitz. It is known that if a frame does stable phase retrieval then any sufficiently small perturbation of the frame vectors will do stable phase retrieval, though with a slightly worse stability constant. We provide new quantitative bounds on how the stability constant for phase retrieval is affected by a small perturbation of the frame vectors. These bounds are significant in that they are independent of the dimension of the Hilbert space and the number of vectors in the frame. 
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