Vinzant's Conjecture on Phase Retrieval Injectivity
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part (1) of the conjecture
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analysis / Frame theory
Vinzant's Conjecture on Phase Retrieval Injectivity
Vinzant conjectured, in a form later restated by Bandeira, that the $4M-4$ threshold for injective complex phase retrieval is sharp. Part (1) holds: for $A \in \mathbb{C}^{N \times M}$ with $N = 4M-5$ and i.i.d. standard complex Gaussian entries, the phase retrieval map generated by $A$ fails to be injective with positive probability.
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Vinzant conjectured, in a form later restated by Bandeira, that the $4M-4$ threshold for injective complex phase retrieval is sharp. Part (1) holds: for $A \in \mathbb{C}^{N \times M}$ with $N = 4M-5$ and i.i.d. standard complex Gaussian entries, the phase retrieval map generated by $A$ fails to be injective with positive probability.
part (1) of the conjecture
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