Fundamental Limits of Weak Recovery with Applications to Phase Retrieval

In phase retrieval, we want to recover an unknown signal x ∈ C d from n quadratic measurements of the form y i = | ⟨ a i , x ⟩ | 2 + w i , where a i ∈ C d are known sensing vectors and w i is measurement noise. We ask the following weak recovery question: What is the minimum number of measurements n...

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