Explicit Frames for Deterministic Phase Retrieval via PhaseLift

Phase Retrieval is the task of reconstructing a signal x ∈ Cn up to a phase from intensity measurements. In [1] it was shown that m ≥ 4n− 2 generic intensity measurements suffice to discriminate any two signals in Cn up to a phase. With a similar approach this result was slightly improved to m ≥ 4n− 4 in [8] 1. The bound m ≥ 4n− 4 is known to be close to optimal. More precisely, by relating phase retrieval to the problem of embedding complex projective space in Euclidean space, it was shown in [12] that, up to terms at most logarithmic in n,