Solving Quadratic Equations via PhaseLift when There Are About As Many Equations As Unknowns
Abstract
This note shows that we can recover a complex vector x in Cn exactly from on the order of n quadratic equations of the form |<ai, x>|2 = bi, i = 1, ..., m, by using a semidefinite program known as PhaseLift. This improves upon earlier bounds in [3], which required the number of equations to be at least on the order of n log n. We also demonstrate optimal recovery results from noisy quadratic measurements; these results are much sharper than previously known results.
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