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Information Center for Mathematical Science

PAC

Information Center for Mathematical Science

PAC

Solving Quadratic Equations via PhaseLift when There Are About As Many Equations As Unknowns
Author Emmanuel J. Candes (Stanford University)
Homepage Url http://www-stat.stanford.edu/~candes/publications.html
Coauthors Xiaodong Li
Abstract This note shows that we can recover any complex vector x0 2 Cn exactly from on the order of n quadratic equations of the form jhai; x0ij2 = bi, i = 1; : : : ;m, by using a semide nite 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. Further, we show that exact recovery holds for all input vectors simultaneously, and also demonstrate optimal recovery results from noisy quadratic measurements; these results are much sharper than previously known results
Abstract Url http://www-stat.stanford.edu/~candes/papers/ImprovedPL.pdf