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PhaseLift: Exact andStable SignalRecovery fromMagnitudeMeasurements viaConvex Programming Emmanuel J. CandèsThomas StrohmerVladislav Voroninski2012 год

PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming
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Аннотация: Abstract Suppose we wish to recover a signal \input amssym $\font\abc=cmmib10\def\bi#1{\hbox{\abc#1}} {\bi x} \in {\Bbb C}^n$ from m intensity measurements of the form $\font\abc=cmmib10\def\bi#1{\hbox{\abc#1}} |\langle \bi x,\bi z_i \rangle|^2$ , $i = 1, 2, \ldots, m$ ; that is, from data in which phase information is missing. We prove that if the vectors $\font\abc=cmmib10\def\bi#1{\hbox{\abc#1}}{\bi z}_i$ are sampled independently and uniformly at random on the unit sphere, then the signal x can be recovered exactly (up to a global phase factor) by solving a convenient semidefinite program–‐a trace‐norm minimization problem; this holds with large probability provided that m is on the order of $n {\log n}$ , and without any assumption about the signal whatsoever. This novel result demonstrates that in some instances, the combinatorial phase retrieval problem can be solved by convex programming techniques. Finally, we also prove that our methodology is robust vis‐à‐vis additive noise. © 2012 Wiley Periodicals, Inc.
Год издания: 2012
Авторы: Emmanuel J. Candès, Thomas Strohmer, Vladislav Voroninski
Издательство: Wiley
Источник: Communications on Pure and Applied Mathematics
Ключевые слова: Advanced X-ray Imaging Techniques, Optical measurement and interference techniques, Sparse and Compressive Sensing Techniques
Другие ссылки: Communications on Pure and Applied Mathematics (HTML)
arXiv (Cornell University) (PDF)
arXiv (Cornell University) (HTML)
arXiv (Cornell University) (PDF)
arXiv (Cornell University) (HTML)