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Phase retrieval from coded diffraction patterns. (English) Zbl 1329.78056

Summary: This paper considers the question of recovering the phase of an object from intensity-only measurements, a problem which naturally appears in X-ray crystallography and related disciplines. We study a physically realistic setup where one can modulate the signal of interest and then collect the intensity of its diffraction pattern, each modulation thereby producing a sort of coded diffraction pattern. We show that PhaseLift, a recent convex programming technique, recovers the phase information exactly from a number of random modulations, which is polylogarithmic in the number of unknowns. Numerical experiments with noiseless and noisy data complement our theoretical analysis and illustrate our approach.

MSC:

78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
78A45 Diffraction, scattering
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
90C25 Convex programming
15B52 Random matrices (algebraic aspects)

Software:

PhaseLift; TFOCS
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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