Phase retrieval from coded diffraction patterns
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 intens...
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| Published in | Applied and computational harmonic analysis Vol. 39; no. 2; pp. 277 - 299 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.09.2015
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| Subjects | |
| Online Access | Get full text |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Soltanolkotabi, Mahdi Candès, Emmanuel J. Li, Xiaodong |
| Author_xml | – sequence: 1 givenname: Emmanuel J. surname: Candès fullname: Candès, Emmanuel J. organization: Departments of Mathematics and of Statistics, Stanford University, Stanford, CA, United States – sequence: 2 givenname: Xiaodong surname: Li fullname: Li, Xiaodong organization: Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, PA, United States – sequence: 3 givenname: Mahdi surname: Soltanolkotabi fullname: Soltanolkotabi, Mahdi organization: Department of Electrical Engineering, Stanford University, Stanford, CA, United States |
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| SubjectTerms | Convex optimization Diffraction Fourier transform Phase retrieval Random matrix theory |
| Title | Phase retrieval from coded diffraction patterns |
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