Phase retrieval from coded diffraction patterns

被引:295
作者
Candes, Emmanuel J. [1 ,2 ]
Li, Xiaodong [3 ]
Soltanolkotabi, Mandi [4 ]
机构
[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA
[2] Stanford Univ, Dept Stat, Stanford, CA 94305 USA
[3] Univ Penn, Wharton Sch, Dept Stat, Philadelphia, PA 19104 USA
[4] Stanford Univ, Dept Elect Engn, Stanford, CA 94305 USA
关键词
Phase retrieval; Diffraction; Fourier transform; Convex optimization; Random matrix theory; RECONSTRUCTION; CONVEX; COEFFICIENTS;
D O I
10.1016/j.acha.2014.09.004
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码:277 / 299
页数:23
相关论文
共 54 条
[1]  
Ahmed A., 2012, ARXIV12115608
[2]  
Alexeev B., 2012, ARXIV12107752
[3]  
[Anonymous], 2011, IFAC P, DOI DOI 10.3182/20120711-3-BE-2027.00415
[4]  
Arkadi Nemirovski AharonBen-Tal., 2001, Lectures on Modern Convex Optimization
[5]   Interior gradient and proximal methods for convex and conic optimization [J].
Auslender, A ;
Teboulle, M .
SIAM JOURNAL ON OPTIMIZATION, 2006, 16 (03) :697-725
[6]  
Balan R., 2009, INT C SAMPL THEOR AP
[7]  
Balan R., 2013, ARXIV13084718
[8]  
Balan R., 2010, INFORM SCI SYSTEMS C, P1
[9]  
Balan R., 2012, ARXIV12071134
[10]  
Balan R., 2013, ARXIV13085465