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Traditional phase retrieval algorithm, which iteratively reconstructs the phase from 2-intensity measurement or 1-intensity measurement, requires Shannon sampling theorem to be satisfied. This could lead to more requirements for data storage when high resolution imaging is concerned. In order to lower the sampling budget, in this paper we purpose a compressed sensing based phase retrieval algorithm. Through 1-intensity measurement in Fourier plane, our improved Hybrid I/O algorithm is used to reconstruct the exact phase retribution of pure phase object. The algorighm proposed in this paper can reconstruct piecewise regular phase distributed pure phase object from far less amplitude measurements than ones for which the sampling theorem requires to be satisfied. The simulated data indicate that the algorithm has a good converge performance.
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Keywords:
- phase retrieval /
- compressed sensing
[1] Gerchberg R W, Saxton W O 1972 Optik 35 237
[2] Fienup J R 1982 Appl. Opt. 21 2758
[3] Yang G Z, Gu B Y 1981 Acta Phys. Sin. 30 410 (in Chinese) [杨国桢,顾本源1981 30 410]
[4] Candes E, Romberg J, Tao T 2006 IEEE Trans. Info. Theory 52 489
[5] Donoho D 2006 IEEE Trans. Info. Theory 52 1289
[6] Candes E, Tao T 2006 IEEE Trans. Info. Theory 52 5406
[7] Gehm M E, John R, Brady D J, Willett R M, Schulz T J 2007 Opt. Express 15 14013
[8] Moravec M L, Romberg J, Baraniuk R G 2007 Proc. SPIE 6701 670120
[9] Chan W, Moravec M, Baraniuk R G, Mittleman D 2008 Opt. Lett. 33 974
[10] Newton M C 2012 Phys. Rev. E 85 056706
[11] Roman P, Marathay A S 1963 Nuovo Cimento 30 1452
[12] Walther A 1963 Opt. Acta 10 41
[13] Wolf E 1962 Proc. Phys. Soc. London 80 1269
[14] Yu B, Peng X, Tian J D, Niu H B 2005 Acta Phys. Sin. 54 2034 (in Chinese) [于斌, 彭翔, 田劲东, 牛憨笨 2005 54 2034]
[15] Liao T H, Gao Q 2006 Chin. Phys. 15 347
[16] Cong W X, Chen N X, Gu B Y 1998 Chin. Phys. Lett. 15 24
[17] Zhou G Z, Dong Y J, Chen C, Ren Y Q, Wang Y D, Xiao T Q 2011 Acta Phys. Sin. 60 028701 (in Chinese) [周光照,佟亚军,陈灿,任玉琦,王玉丹,肖体乔 2011 60 028701]
[18] Candes E, Tao T 2005 IEEE Trans. Info. Theory 51 4203
[19] Rudin L I, Osher S, Fatemi E 1992 Physica D 60 259
[20] Chambolle A 2004 J. Math. Imaging. Vis. 20 89
[21] Stern A 2007 Opt. Lett. 32 3077
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[1] Gerchberg R W, Saxton W O 1972 Optik 35 237
[2] Fienup J R 1982 Appl. Opt. 21 2758
[3] Yang G Z, Gu B Y 1981 Acta Phys. Sin. 30 410 (in Chinese) [杨国桢,顾本源1981 30 410]
[4] Candes E, Romberg J, Tao T 2006 IEEE Trans. Info. Theory 52 489
[5] Donoho D 2006 IEEE Trans. Info. Theory 52 1289
[6] Candes E, Tao T 2006 IEEE Trans. Info. Theory 52 5406
[7] Gehm M E, John R, Brady D J, Willett R M, Schulz T J 2007 Opt. Express 15 14013
[8] Moravec M L, Romberg J, Baraniuk R G 2007 Proc. SPIE 6701 670120
[9] Chan W, Moravec M, Baraniuk R G, Mittleman D 2008 Opt. Lett. 33 974
[10] Newton M C 2012 Phys. Rev. E 85 056706
[11] Roman P, Marathay A S 1963 Nuovo Cimento 30 1452
[12] Walther A 1963 Opt. Acta 10 41
[13] Wolf E 1962 Proc. Phys. Soc. London 80 1269
[14] Yu B, Peng X, Tian J D, Niu H B 2005 Acta Phys. Sin. 54 2034 (in Chinese) [于斌, 彭翔, 田劲东, 牛憨笨 2005 54 2034]
[15] Liao T H, Gao Q 2006 Chin. Phys. 15 347
[16] Cong W X, Chen N X, Gu B Y 1998 Chin. Phys. Lett. 15 24
[17] Zhou G Z, Dong Y J, Chen C, Ren Y Q, Wang Y D, Xiao T Q 2011 Acta Phys. Sin. 60 028701 (in Chinese) [周光照,佟亚军,陈灿,任玉琦,王玉丹,肖体乔 2011 60 028701]
[18] Candes E, Tao T 2005 IEEE Trans. Info. Theory 51 4203
[19] Rudin L I, Osher S, Fatemi E 1992 Physica D 60 259
[20] Chambolle A 2004 J. Math. Imaging. Vis. 20 89
[21] Stern A 2007 Opt. Lett. 32 3077
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