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Correlated imaging offers great potentiality, with respect to standard imaging, to obtain the imaging of objects located in optically harsh or noisy environment. It can solve the problems which are difficult to solve by conventional imaging techniques. Recently, it has become one of the hot topics in quantum optics. In this paper, we propose a new scheme of correlated imaging with differential correlated imaging based on compressive sensing, named differential compressive correlated imaging. The new scheme takes advantage of the high signal-to-noise ratio of the differential correlated imaging and low-imaging sampling frequency of the compressed sensing technique. In the scheme, we utilize the intensity of the thermal light, which is in line with the Gaussian distribution, as the measurement matrix of compressive sensing. We extract the differential object information as the image object information which could be recovered via orthogonal matching pursuit algorithm with high quality. By numerical simulations, we verify the proposed scheme. Here, we select the two gray-scale images, such as double-slit and NUPT, as well as the two multi-grayscale images (Lena and Boats) as the object. We take sampling 350 times in differential compressive correlated imaging for measurement. The numerical simulation results show that for the above image objects, the average mean-square error (MSE) over 10 times for the differential compressive correlated imaging scheme is reduced by 97.7%, 93.9%, 92.5% and 71.4% respectively with respect to that of the differential correlated imaging scheme. Moreover, compared with the compressive ghost imaging, the MSE value of the same double-slit in CDGI, as well as Lena and Boats under the same conditions, is reduced by 50.4%, 72.9% and 66.8% separately, which indicates that the compressive differential correlated imaging scheme can greatly improve the signal-to-noise ratio of the imaging, and significantly reduce the imaging time.
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Keywords:
- correlated imaging /
- differential /
- compressive sensing /
- mean square error
[1] Pittman T B, Shih Y H, Strekalov D V, Sergienko A V 1995 Phys. Rev. A 52 R3429
[2] Klyshko D N 1988 Sov. Phys. JETP 67 1131
[3] Gatti A, Brambilla E, Bache M, Lugiato L A 2004 Phys. Rev. Lett. 93 093602
[4] Ferri F, Magatti D, Gatti A, Bache M, Brambilla E, Lugiato L A 2005 Phys. Rev. Lett. 94 183602
[5] Gatti A, Bache M, Magatti D, Brambilla E, Ferri F, Lugiato L A 2006 J. Mod. Opt. 53 739
[6] Gatti A, Bondani M, Lugiato L A, Paris M G A, Fabre C 2007 Phys. Rev. Lett. 98 039301
[7] Shih Y H 2007 IEEE Sel. Top. Quan. Elec. 13 1016
[8] Zhang E F, Dai H Y, Chen P X 2011 Chin. Phys. B 20 024201
[9] Tian N, Guo Q C, Wang A L, Xu D L, Fu L 2011 Opt. Lett. 36 3302
[10] Bai Y F, Yang W X, Yu X Q 2012 Chin. Phys. B 21 044206
[11] Cheng J, Han S S 2004 Phys. Rev. Lett. 92 093903
[12] Cheng J, Han S S, Yan Y J 2006 Chin. Phys. 15 2002
[13] Zhang M H, Wei Q, Shen X, Liu Y F, Liu H L, Cheng J, Han S S 2007 Phys. Rev. A 75 021803
[14] Shen X, Bai Y F, Qin T, Han S S 2008 Chin. Phys. Lett. 25 3968
[15] Karmakar S, Zhai Y H, Chen H, Shih Y H 2011 Quantum Electronics and Laser Science Conference Baltimore, USA May 1-6, 2011 p1
[16] Chen X H, Liu Q, Luo K H, Wu L A 2009 Opt. Lett. 34 695
[17] Zhang E F, Dai H Y 2011 Acta Phys. Sin. 60 064209 (in Chinese) [张二峰, 戴宏毅 2011 物理学报 60 064209]
[18] Zhang P L, Gong W L, Shen X, Han S S 2010 Phys. Rev. A 82 033817
[19] Meyers R E, Deacon K S, Shih Y H 2011 Appl. Phys. Lett. 98 111115
[20] Liu Q, Luo K H, Chen X H, Wu L A 2010 Chin. Phys. B 19 094211
[21] Brida G, Degiovanni I P, Fornaro G A, Genovese M, Meda A 2011 Int. J. Quant. Inf. 9 341
[22] Li H G, Zhang Y T, Cao D Z, Xiong J, Wang K G 2008 Chin. Phys. B 17 4510
[23] Xiong J, Li H G, Sun X J, Lin L F, Wang K G 2006 Chin. Phys. 15 2942
[24] Zhang Y T, He C J, Li H G, Wang K G 2008 Chin. Phys. Lett. 25 2481
[25] Lu M H, Shen X, Han S S 2011 Acta Opt. Sin. 31 0711002 (in Chinese) [陆明海, 沈夏, 韩申生 2011 光学学报 31 0711002]
[26] Shechtman Y, Gazit S, Szameit A, Eldar Y C, Segev M 2010 Opt. Lett. 35 1148
[27] Du J, Gong W L, Han S S 2012 Opt. Lett. 37 1067
[28] Gong W L, Han S S 2012 Phys. Lett. A 376 1519
[29] Wang H, Han S S 2012 Euro. Phys. Lett. 98 24003
[30] Liu J Y, Zhu J B, Lu C, Huang S S 2010 Opt. Lett. 35 1206
[31] Gong W L, Han S S 2010 Phys. Lett. A 374 1005
[32] Gong W L, Han S S 2011 Opt. Lett. 36 394
[33] Bromberg Y, Katz O, Silberberg Y 2009 Phys. Rev. A 79 053840
[34] Ferri F, Magatti D, Lugiato L A, Gatti A 2010 Phys. Rev. Lett. 104 253603
[35] Donoho D L 2006 IEEE Trans. Inform. Theory 52 1289
[36] Baraniuk R G 2007 IEEE Sig. Proc. Mag. 24 118
[37] Candés E J, Wakin M B 2008 IEEE Sig. Proc. Mag. 25 21
[38] Candés E J 2008 Comptes. Rendus Math. 346 589
[39] Lustig M, Donoho D, Pauly J M 2007 Magn. Reson. Med. 58 1182
[40] Bobin J, Starck J L, Ottensamer R 2008 IEEE Sel. Top. Sig. Proc. 2 718
[41] Chan W L, Charan K, Takhar D, Kelly K F, Baraniuk R G, Mittleman D M 2008 Appl. Phys. Lett. 93 121105
[42] Duarte M F, Davenport M A, Takhar D, Laske J N, Sun T, Kelly K F, Baraniuk R G 2008 IEEE Sig. Proc. Mag. 25 83
[43] Katz O, Bromberg Y, Silberberg Y 2009 Appl. Phys. Lett. 95 131110
[44] Glouber R J 1963 Phys. Rev. 130 2529
[45] Tropp J A, Gilbert A C 2007 IEEE Trans. Inform. Theory 53 4655
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[1] Pittman T B, Shih Y H, Strekalov D V, Sergienko A V 1995 Phys. Rev. A 52 R3429
[2] Klyshko D N 1988 Sov. Phys. JETP 67 1131
[3] Gatti A, Brambilla E, Bache M, Lugiato L A 2004 Phys. Rev. Lett. 93 093602
[4] Ferri F, Magatti D, Gatti A, Bache M, Brambilla E, Lugiato L A 2005 Phys. Rev. Lett. 94 183602
[5] Gatti A, Bache M, Magatti D, Brambilla E, Ferri F, Lugiato L A 2006 J. Mod. Opt. 53 739
[6] Gatti A, Bondani M, Lugiato L A, Paris M G A, Fabre C 2007 Phys. Rev. Lett. 98 039301
[7] Shih Y H 2007 IEEE Sel. Top. Quan. Elec. 13 1016
[8] Zhang E F, Dai H Y, Chen P X 2011 Chin. Phys. B 20 024201
[9] Tian N, Guo Q C, Wang A L, Xu D L, Fu L 2011 Opt. Lett. 36 3302
[10] Bai Y F, Yang W X, Yu X Q 2012 Chin. Phys. B 21 044206
[11] Cheng J, Han S S 2004 Phys. Rev. Lett. 92 093903
[12] Cheng J, Han S S, Yan Y J 2006 Chin. Phys. 15 2002
[13] Zhang M H, Wei Q, Shen X, Liu Y F, Liu H L, Cheng J, Han S S 2007 Phys. Rev. A 75 021803
[14] Shen X, Bai Y F, Qin T, Han S S 2008 Chin. Phys. Lett. 25 3968
[15] Karmakar S, Zhai Y H, Chen H, Shih Y H 2011 Quantum Electronics and Laser Science Conference Baltimore, USA May 1-6, 2011 p1
[16] Chen X H, Liu Q, Luo K H, Wu L A 2009 Opt. Lett. 34 695
[17] Zhang E F, Dai H Y 2011 Acta Phys. Sin. 60 064209 (in Chinese) [张二峰, 戴宏毅 2011 物理学报 60 064209]
[18] Zhang P L, Gong W L, Shen X, Han S S 2010 Phys. Rev. A 82 033817
[19] Meyers R E, Deacon K S, Shih Y H 2011 Appl. Phys. Lett. 98 111115
[20] Liu Q, Luo K H, Chen X H, Wu L A 2010 Chin. Phys. B 19 094211
[21] Brida G, Degiovanni I P, Fornaro G A, Genovese M, Meda A 2011 Int. J. Quant. Inf. 9 341
[22] Li H G, Zhang Y T, Cao D Z, Xiong J, Wang K G 2008 Chin. Phys. B 17 4510
[23] Xiong J, Li H G, Sun X J, Lin L F, Wang K G 2006 Chin. Phys. 15 2942
[24] Zhang Y T, He C J, Li H G, Wang K G 2008 Chin. Phys. Lett. 25 2481
[25] Lu M H, Shen X, Han S S 2011 Acta Opt. Sin. 31 0711002 (in Chinese) [陆明海, 沈夏, 韩申生 2011 光学学报 31 0711002]
[26] Shechtman Y, Gazit S, Szameit A, Eldar Y C, Segev M 2010 Opt. Lett. 35 1148
[27] Du J, Gong W L, Han S S 2012 Opt. Lett. 37 1067
[28] Gong W L, Han S S 2012 Phys. Lett. A 376 1519
[29] Wang H, Han S S 2012 Euro. Phys. Lett. 98 24003
[30] Liu J Y, Zhu J B, Lu C, Huang S S 2010 Opt. Lett. 35 1206
[31] Gong W L, Han S S 2010 Phys. Lett. A 374 1005
[32] Gong W L, Han S S 2011 Opt. Lett. 36 394
[33] Bromberg Y, Katz O, Silberberg Y 2009 Phys. Rev. A 79 053840
[34] Ferri F, Magatti D, Lugiato L A, Gatti A 2010 Phys. Rev. Lett. 104 253603
[35] Donoho D L 2006 IEEE Trans. Inform. Theory 52 1289
[36] Baraniuk R G 2007 IEEE Sig. Proc. Mag. 24 118
[37] Candés E J, Wakin M B 2008 IEEE Sig. Proc. Mag. 25 21
[38] Candés E J 2008 Comptes. Rendus Math. 346 589
[39] Lustig M, Donoho D, Pauly J M 2007 Magn. Reson. Med. 58 1182
[40] Bobin J, Starck J L, Ottensamer R 2008 IEEE Sel. Top. Sig. Proc. 2 718
[41] Chan W L, Charan K, Takhar D, Kelly K F, Baraniuk R G, Mittleman D M 2008 Appl. Phys. Lett. 93 121105
[42] Duarte M F, Davenport M A, Takhar D, Laske J N, Sun T, Kelly K F, Baraniuk R G 2008 IEEE Sig. Proc. Mag. 25 83
[43] Katz O, Bromberg Y, Silberberg Y 2009 Appl. Phys. Lett. 95 131110
[44] Glouber R J 1963 Phys. Rev. 130 2529
[45] Tropp J A, Gilbert A C 2007 IEEE Trans. Inform. Theory 53 4655
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