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Single-pixel imaging has become a topic of intense interest amongst theoreticians and experimentalists in recent years, and is still attracting great attention due to its potential applications in biomedical imaging, remote sensing, defence monitoring, etc. Two main fields should be involved in single-pixel imaging scheme: single-pixel camera and computational quantum imaging, which are proposed in the year 2006 and 2008, respectively. Although these two single-pixel imaging schemes belong to different research fields, they are nearly identical in the realization setup and using the similar image recovering algorithm. The single-pixel camera scheme is mainly based on compressive sensing algorithms, which can recover the image with about 30 percent measurements of its total pixels (raster scan method), but need the prior knowledge of the image. While the computational quantum imaging method usually recovers the image by using the second-order correlation function, which is computational fast but need more measurements to retrieve a high quality image. Thus, both the methods mentioned above are time consuming. In this paper, a single-pixel imaging scheme based on Walsh-Hadamard transform is proposed and is demonstrated both theoretically and experimentally. The retrieving times of different algorithms are discussed and compared with each other. An image of 10241024 pixels can be acquired around 1 second with our method while it will take 8 seconds by using TVAL3 algorithm on the general computer in our numerical simulation experiment. It is also experimentally demonstrated that the nature targets from 500 meters to 5000 meters away are acquired, with pixels of 128128 and in the waveband of 350-900 nm, and the speed of the imaging frame rate is achieved at 0.5 frame per second. The differences and commons between single-pixel imaging and computational quantum imaging are also discussed in this article. It is found that the Walsh-Hadamard transform we proposed is stable and can be sufficiently saving the imaging time of the single-pixel imaging schemes while maintaining a high imaging quality. Moreover, the single-pixel remote imaging scheme can be used in other wave band such as infrared and micro wave imaging, or will be useful in the case when the array detector technique is difficult to meet the requirements such as the sensitivity or the volume. And our scheme proposed here can make the single-pixel imaging technique step further toward its real applications.
[1] Pittman T B, Shih Y H, Strekalov D V, Sergienko A V 1995 Phys. Rev. A 52 83429
[2] Strekalov D V, Sergienko A V, Klyshko D N, Shih Y H 1995 Phys. Rev. Lett. 74 3600
[3] Abouraddy A F, Saleh B E A, Sergienko A V, Teich M C 2001 Phys. Rev. Lett. 87 123602
[4] Bennink R S, Benley S J, Boyd R W 2002 Phys. Rev. Lett. 89 113601
[5] Chan K W C 2012 Opt. Lett. 37 2739
[6] Shapiro J H 2008 Phys. Rev. A 76 061802
[7] Duarte M, Davenport M, Takhar D, Laska J, Sun T, Kelly K, Baraniuk R 2008 IEEE Signal Process. Mag. 25 83
[8] Gatti A, Brambilla E, Bache M, Lugiato L A 2004 Phys. Rev. Lett. 93 093602
[9] Donoho D 2006 IEEE Trans. Inform. Theory 52 1289
[10] Cheng J, Han S S 2004 Phys. Rev. Lett. 92 093903
[11] Gong W L, Han S S 2009 arXiv preprint arXiv:0911.4750
[12] Yao X R, Li L Z, Liu X F, Yu W K, Zhai G J 2015 Chin. Phys. B 24 044203
[13] Bai Y F, Yang W X, Yu X Q 2012 Chin. Phys. B 21 044206
[14] Cands E J 2006 in Proc. Int. Cong. Math., European Mathematical Society, Madrid, Spain 3 1433
[15] Romberg J 2008 IEEE Signal Process. Mag. 25 14
[16] Beer T 1981 Am. J. Phys. 49 Issue 5
[17] Li Q, Zhou M L, Shi B C, Wang N C 1998 Chin. Sci. Bull. 43 627
[18] Xing S H, Yang Y D, Wang X H 2015 Navigtion and Control 14 97 (in Chinese) [邢世宏, 杨晓东, 王小海 2015 导航与控制 14 97]
[19] Welsh S S, Edgar M P, Bowman R, Jonathan P, Sun B Q, Padgett M J 2013 Opt. Express 21 23068
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[1] Pittman T B, Shih Y H, Strekalov D V, Sergienko A V 1995 Phys. Rev. A 52 83429
[2] Strekalov D V, Sergienko A V, Klyshko D N, Shih Y H 1995 Phys. Rev. Lett. 74 3600
[3] Abouraddy A F, Saleh B E A, Sergienko A V, Teich M C 2001 Phys. Rev. Lett. 87 123602
[4] Bennink R S, Benley S J, Boyd R W 2002 Phys. Rev. Lett. 89 113601
[5] Chan K W C 2012 Opt. Lett. 37 2739
[6] Shapiro J H 2008 Phys. Rev. A 76 061802
[7] Duarte M, Davenport M, Takhar D, Laska J, Sun T, Kelly K, Baraniuk R 2008 IEEE Signal Process. Mag. 25 83
[8] Gatti A, Brambilla E, Bache M, Lugiato L A 2004 Phys. Rev. Lett. 93 093602
[9] Donoho D 2006 IEEE Trans. Inform. Theory 52 1289
[10] Cheng J, Han S S 2004 Phys. Rev. Lett. 92 093903
[11] Gong W L, Han S S 2009 arXiv preprint arXiv:0911.4750
[12] Yao X R, Li L Z, Liu X F, Yu W K, Zhai G J 2015 Chin. Phys. B 24 044203
[13] Bai Y F, Yang W X, Yu X Q 2012 Chin. Phys. B 21 044206
[14] Cands E J 2006 in Proc. Int. Cong. Math., European Mathematical Society, Madrid, Spain 3 1433
[15] Romberg J 2008 IEEE Signal Process. Mag. 25 14
[16] Beer T 1981 Am. J. Phys. 49 Issue 5
[17] Li Q, Zhou M L, Shi B C, Wang N C 1998 Chin. Sci. Bull. 43 627
[18] Xing S H, Yang Y D, Wang X H 2015 Navigtion and Control 14 97 (in Chinese) [邢世宏, 杨晓东, 王小海 2015 导航与控制 14 97]
[19] Welsh S S, Edgar M P, Bowman R, Jonathan P, Sun B Q, Padgett M J 2013 Opt. Express 21 23068
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