Fast reconstructed and high-quality ghost imaging with fast Walsh–Hadamard transform
In this paper, we propose a ghost imaging scheme with fast Walsh–Hadamard transform, named GIFWHT. In the scheme, Walsh–Hadamard pattern pairs are used to illuminate an object to generate pairs of detection results, and the corresponding differential detection result is used as the result as that from the conventional bucket detector. By performing the fast Walsh–Hadamard transform on 2k (k is a positive integer) differential detection results, the image of the object can be recovered. The experimental and numerical simulation results show that the reconstruction time of GIFWHT is greatly reduced, and the quality of the recovered image is noticeably improved. In addition, GIFWHT is robust against interference from environmental illumination and could savememory.Network Technology, Ministry of Education (NYKL2015011).
基金项目：National Natural Science Foundation of China (NSFC) (61271238, 61475075); Open research fund of Key Lab of Broadband Wireless Communication and Sensor
Shengmei Zhao：Institute of Signal Processing and Transmission, Nanjing University of Posts and Telecommunications (NUPT), Nanjing 210003, China
【1】S. M. Zhao, H. Yang, Y. Q. Li, F. Cao, Y. B. Sheng, W. W. Cheng, and L. Y. Gong, “The influence of atmospheric turbulence on holographic ghost imaging using orbital angular momentum entanglement: simulation and experimental studies,” Opt. Commun. 294, 223–228 (2013).
【2】N. Radwell, K. J. Mitchell, G. M. Gibson, M. P. Edgar, R. Bowman, and M. J. Padgett, “Single-pixel infrared and visible microscope,” Optica 1, 285–289 (2014).
【3】D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ‘ghost’ interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
【4】X. Gu and S. M. Zhao, “Nonorthogonal object identification based on ghost imaging,” Photon. Res. 3, 238–242 (2015).
【5】R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Two-photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
【6】R. Liu, A. Fang, Y. Zhou, P. Zhang, S. Gao, H. Li, H. Gao, and F. Li, “Enhanced visibility of ghost imaging and interference using squeezed thermal light,” Phys. Rev. A 93, 013822 (2016).
【7】X. Li, C. Deng, M. Chen, W. Gong, and S. Han, “Ghost imaging for an axially moving target with an unknown constant speed,” Photon. Res. 3, 153–157 (2015).
【8】D. J. Zhang, H. G. Li, Q. L. Zhao, S. Wang, H. B. Wang, J. Xiong, and K. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92, 013823 (2015).
【9】E. F. Zhang, W. T. Liu, and P. X. Chen, “Ghost imaging with nonnegative exponential speckle patterns,” J. Opt. 17, 085602 (2015).
【10】W. Gong, “High-resolution pseudo-inverse ghost imaging,” Photon. Res. 3, 234–237 (2015).
【11】X. F. Liu, X. H. Chen, X. R. Yao, W. K. Yu, G. J. Zhai, and L. A. Wu, “Lensless ghost imaging with sunlight,” Opt. Lett. 39, 2314–2317 (2014).
【12】L. Nie, Y. Bai, and X. Fu, “Ghost telescope imaging system from the perspective of coherent-mode representation,” Opt. Commun. 358, 88–91 (2016).
【13】Y. Yang, J. Shi, F. Cao, J. Peng, and G. Zeng, “Computational imaging based on time-correlated single-photon-counting technique at low light level,” Appl. Opt. 54, 9277–9283 (2015).
【14】J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802(R) (2008).
【15】S. M. Zhao, L. Wang, W. Q. Liang, W. W. Cheng, and L. Y. Gong, “High performance optical encryption based on computational ghost imaging with QR code and compressive sensing technique,” Opt. Commun. 353, 90–95 (2015).
【16】S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear Stokes imaging with single-pixel detectors,” J. Opt. 17, 025705 (2015).
【17】Z. Zhang, X. Ma, and J. S. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 6225–6230 (2015).
【18】Y. A. Geadah and M. J. G. Corinthios, “Natural, dyadic, and sequency order algorithms and processors for the Walsh-Hadamard transform,” IEEE Trans. Comput. C-26, 435–442 (1977).
【19】M. Corinthios, Signals, Systems, Transforms, and Digital Signal Processing with MATLAB (CRC Press, 2009).
【20】W. K. Yu, X. R. Yao, X. F. Liu, L. Z. Li, and G. J. Zhai, “Threedimensional single-pixel compressive reflectivity imaging based on complementary modulation,” Appl. Opt. 54, 363–367 (2015).
Le Wang and Shengmei Zhao, "Fast reconstructed and high-quality ghost imaging with fast Walsh–Hadamard transform," Photonics Research 4(6), 240-244 (2016)