In single-pixel imaging or computational ghost imaging, the measurement matrix has a great impact on the performance of the imaging system, because it involves modulation of the optical signal and image reconstruction. The measurement matrix reported in the existing literatures is first binarized and then loaded onto the digital micro-mirror device (DMD) for optical modulation, that is, each pixel can only be modulated into on-off states. In this paper, we propose a digital grayscale modulation method for more efficient compressive sampling. On the basis of this, we demonstrate a single photon compressive imaging system. A control and counting circuit, based on field-programmable gate array (FPGA), is developed to control DMD to conduct digital grayscale modulation and count single-photon pulse output from the photomultiplier tube (PMT) simultaneously. The experimental results show that the imaging reconstruction quality can be improved by increasing the sparsity ratio properly and compressive sampling ratio (SR) of these gray-scale matrices. However, when the compressive SR and sparsity ratio are increased appropriately to a certain value, the reconstruction quality is usually saturated, and the imaging reconstruction quality of the digital grayscale modulation is better than that of binary modulation.
R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Physical Review Letters, 2004, 92(3): 033601.
Q. R. Yan, H. Wang, C. L. Yuan, B. Li, and Y. H. Wang, “Large-area single photon compressive imaging based on multiple micro-mirrors combination imaging method,” Optics Express, 2018, 26(15): 19080–19090.
W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, S. Q. Gao, G. J. Zhai, et al., “Single photon counting imaging system via compressive sensing,” Preprint arXiv, 2012: 1202.5866.
Y. S. Zhang, Y. Xiang, L. Y. Zhang, L. X. Yang, and J. Zhou, “Efficiently and securely outsourcing compressed sensing reconstruction to a cloud,” Information Sciences, 2019, 496(1): 150–160.
D. Liu, Q. S. Wang, Y. Zhang, X. Liu, J. Lu, and J. Sun, “FPGA-based real-time compressed sensing of multichannel EEG signals for wireless body area networks,” Biomedical Signal Processing and Control, 2019, 49(1): 221–230.
Z. Cui, J. L. Yang, S. D. Jiang, J. Li, L. Lin, and Y. Gu, “An infrared-small-target detection method in compressed sensing domain based on local segment contrast measure,” Infrared Physics & Technology, 2018, 93(1): 41–52.
W. Becker, A. Bergmann, M. A. Hink, K. König, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microscopy Research and Technique, 2004, 63(1): 58–66.
J. Romberg, “Imaging via compressive sampling,” IEEE Signal Processing Magazine, 2008, 25(2): 14–20.
M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, et al., “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine, 2008, 25(2): 83–91.
R. G. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Processing Magazine, 2007, 24(4): 118–121.
Q. Tong, Y. L. Jiang, H. Y. Wang, and L. Guo, “Image reconstruction of dynamic infrared single-pixel imaging system,” Optics Communications, 2018, 410: 35–39.
Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nature Communications, 2015, DOI: https://doi.org/10.1038/ncomms7225.
K. Taguchi and J. S. Iwanczyk, “Vision 20/20: Single photon counting x-ray detectors in medical imaging,” Medical Physics, 2013, DOI: https://doi.org/10.1118/1.4820371.
Y. Chen and Y. Chi, “Robust spectral compressed sensing via structured matrix completion,” IEEE Transactions on Information Theory, 2014, 60(10): 6576–6601.
M. J. Sun and J. M. Zhang, “Single-pixel imaging and its application in three-dimensional reconstruction: a brief review,” Sensors, 2019, DOI: https://doi.org/10.3390/s19030732.
M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, et al., “Single-pixel three-dimensional imaging with time-based depth resolution,” Nature Communications, 2016, 7(1): 429–430.
B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, et al., “3D computational imaging with single-pixel detectors,” Science, 2013, 340(6134): 844–847.
Y. Xiao, W. L. Gao, G. H. Zhang, and H. Zhang, “Compressed sensing based apple image measurement matrix selection,” International Journal of Distributed Sensor Networks, 2015, 11(7): 5 862–5 875.
Y. Yu, A. P. Petropulu, and H. V. Poor, “Measurement matrix design for compressive sensing based MIMO radar,” IEEE Transactions on Signal Processing, 2011, 59(11): 5338–5352.
V. Tiwari, P. P. Bansod, and A. Kumar, “Designing sparse sensing matrix for compressive sensing to reconstruct high resolution medical images,” Cogent Engineering, 2015, DOI: https://doi.org/10.1080/23311916.2015.1017244.
H. Nouasria and M. Et-tolba, “New constructions of Bernoulli and Gaussian sensing matrices for compressive sensing,” in 2017 International Conference on Wireless Networks and Mobile Communications (WINCOM), Morocco, December 25, 2017, pp. 1–6.
J. Ding, D. Bao, Q. Wang, X. He, H. Bai, and S. Li, “A novel multi-dictionary framework with global sensing matrix design for compressed sensing,” Signal Processing, 2018, 152(1): 69–78.
W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, G. J. Zhai, and Q. Zhao, “Single-photon compressive imaging with some performance benefits over raster scanning,” Physics Letters A, 2014, 378(45): 3406–3411.
X. F. Liu, W. K. Yu, X. R. Yao, B. Dai, L. Z. Li, C. Wang, et al., “Measurement dimensions compressed spectral imaging with a single point detector,” Optics Communications, 2016, 365: 173–179.
E. J. Candes, “The restricted isometry property and its implications for compressed sensing,” Comptes Rendus Mathematique, 2008, 346(9): 589–592.
Y. T. Chen and J. G. Peng, “Influences of preconditioning on the mutual coherence and the restricted isometry property of Gaussian/Bernoulli measurement matrices,” Linear and Multilinear Algebra, 2016, 64(9): 1750–1759.
H. Monajemi, S. Jafarpour, M. Gavish, Stat 330/CME 362 Collaboration, and D. L. Donoho, “Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices,” Proceedings of the National Academy of Sciences, 2013, 110(4): 1181–1186.
T. Huang, Y. Z. Fan, and M. Hu, “Compressed sensing based on random symmetric Bernoulli matrix,” in 2017 32nd Youth Academic Annual Conference of Chinese Association of Automation (YAC), China, May 19–21, 2017, DOI: https://doi.org/10.1109/YAC.2017.7967403.
D. Dudley, W. M. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proceedings of SPIE, 2003, DOI: f10.1117/12.480761.
K. Zhang, Y. Huang, J. Yan, and L. Sun, “Dynamic infrared scene simulation using grayscale modulation of digital micro-mirror device,” Chinese Journal of Aeronautics, 2013, 26(2): 394–400.
R. Höfling and E. Ahl, “ALP: Universal DMD controller for metrology and testing,” Proceedings of SPIE, 2004, DOI: 10.1117/12.528336.
This work was supported in part by the National Natural Science Foundation of China (Grants Nos. 61865010 and 61565012), in part by the China Postdoctoral Science Foundation (Grant No. 2015T80691), in part by the Science and Technology Plan Project of Jiangxi Province (Grant No. 20151BBE50092), and in part by the Funding Scheme to Outstanding Young Talents of Jiangxi Province (Grant No. 20171BCB23007).
About this article
Cite this article
Yuan, C., Yan, Q., Wu, Y. et al. Single Photon Compressive Imaging Based on Digital Grayscale Modulation Method. Photonic Sens (2020). https://doi.org/10.1007/s13320-020-0597-y
- Single photon imaging
- single pixel imaging
- measurement matrix
- grayscale modulation