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时空域联合编码扩频单光子计数成像方法

沈姗姗 顾国华 陈钱 何睿清 曹青青

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时空域联合编码扩频单光子计数成像方法

沈姗姗, 顾国华, 陈钱, 何睿清, 曹青青

Time-space united coding spread spectrum single photon counting imaging method

Shen Shan-Shan, Gu Guo-Hua, Chen Qian, He Rui-Qing, Cao Qing-Qing
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  • 本文结合空间编码单像素成像技术和扩频时间编码扫描成像技术, 提出一种时空域联合编码扩频单光子计数成像方法. 该方法具备可避免距离模糊、大时宽带宽积的优势, 并且在噪声干扰下, 能够准确恢复距离像. 本文推导了基于单光子探测的时空域联合相关非线性探测模型、成像正向模型和信噪比模型, 并通过凸优化反演算法恢复深度图像, 理论模型和仿真实验均证明, 与传统的基于空间编码的单像素成像方法相比, 本方法提高了重建的质量. 其中, 采用m序列作为时间编码, 成像的噪声鲁棒性更高. 和传统的空间编码单像素成像技术相比, 本文提出方法的成像均方误差降低了4/5, 引入二次相关方法后, 成像均方误差降低了9/10. 本文所提出的成像架构为非扫描激光雷达成像方法提供了新思路.
    In this paper, we demonstrate a new imaging architecture called time-space united coding spread spectrum single photon counting imaging technique by combining the space coding based single-pixel imaging technology and spread spectrum time coding based scanning imaging technology. This method has the advantages of range ambiguity-free and large time-bandwidth product. Under the interference of noise, this method can accurately restore depth images. In this work, the time-space united correlation nonlinear detection model based on single photon detection, forward imaging model and signal-to-noise ratio model is derived, and the depth image is restored by convex optimization inversion algorithm. The theoretical model and simulation experiments show that compared with the traditional single pixel imaging method based on spatial coding, this method improves the quality of scene reconstruction. Using m-sequence as time coding, imaging has higher noise robustness. In addition, compared with the traditional space coding single pixel imaging technology, the imaging mean square error of the proposed method is reduced by 4/5 and the imaging mean squared error is reduced by 9/10 after introducing the second correlated method. The proposed imaging architecture in this paper may provide a new path for non-scanning lidar imaging methods.
      通信作者: 沈姗姗, ssssoner@niit.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 62205144, 61905108, 62005128)、江苏省高等学校自然科学研究项目(批准号: 19KJB140010, 21KJB510049)和南京工业职业技术大学人才引进基金项目(批准号: YK-20-03-02, YK-20-03-03)资助的课题.
      Corresponding author: Shen Shan-Shan, ssssoner@niit.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 62205144, 61905108, 62005128), the Natural Science Research Project of Higher Education Institutions of Jiangsu Province, China (Grant Nos. 19KJB140010, 21KJB510049), and the Talent Introduction Foundation of Nanjing Vocational University of Industry Technology, China (Grant Nos. YK-20-03-02, YK-20-03-03).
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    Rehain P, Sua Y M, Zhu S Y, Dickson I, Muthuswamy B, Ramanathan J, Shahverdi A, Huang Y P 2020 Nat. Commun. 11 921Google Scholar

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    Tachella J, Altmann Y, Mellado N, McCarthy A, Tobin R, Buller G S, Tourneret J Y, McLaughlin S 2019 Nat. Commun. 10 4984Google Scholar

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    Brock J C, Purkis S J 2009 J. Coastal Res. 25 1Google Scholar

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    Howland G A, Lum D J, Ware M R, Howell J C 2013 Opt. Express 21 23822Google Scholar

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    Zhao Y N, Hou H Y, Han J C, Liu H C, Zhang S H, Cao D Z, Liang B L 2021 Opt. Lett. 46 4900Google Scholar

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    Radwell N, Johnson S D, Edgar M P, Higham C F, Murray-Smith R, Padget M J 2019 Appl. Phys. Lett. 115 231101Google Scholar

    [7]

    Li F Q, Chen H J, Pediredla A, Yeh C, He K, Veeraraghavan A, Cossairt O 2017 Opt. Express 11 31096

    [8]

    Liu X L, Shi J H, Sun L, Li Y H, Fan J P, Zeng G H 2020 Opt. Express 28 8132Google Scholar

    [9]

    Asmann A, Mota J F C, Stewart B D, Wallace A M 2019 IEEE Trans. Comput. Imaging 8 385

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    Misra P, Hu W, Yang M R, Duarte M, Jha S 2017 IEEE Trans. Mob. Comput. 16 2037Google Scholar

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    Krichel N J, McCarthy A, Buller G S 2010 Opt. Express 18 9192Google Scholar

    [12]

    Zhang Y F, He Y, Yang F, Luo Y, Chen W B 2016 Chin. Opt. Lett. 14 111101Google Scholar

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    Yu Y, Liu B, Chen Z 2018 Appl. Opt. 57 7733Google Scholar

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    Norman D M, Gardner C S 1988 Appl. Opt. 27 3650Google Scholar

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    Ding Y C, Wu H X, Gao X L, Wu B, Shen Y H 2022 J. Opt. Soc. Am. A 39 206

    [16]

    Hiskett P A, Parry C S, McCarthy A, Buller G S 2008 Opt. Express 16 13685Google Scholar

    [17]

    Yu Y, Liu B, Chen Z, Kang Li Z K 2020 Sensors 20 2204Google Scholar

    [18]

    Wu F, Yang L, Chen X L, Li Z H, Wu G 2022 Chin. Opt. Lett. 20 021202Google Scholar

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    Bioucas-Dias J M, Figueiredo M A T 2007 IEEE Trans. Image Process. 16 2992Google Scholar

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    Mandel L, Wolf E 1995 Optical Coherence and Quantum Optics (Cambridge: Cambridge University Press) p123

    [21]

    冒添逸, 陈钱, 何伟基, 庄佳衍, 邹云浩, 戴慧东, 顾国华 2016 物理学报 65 08427Google Scholar

    Mao T Y, Chen Q, He W J, Zhuang J Y, Zou Y H, Dai H D, Gu G H 2016 Acta Phys. Sin. 65 08427Google Scholar

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    Gatt P, Johnson S, Nichols T 2009 Appl. Opt. 48 3261Google Scholar

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    沈姗姗, 陈钱, 何伟基, 陈云飞, 尹文也, 戴慧东 2014 光学学报 34 1012001Google Scholar

    Shen S S, Chen Q, He W J, Chen Y F, Yin W Y, Dai H D 2014 Acta Opt. Sin. 34 1012001Google Scholar

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    Dai H D, Gu G H, He W J, Liao F J, Zhuang J Y, Liu Xiao J, Chen Q 2014 Appl. Opt. 53 6619Google Scholar

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    Zierler N, Siam J 1996 Electron. Commun. Eng. J. 1996 79

    [26]

    Molisch A F 2011 Wireless Communications (2nd Ed.) (New York: John Wiley & Sons Ltd.) p334

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    Shen S S, Chen Q, He W J, Gu G H 2020 Opt. Quantum Electron. 52 2020Google Scholar

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    Shen S S, Chen Q, He W J, Wang Y Q 2017 Chin. Opt. Lett. 15 090101Google Scholar

  • 图 1  时空域联合编码扩频单光子计数成像架构

    Fig. 1.  Time-space united coding spread spectrum single photon counting imaging method architecture.

    图 2  不同压缩比的时空域联合编码扩频单光子计数成像 (a) “飞机”深度真值; (b)−(g)不同压缩比的深度成像 (b) 5%, (c)15%, (d) 25%, (e) 45%, (f) 65%, (g) 85%. 颜色条表示深度数值, 单位为m

    Fig. 2.  Time-space united coding spread spectrum single photon counting image with different compression proportions: (a) Depth ground truth of ‘airplane’; (b)−(g) depth maps with different compression proportions of (b) 5%, (c)15%, (d) 25%, (e) 45%, (f) 65% and (g) 85%. Colorbars show the depth with unit of meter.

    图 3  时空域联合编码扩频单光子计数成像性能模拟 (a) 1码概率为0.1的伪随机序列深度图像; (b) 1码概率为0.3的伪随机序列深度图像; (c) Gold序列的深度图像; (d) m序列的深度图像; (e) 死时间对成像性能的影响理论模拟; (f) 死时间为200 ns; (g) 死时间为20 ns; (h) 死时间为1ns. 颜色条表示深度数值, 单位为m

    Fig. 3.  Time-space united coding image spread spectrum single photon counting imaging performance simulation: (a) Depth maps by pseudo-random sequences with ‘1’ bit of 0.1; (b) depth maps by pseudo-random sequences with ‘1’ bit of 0.3; (c) depth maps by Gold sequences; (d) depth maps by m-sequences; (e) theoretical simulation of dead time influence on imaging performance; (f) dead time is 200 ns; (g) dead time is 20 ns; (d) dead time is 1 ns. Colorbars show the depth information with unit of meter.

    图 4  不引入二次相关法的时空域联合编码扩频单光子计数深度成像, 码长为 (a) 2048, (b) 4096, (c) 8192, (d) 16384. 引入二次相关法的时空域联合编码扩频单光子计数深度图像, 码长为(e) 2048, (f) 4096, (g) 8192, (h)16384; (i) 传统的基于空间编码的单像素深度图像; (j) 引入二次相关法(点虚线)和不引入二次相关法(虚线)的深度MSE

    Fig. 4.  Time-space united coding image spread spectrum single photon counting imaging without second correlated method by code length of (a) 2048, (b) 4096, (c) 8192, (d)16384. Depth maps simulations with second correlated method by code length of (e) 2048, (f) 4096, (g) 8192 and (h) 16384. (i) Traditional single pixel imaging method based on space coding. (j) The depth MSE with second correlated method (dot dashed line) and without second correlated method (dashed line).

    图 5  成像边缘检测 (a) 不引入二次相关法的时空域联合编码扩频单光子成像边缘检测; (b) 引入二次相关法的时空域联合编码扩频单光子计数成像边缘检测; (c) 传统的基于空间编码的单像素成像边缘检测

    Fig. 5.  Image edge detection: (a) Time-space united coding spread spectrum single photon counting imaging without second correlated method image edge detection; (b) time-space united coding spread spectrum single photon counting imaging with second correlated method image edge detection; (c) traditional single pixel imaging method based on space coding image edge detection.

    图 6  单光子计数扫描成像测试图像深度重建仿真 (a) 玩偶深度真值; (b) $ {m_n} = 10 $, $ {\text{MSE = 0}}{\text{.176 m}} $, 传统的基于空间编码的单像素成像深度图; 在(c) ${m_{\rm{n}}} = 5$, $ {\text{MSE = 0}}{\text{.019 m}} $, (d) ${m_{\rm{n}}} = 8$, ${\text{MSE = 0}}{\text{.03\; m}}$, (e) $ {m_n} = 10 $, ${\text{MSE = 0}}{\text{.035 \;m}}$条件下, 不引入二次相关法的时空域联合编码扩频单光子计数深度图; 在(f) ${m_{\rm{n}}} = 5$, ${\text{MSE = 0}}{\text{.005\; m}}$, (g) ${m_{\rm{n}}} = 8$, ${\text{MSE = 0}}{\text{.011\; m}}$, (h) ${m_{\rm{n}}} = 10$, ${\text{MSE = 0}}{\text{.017 \;m}}$条件下, 引入二次相关法的时空域编码扩频单光子计数深度图, 深度单位为m

    Fig. 6.  Depth reconstruction simulation by using single photon counting scanning imaging test image: (a) Ground truth of ‘doll’; (b) the depth map by traditional single pixel imaging method based on space coding image when ${m_{\rm{n}}} = 10$, ${\text{MSE = 0}}{\text{.176\; m}}$. Depth maps by time-space united coding spread spectrum single photon counting imaging without second correlated method when (c) ${m_{\rm{n}}} = 5$, ${\text{MSE = 0}}{\text{.019\; m}}$, (d) ${m_{\rm{n}}} = 8$, ${\text{MSE = 0}}{\text{.03\; m}}$ and (e) ${m_{\rm{n}}} = 10$, ${\text{MSE = 0}}{\text{.035\; m}}$. Depth maps by time-space united coding spread spectrum single photon counting imaging with second correlated method when (f) ${m_{\rm{n}}} = 5$, ${\text{MSE = 0}}{\text{.005\; m}}$, (g) ${m_{\rm{n}}} = 8$, ${\text{MSE = 0}}{\text{.011\; m}}$, and (h) ${m_{\rm{n}}} = 10$, ${\text{MSE = 0}}{\text{.017\; m}}$. The depth unit is m.

    图 7  成像边缘检测 (a) 不引入二次相关法的时空域联合编码扩频单光子成像边缘检测; (b) 引入二次相关法的时空域联合编码扩频单光子成像边缘检测; (c) 传统的基于空间编码的单像素成像边缘检测

    Fig. 7.  Image edge detection: (a) Time-space united coding spread spectrum single photon counting imaging without second correlated method image edge detection; (b) time-space united coding spread spectrum single photon counting imaging with second correlated method image edge detection; (c) traditional single pixel imaging method based on space coding image edge detection.

    图 8  噪声$ {m_n} $=10不同的凸优化反演方法的图像重建 (a) TVAL3; (b) GPSR; (c) FISTA

    Fig. 8.  Different convex optimization inversion methods imaging reconstruction when$ {m_n} $=10: (a) TVAL3; (b) GPSR; (c) FISTA.

    表 1  不同重建方法的性能统计

    Table 1.  Performance statistical record of different reconstruction methods.

    MSE/m Time/s
    Method${m_{\rm{n} } } = 5$ ${m_{\rm{n}}} = 10$ ${m_{\rm{n}}} = 5$ ${m_{\rm{n}}} = 10$
    TVAL30.033 0.011 3557
    GPSR0.060 0.018 1324
    FISTA0.042 0.019 1624
    下载: 导出CSV
  • [1]

    Rehain P, Sua Y M, Zhu S Y, Dickson I, Muthuswamy B, Ramanathan J, Shahverdi A, Huang Y P 2020 Nat. Commun. 11 921Google Scholar

    [2]

    Tachella J, Altmann Y, Mellado N, McCarthy A, Tobin R, Buller G S, Tourneret J Y, McLaughlin S 2019 Nat. Commun. 10 4984Google Scholar

    [3]

    Brock J C, Purkis S J 2009 J. Coastal Res. 25 1Google Scholar

    [4]

    Howland G A, Lum D J, Ware M R, Howell J C 2013 Opt. Express 21 23822Google Scholar

    [5]

    Zhao Y N, Hou H Y, Han J C, Liu H C, Zhang S H, Cao D Z, Liang B L 2021 Opt. Lett. 46 4900Google Scholar

    [6]

    Radwell N, Johnson S D, Edgar M P, Higham C F, Murray-Smith R, Padget M J 2019 Appl. Phys. Lett. 115 231101Google Scholar

    [7]

    Li F Q, Chen H J, Pediredla A, Yeh C, He K, Veeraraghavan A, Cossairt O 2017 Opt. Express 11 31096

    [8]

    Liu X L, Shi J H, Sun L, Li Y H, Fan J P, Zeng G H 2020 Opt. Express 28 8132Google Scholar

    [9]

    Asmann A, Mota J F C, Stewart B D, Wallace A M 2019 IEEE Trans. Comput. Imaging 8 385

    [10]

    Misra P, Hu W, Yang M R, Duarte M, Jha S 2017 IEEE Trans. Mob. Comput. 16 2037Google Scholar

    [11]

    Krichel N J, McCarthy A, Buller G S 2010 Opt. Express 18 9192Google Scholar

    [12]

    Zhang Y F, He Y, Yang F, Luo Y, Chen W B 2016 Chin. Opt. Lett. 14 111101Google Scholar

    [13]

    Yu Y, Liu B, Chen Z 2018 Appl. Opt. 57 7733Google Scholar

    [14]

    Norman D M, Gardner C S 1988 Appl. Opt. 27 3650Google Scholar

    [15]

    Ding Y C, Wu H X, Gao X L, Wu B, Shen Y H 2022 J. Opt. Soc. Am. A 39 206

    [16]

    Hiskett P A, Parry C S, McCarthy A, Buller G S 2008 Opt. Express 16 13685Google Scholar

    [17]

    Yu Y, Liu B, Chen Z, Kang Li Z K 2020 Sensors 20 2204Google Scholar

    [18]

    Wu F, Yang L, Chen X L, Li Z H, Wu G 2022 Chin. Opt. Lett. 20 021202Google Scholar

    [19]

    Bioucas-Dias J M, Figueiredo M A T 2007 IEEE Trans. Image Process. 16 2992Google Scholar

    [20]

    Mandel L, Wolf E 1995 Optical Coherence and Quantum Optics (Cambridge: Cambridge University Press) p123

    [21]

    冒添逸, 陈钱, 何伟基, 庄佳衍, 邹云浩, 戴慧东, 顾国华 2016 物理学报 65 08427Google Scholar

    Mao T Y, Chen Q, He W J, Zhuang J Y, Zou Y H, Dai H D, Gu G H 2016 Acta Phys. Sin. 65 08427Google Scholar

    [22]

    Gatt P, Johnson S, Nichols T 2009 Appl. Opt. 48 3261Google Scholar

    [23]

    沈姗姗, 陈钱, 何伟基, 陈云飞, 尹文也, 戴慧东 2014 光学学报 34 1012001Google Scholar

    Shen S S, Chen Q, He W J, Chen Y F, Yin W Y, Dai H D 2014 Acta Opt. Sin. 34 1012001Google Scholar

    [24]

    Dai H D, Gu G H, He W J, Liao F J, Zhuang J Y, Liu Xiao J, Chen Q 2014 Appl. Opt. 53 6619Google Scholar

    [25]

    Zierler N, Siam J 1996 Electron. Commun. Eng. J. 1996 79

    [26]

    Molisch A F 2011 Wireless Communications (2nd Ed.) (New York: John Wiley & Sons Ltd.) p334

    [27]

    Shen S S, Chen Q, He W J, Gu G H 2020 Opt. Quantum Electron. 52 2020Google Scholar

    [28]

    Shen S S, Chen Q, He W J, Wang Y Q 2017 Chin. Opt. Lett. 15 090101Google Scholar

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出版历程
  • 收稿日期:  2022-07-19
  • 修回日期:  2022-09-29
  • 上网日期:  2022-10-27
  • 刊出日期:  2023-01-20

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