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基于累积量标准差的超分辨光学涨落成像解卷积优化

王雪花 陈丹妮 于斌 牛憨笨

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基于累积量标准差的超分辨光学涨落成像解卷积优化

王雪花, 陈丹妮, 于斌, 牛憨笨

Deconvolution optimization in super-resolution optical fluctuation imaging based on cumulant standard deviation

Wang Xue-Hua, Chen Dan-Ni, Yu Bin, Niu Han-Ben
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  • 超分辨光学涨落成像方法通过计算一组随机闪烁图像序列的累积量来提高空间分辨率.在实际实验中,由于计算的图像序列帧数有限,每个像素上累积量估计的误差将显著影响重构图像的均匀性和连续性.传统超分辨光学涨落成像技术由于缺乏对累积量估计的误差分析,在其后续的Lucy-Richardson解卷积算法中,没有对累积量重构图像的噪声添加约束条件.本文利用基于单组有限长数据的累积量标准差公式,计算了超分辨光学涨落显微图像每个像素上的累积量标准差,并将结果引入Lucy-Richardson解卷积算法中作为迭代优化的偏差阈值.模拟和实验结果表明,在相同图像序列长度下,该优化方法显著提高了超分辨重构图像的均匀性和连续性;在同等图像质量下,该方法可缩短图像序列帧数至原来的一半以下,有望用于活细胞动态超分辨成像.
    The super-resolution optical fluctuation imaging (SOFI) technique enhances image spatial resolution by evaluating the independent stochastic intensity fluctuations of emitters. In principle, it eliminates any noise uncorrelated temporally, and provides unlimited spatial resolution since the calculation of the nth-order cumulant followed by a deconvolution results in an image with n-fold resolution improvement in three dimensions. But in practice, due to limited data length, the statistical uncertainty of cumulants will affect the continuity and homogeneity of SOFI image, which results in the fact that the high order SOFI (typically over 3rd order) cannot improve spatial resolution significantly. Since the variance characterizes the statistical uncertainty of cumulant, we deduce its theoretical expression based on a single dataset. In traditional SOFI techniques, due to lack of statistical analysis of cumulant, there is no noise constraint condition of cumulant in the Lucy-Richardson deconvolution to prevent the algorithm from causing noise amplification. In this paper, based on the cumulant variance formula, we calculate the cumulant standard deviation in each pixel of SOFI image and introduce the results into the Lucy-Richardson algorithm as a DAMPAR to suppress the noise generation in such pixels. The simulation and experimental results show that under the same data length, the deconvolution optimization based on cumulant standard deviation significantly improves the uniformity and continuity of SOFI image. On the other hand, under the premise of identical image quality, this optimization technique can also greatly shorten the image frames to less than half the original, thus promoting the development of super-resolution imaging of living cells.
      通信作者: 陈丹妮, danny@szu.edu.cn;hbniu@szu.edu.cn ; 牛憨笨, danny@szu.edu.cn;hbniu@szu.edu.cn
    • 基金项目: 国家重点基础研究发展计划(批准号:2012CB825802)、国家自然科学基金(批准号:61335001,61178080,61235012,11004136)、国家重大科学仪器设备开发专项(批准号:2012YQ15009203)和深圳市科技计划项目(批准号:JCYJ20120613173049560,GJHS20120621155433884)资助的课题.
      Corresponding author: Chen Dan-Ni, danny@szu.edu.cn;hbniu@szu.edu.cn ; Niu Han-Ben, danny@szu.edu.cn;hbniu@szu.edu.cn
    • Funds: Project supported by the National Basic Research Program of China (Grant No. 2012CB825802), National Natural Science Foundation of China (Grant Nos. 61335001, 61178080, 61235012, 11004136), the Special Funds of the Major Scientific Instruments Equipment Development of China (Grant No. 2012YQ15009203), and the Science and Technology Planning Project of Shenzhen, China (Grant Nos. JCYJ20120613173049560, GJHS20120621155433884).
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    Li H, Yu B, Chen D N, Niu H B 2013 Acta Phys. Sin. 62 124201 (in Chinese) [李恒, 于斌, 陈丹妮, 牛憨笨2013物理学报62 124201]

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    Wang X, Chen D, Yu B, Niu H 2015 Appl. Opt. 54 6919

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    Koppel D E 1974 Phys. Rev. A 10 1938

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    Qian H 1990 Biophys. Chem. 38 49

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    Zeng Z, Chen X, Wang H, Huang N, Shan C, Zhang H, Teng J, Xi P 2015 Sci. Rep. 5 1

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    Wang X, Chen D, Yu B, Niu H 2016 Appl. Opt. 55 7911

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    Kendall M G, Stuart A 1977 The Advanced Theory of Statistics (Vol. 1) (New York: MacMillan Publishing) pp57-96

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    Vandenberg W, Duwé S, Leutenegger M, Moeyaert B, Krajnik B, Lasser T, Dedecker P 2016 Biomed. Opt. Express 7 467

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    Mller J D 2004 Biophys. J. 86 3981

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    Biggs D S C, Andrews M 1997 Appl. Opt. 36 1766

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    Arganda-Carreras I, Fernández-González R, Muöoz-Barrutia A, Ortiz-De-Solorzano C 2010 Microsc. Res. Tech. 73 1019

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    Lee T C, Kashyap R L, Chu C N 1994 Graph. Model. Im. Proc. 56 462

  • [1]

    Dertinger T, Colyer R, Iyer G, Weiss S, Enderlein J 2009 Proc. Nat. Acad. Sci. 106 22287

    [2]

    Geissbuehler S, Dellagiacoma C, Lasser T 2011 Biomed. Opt. Express 2 408

    [3]

    Dertinger T, Colyer R, Vogel R, Enderlein J, Weiss S 2010 Opt. Express 18 18875

    [4]

    Geissbuehler S, Bocchio N L, Dellagiacoma C, Berclaz C, Leutenegger M, Lasser T 2012 Opt. Nanoscopy 1 1

    [5]

    Stein S C, Huss A, Höhnel D, Gregor I, Enderlein J 2015 Opt. Express 23 16154

    [6]

    Betzig E, Patterson G H, Sougrat R, Lindwasser O W, Olenych S, Bonifacino J S, Davidson M W, Lippincott-Schwartz J, Hess H F 2006 Science 313 1642

    [7]

    Rust M J, Bates M, Zhuang X 2006 Nat. Methods 3 793

    [8]

    Chen D N, Liu L, Yu B, Niu H B 2010 Acta Phys. Sin. 59 6948 (in Chinese) [陈丹妮, 刘磊, 于斌, 牛憨笨2010物理学报59 6948]

    [9]

    Li H, Yu B, Chen D N, Niu H B 2013 Acta Phys. Sin. 62 124201 (in Chinese) [李恒, 于斌, 陈丹妮, 牛憨笨2013物理学报62 124201]

    [10]

    Wang X, Chen D, Yu B, Niu H 2015 Appl. Opt. 54 6919

    [11]

    Koppel D E 1974 Phys. Rev. A 10 1938

    [12]

    Qian H 1990 Biophys. Chem. 38 49

    [13]

    Zeng Z, Chen X, Wang H, Huang N, Shan C, Zhang H, Teng J, Xi P 2015 Sci. Rep. 5 1

    [14]

    Wang X, Chen D, Yu B, Niu H 2016 Appl. Opt. 55 7911

    [15]

    Kendall M G, Stuart A 1977 The Advanced Theory of Statistics (Vol. 1) (New York: MacMillan Publishing) pp57-96

    [16]

    Rose C, Smith M D 2002 Mathematical Statistics with Mathematica (New York: Springer) pp31-80

    [17]

    Vandenberg W, Duwé S, Leutenegger M, Moeyaert B, Krajnik B, Lasser T, Dedecker P 2016 Biomed. Opt. Express 7 467

    [18]

    Mller J D 2004 Biophys. J. 86 3981

    [19]

    Biggs D S C, Andrews M 1997 Appl. Opt. 36 1766

    [20]

    Arganda-Carreras I, Fernández-González R, Muöoz-Barrutia A, Ortiz-De-Solorzano C 2010 Microsc. Res. Tech. 73 1019

    [21]

    Lee T C, Kashyap R L, Chu C N 1994 Graph. Model. Im. Proc. 56 462

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出版历程
  • 收稿日期:  2016-06-13
  • 修回日期:  2016-07-12
  • 刊出日期:  2016-10-05

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