Turn off MathJax
Article Contents
ZHANG Kang-yang, NI Zi-hao, DONG Bo, BAI Yu-lei. Phase gradient estimation using Bayesian neural network[J]. Chinese Optics. doi: 10.37188/CO.2023-0168
Citation: ZHANG Kang-yang, NI Zi-hao, DONG Bo, BAI Yu-lei. Phase gradient estimation using Bayesian neural network[J]. Chinese Optics. doi: 10.37188/CO.2023-0168

Phase gradient estimation using Bayesian neural network

doi: 10.37188/CO.2023-0168
Funds:  Supported by National Natural Science Foundation of China (No. 61705047;No. 62171140) and Natural Science Foundation of Guangdong Province (No. 2021A1515011945;No. 2021A1515012598;No. 2021A1515011343).
More Information
  • Objective 

    Strain reconstruction is a vital component in the characterization of mechanical properties using phase-contrast optical coherence tomography (PC-OCT). It requires an accurate calculation for gradient distributions on the wrapped phase map. In order to address the challenge of low signal-to-noise ratio (SNR) in phase gradient calculation under severe noise interference, a Bayesian-neural-network-based phase gradient calculation is presented.


    Initially, wrapped phase maps with varying levels of speckle noise and their corresponding ideal phase gradient distributions are generated through a computer simulation. These wrapped phase maps and phase gradient distributions serve as the training datasets. Subsequently, the network learns the “end-to-end” relationship between the wrapped phase maps and phase gradient distributions in a noisy environment by utilizing a Bayesian inference theory. Finally, the Bayesian neural network (BNN), after being trained, accurately predicts the high-quality distribution of phase gradients by inputting the measured wrapped phase-difference maps into the network. Additionally, the statistical process introduced by BNN allows for the utilization of model uncertainty in the quantitative assessment of the network predictions’ reliability.


    Computer simulation and three-point bending mechanical loading experiment compare the performance of the BNN and the popular vector method. The results indicate that the BNN can enhance the SNR of estimated phase gradients by 8% in the presence of low noise levels. Importantly, the BNN successfully recovers the phase gradients that the vector method is unable to calculate due to the unresolved phase fringes in the presence of strong noise. Moreover, the BNN model uncertainty can be used to quantitatively analyze the prediction errors.


    It is expected that the contribution of this work can offer effective strain estimation for PC-OCT, enabling the internal mechanical property characterization to become high-quality and high-reliability.


  • loading
  • [1]
    吴哲, 陆冬筱, 李金华. 金纳米星诊疗剂的光热特性及其在光热治疗和光学相干层析成像中的应用研究[J]. 中国光学,2022,15(2):233-241. doi: 10.37188/CO.2021-0205

    WU ZH, LU D X, LI J H. Photothermal properties of gold nanostars therapeutic agent and its application in photothermal therapy and optical coherence tomography[J]. Chinese Optics, 2022, 15(2): 233-241. (in Chinese). doi: 10.37188/CO.2021-0205
    WANG X D, YUAN X, SHI L P. Optical coherence tomography-in situ and high-speed 3D imaging for laser materials processing[J]. Light:Science & Applications, 2022, 11(1): 280.
    FANG B, ZHONG SH C, ZHANG Q K, et al. Full-range line-field optical coherence tomography for high-accuracy measurements of optical lens[J]. IEEE Transactions on Instrumentation and Measurement, 2020, 69(9): 7180-7190. doi: 10.1109/TIM.2020.2978313
    谢胜利, 廖文建, 白玉磊, 等. 相衬光学相干层析在无损检测领域的应用[J]. 广东工业大学学报,2021,38(6):20-28.

    XIE SH L, LIAO W J, BAI Y L, et al. Phase-contrast optical coherence tomography in applications of non-destructive testing[J]. Journal of Guangdong University of Technology, 2021, 38(6): 20-28. (in Chinese).
    WU Z, WEI W B, GAO K, et al. Prototype system of noninterferometric phase-contrast computed tomography utilizing medical imaging components[J]. Journal of Applied Physics, 2021, 129(7): 074901. doi: 10.1063/5.0031392
    BAI Y L, CAI SH Y, XIE SH L, et al. Adaptive incremental method for strain estimation in phase-sensitive optical coherence elastography[J]. Optics Express, 2021, 29(16): 25327-25336. doi: 10.1364/OE.433245
    KENNEDY B F, HILLMAN T R, MCLAUGHLIN R A, et al. In vivo dynamic optical coherence elastography using a ring actuator[J]. Optics Express, 2009, 17(24): 21762-21772.
    GRIMWOOD A, GARCIA L, BAMBER J, et al. Elastographic contrast generation in optical coherence tomography from a localized shear stress[J]. Physics in Medicine and Biology, 2010, 55(18): 5515-5528. doi: 10.1088/0031-9155/55/18/016
    KENNEDY B F, KOH S H, MCLAUGHLIN R A, et al. Strain estimation in phase-sensitive optical coherence elastography[J]. Biomedical Optics Express, 2012, 3(8): 1865-1879. doi: 10.1364/BOE.3.001865
    ZAITSEV V Y, MATVEYEV A L, MATVEYEV L A, et al. Optimized phase gradient measurements and phase-amplitude interplay in optical coherence elastography[J]. Journal of Biomedical Optics, 2016, 21(11): 116005. doi: 10.1117/1.JBO.21.11.116005
    MATVEYEV A L, MATVEEV L A, SOVETSKY A A, et al. Vector method for strain estimation in phase-sensitive optical coherence elastography[J]. Laser Physics Letters, 2018, 15(6): 065603. doi: 10.1088/1612-202X/aab5e9
    朱新军, 赵浩淼, 王红一, 等. 基于轻型自限制注意力的结构光相位及深度估计混合网络[J]. 中国光学(中英文),2024,17(1):118-127. doi: 10.37188/CO.2023-0066

    ZHU X J, ZHAO H M, WANG H Y, et al. A hybrid network based on light self-limited attention for structured light phase and depth estimation[J]. Chinese Optics, 2024, 17(1): 118-127. (in Chinese). doi: 10.37188/CO.2023-0066
    GONTARZ M, DUTTA V, KUJAWIŃSKA M, et al. Phase unwrapping using deep learning in holographic tomography[J]. Optics Express, 2023, 31(12): 18964-18992. doi: 10.1364/OE.486984
    DE LA TORRE-IBARRA M H, RUIZ P D, HUNTLEY J M. Double-shot depth-resolved displacement field measurement using phase-contrast spectral optical coherence tomography[J]. Optics Express, 2006, 14(21): 9643-9656. doi: 10.1364/OE.14.009643
    BADRINARAYANAN V, KENDALL A, CIPOLLA R. SegNet: a deep convolutional encoder-decoder architecture for image segmentation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2017, 39(12): 2481-2495. doi: 10.1109/TPAMI.2016.2644615
    刘泽隆, 李茂月, 卢新元, 等. 高动态范围条纹结构光在机检测技术及应用进展[J]. 中国光学(中英文),2024,17(1):1-18.

    LIU Z L, LI M Y, LU X Y, et al. On-machine detection technology and application progress of high dynamic range fringe structured light[J]. Chinese Optics, 2024, 17(1): 1-18. (in Chinese).
    FENG SH J, ZUO CH, HU Y, et al. Deep-learning-based fringe-pattern analysis with uncertainty estimation[J]. Optica, 2021, 8(12): 1507-1510. doi: 10.1364/OPTICA.434311
    LYU Z L, BAI Y L, HE ZH SH, et al. Super-resolution reconstruction of speckle phase in depth-resolved wavelength scanning interference using the total least-squares analysis[J]. Journal of the Optical Society of America A, 2019, 36(5): 869-876. doi: 10.1364/JOSAA.36.000869
    CHAKRABORTY S, GHOSH M. Applications of Bayesian neural networks in prostate cancer study[J]. Handbook of Statistics, 2012, 28: 241-262.
    JOSPIN L V, LAGA H, BOUSSAID F, et al. Hands-on Bayesian neural networks-a tutorial for deep learning users[J]. IEEE Computational Intelligence Magazine, 2022, 17(2): 29-48. doi: 10.1109/MCI.2022.3155327
    LEMAY A, HOEBEL K, BRIDGE C P, et al. Improving the repeatability of deep learning models with Monte Carlo dropout[J]. npj Digital Medicine, 2022, 5(1): 174. doi: 10.1038/s41746-022-00709-3
  • 加载中


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索


    Article views(115) PDF downloads(11) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint