Open Access
September 2019 Fast dynamic nonparametric distribution tracking in electron microscopic data
Yanjun Qian, Jianhua Z. Huang, Chiwoo Park, Yu Ding
Ann. Appl. Stat. 13(3): 1537-1563 (September 2019). DOI: 10.1214/19-AOAS1245


In situ transmission electron microscope (TEM) adds a promising instrument to the exploration of the nanoscale world, allowing motion pictures to be taken while nano objects are initiating, crystalizing and morphing into different sizes and shapes. To enable in-process control of nanocrystal production, this technology innovation hinges upon a solution addressing a statistical problem, which is the capability of online tracking a dynamic, time-varying probability distribution reflecting the nanocrystal growth. Because no known parametric density functions can adequately describe the evolving distribution, a nonparametric approach is inevitable. Towards this objective, we propose to incorporate the dynamic evolution of the normalized particle size distribution into a state space model, in which the density function is represented by a linear combination of B-splines and the spline coefficients are treated as states. The closed-form algorithm runs online updates faster than the frame rate of the in situ TEM video, making it suitable for in-process control purpose. Imposing the constraints of curve smoothness and temporal continuity improves the accuracy and robustness while tracking the probability distribution. We test our method on three published TEM videos. For all of them, the proposed method is able to outperform several alternative approaches.


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Yanjun Qian. Jianhua Z. Huang. Chiwoo Park. Yu Ding. "Fast dynamic nonparametric distribution tracking in electron microscopic data." Ann. Appl. Stat. 13 (3) 1537 - 1563, September 2019.


Received: 1 April 2018; Revised: 1 February 2019; Published: September 2019
First available in Project Euclid: 17 October 2019

zbMATH: 07145967
MathSciNet: MR4019149
Digital Object Identifier: 10.1214/19-AOAS1245

Keywords: Kalman filter , nanotechnology , nonparametric density , online density estimation , state space model

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.13 • No. 3 • September 2019
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