DOI: 10.5061/dryad.9w0vt4bf5
title: Expectation maximization based framework for joint localization and parameter estimation in single particle tracking from segmented images - Simulation Data

description: The datasets contain simulated Single Particle Tracking
 (SPT) data consisting of sequences of camera images of a single
 fluorescent sub-diffraction limit-sized particle undergoing
 two-dimensional diffusion. We simulated a variety of experimental
 conditions, including different Signal-to-Background Ratios (SBRs), two
 different camera types, different diffusion speeds, and two different
 settings for motion blur. SPT is a class of experimental methods and data
 analysis techniques for exploring the motion of individual biological
 macromolecules. Typical estimation algorithms split the problem into two
 parts: first localize the particle at each data point to generate a
 trajectory and then estimate model parameters from that trajectory. We
 have recently introduced a class of algorithms for jointly estimating both
 trajectory and model parameters. In this study, we used the data to
 perform quantitative comparisons between two variants of our approach, one
 relying on a Sequential Monte Carlo methods combined with
 Expectation Maximization (SMC-EM) that is applicable to a very broad set
 of motion and observation models, and one that replaces the SMC elements
 with methods based on the Unscented Kalman Filter (UKF) to improve upon
 the computational complexity. We also compared our methods to two current
 standards in the field. The first uses Gaussian Fitting to localize the
 particle, following by a Mean Square Displacement (GF-MSD) analysis to
 determine model parameters while the other replaces MSD with
 Maximum Likelihood Estimation (GF-MLE). The main results of our study
 indicate that our EM-based schemes significantly outperform the existing
 algorithms at low SBR while at high SBR, GF-MLE performs equally well but
 at a lower computational cost.
description: All datasets were simulated using MATLAB (MathWorks, Natick, MA).
 Two camera types were considered: (1) An ideal camera with Poisson
 distributed shot noise but no readout noise; (2) A camera with both shot
 noise and the pixel-dependent readout noise that is common to scientific
 complementary metal-oxide semiconductor (sCMOS) cameras. For each run, the
 diffusive motion of a single particle was generated at a time step of 1
 ms. At each time step, a pixelated image was generated by integrating a
 standard Gaussian model of the Point Spread Function (PSF) of the
 microscope over each of the pixels in the camera image. The cameras were
 assumed to take images at a rate of 10 Hz with a shutter period of 10 ms.
 For data that included motion blur, the 10 pixelated images in the shutter
 period were accumulated to generate a single camera image. For data that
 ignored motion blur, only the first pixelated image was used. In each
 case, both background and camera readout noise were included based on the
 model of the camera being considered. Datasets were generated at a range
 of SBRs and diffusion coefficients (see Usage Notes for
 details).
description: * DATA-SPECIFIC INFORMATION FOR:
 [type1_data_with_different_N_G.zip] Images
 were captured by the camera with Poisson distributed shot noise but no
 readout noise. The background noise ranges from 1 to
 15, while the signal level ranges from 1 to 100.
 Motion blur is considered (each image contains 100 sub-samples,
 and only the first 10 sub-samples of every 100 sub-samples were
 accumulated). Taking the sub-directory
 [N10G100Image100] as an example, the dataset name indicates the following
 parameter values: background noise=10, signal intensity=100, number of
 images per dataset=100. Under each experimental setting, 100 datasets were
 simulated. Taking the first dataset under
 [N10G100Image100] as an example, the details of the provided data are as
 follows: [photon_observation_1.csv]
 row*column=100*25; There are the simulated images with each row containing
 a single image, organized sequentially from the initial time down to the
 final time. The 25 entries in each row are the intensity values from the
 5-by-5 pixel array, organized starting from the top-left pixel, going
 horizontally across the top five pixels, and continuing to the bottom
 right pixel.
 [sensor_position_1.csv] row*column=100*2; In generating images,
 we assumed segmentation of the full camera image was done previously and
 thus the location of the 5-by-5 array of pixels may change at each time
 step. This data gives the position of the pixel array starting from the
 initial time down to the final time, with the first column corresponding
 to the x-coordinate and the second column to the y-coordinate.
 [x_ground_truth.mat] row*column=100*100; This data contains the
 true location of the particle in the x-direction at each time step.
 Because of the motion blur model, this location was taken to be the mean
 of the position across the shutter period. The data is organized starting
 with the first time step and proceeding down to the last.
 [y_ground_truth.mat] row*column=100*100; This data is the true
 location of the particle in the y-direction at each time step, and it is
 organized as [x_ground_truth.mat]. 
 * DATA-SPECIFIC INFORMATION FOR:
 [type1_N10G100Image100D_different.zip] 
 Images were captured by the camera with Poisson distributed shot
 noise but no readout noise. Background noise=10,
 signal intensity=100, number of images per dataset =100, diffusion
 coefficient ranges from 0.001 to 10. The
 sub-directory [100datasets_withSub] contains the data with motion blur,
 while the sub-directory [100datasets_noSub] contains the data without
 motion blur. Taking the files
 in [100datasets_withSub/N10G100D0.01] as an example, the diffusion
 coefficient is Dx=Dy=0.01(um<sup>2</sup>/s). The variable
 names and their corresponding dimensions are the same as the descriptions
 of [type1_data_with_different_N_G.zip]. *
 DATA-SPECIFIC INFORMATION FOR: [type2_camera.zip] 
 Images were captured by the camera with both shot noise and the
 pixel-dependent readout noise. [N10G100Image100sCMOS]
 background noise=10, signal intensity=100, number of images per
 dataset=100. For each experimental setting, 100 datasets were simulated.
 Taking the 1st dataset as an example, the provided data is:  
 [local_sigma_1.csv] row*column=100*25; row denotes the time
 steps, column denotes the pixel. Each pixel contains information of
 "sigma" characterizing the readout noise of the Hamamatsu ORCA
 Flash 4.0 camera. [photon_observation_1.csv] are the
 measured intensities, organized as described above.
 [sensor_position_1.csv] are the global locations of the 5-by-5
 pixel arrays, organized as described above.
 [x_ground_truth.mat] are the ground truth in the x-direction,
 organized as described above. 
  [N10G30Image100sCMOS] background noise=10, signal intensity=30, number of images per dataset=100. For each experimental setting, 100 datasets were simulated. This data is organized in the same manner as described above. * DATA-SPECIFIC INFORMATION FOR: [Data_for_figures_PlosOne.zip] Figures and their corresponding data used for reproducing the figures in paper “Ye Lin and Sean B. Andersson. Expectation maximization based framework for joint localization and parameter estimation in single particle tracking from segmented images. Plos One (2021).”