This package is for scattering analysis of microscopy. The code has been tested in MATLAB version 2022b.
version 0.5.1.
Description:
The package allows users to simulate 2D movements of some particles from different anisotropic or isotropic stochastic processes and model the mean squared displacement (MSD) given a dataset using Gaussian processes. Parameter estimation is performed in a fast approach, making use of the Toeplitz structure of covariance matrices.
References:
- M. Gu, Y. He, X. Liu, and Y. Luo, Ab initio uncertainty quantification in scattering analysis of microscopy, arXiv preprint arXiv:2309.02468
- Y. Ling, Superfast Inference for Stationary Gaussian Processes in Particle Tracking Microrheology, Ph.D. thesis, University of Waterloo (2019).
- Cerbino, R. and Trappe, V., 2008. Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Physical review letters, 100(18), p.188102.
Installation:
To use this package, please install the optimization toolbox in MATLAB and install the FFTW3 library. For Windows users and Mac users whose system is based on X86_64 architecture (usually before 2021), FFTW3 library can be linked easily, and for Mac users with ARM architecture (M chips) the procedure may be more complicated.
To install and link FFTW3 to your system, please refer to the FFTW_install_tutorial_2024.pdf
Contents:
example_anisotropic.m - Show anisotropic examples of some simulations and implement aniso_SAM() to real intensity data aniso_simulation.m - Simulation code for different anisotropic stochastic processes anisotropic_neg_log_lik - Compute the negative log-likelihood of the processed intensity data. anisotropic_log_lik_grad - Compute the derivative of negative log-likelihood w.r.t parameters. aniso_SAM - Parameter estimation example.m - Show isotropic examples of some simulations and implement aniso_SAM() to real intensity data simulation.m - Simulation code for different isotropic stochastic processes neg_log_lik - Compute the negative log-likelihood of the processed intensity data. log_lik_grad - Compute the derivative of negative log-likelihood w.r.t parameters. SAM - Parameter estimation cpp files: log_density, phi_log_det, toeplitz_prod, toeplitz_solve, toeplitz_trace_gradient, toeplitz_trace_hess
The main functions are aniso_simulation(), simulation() aniso_SAM() and SAM().
Authors: Xubo Liu, Yue He, Mengyang Gu
Department of Statistics and Applied Probability, University of California, Santa Barbara
Email: mengyang@pstat.ucsb.edu, xubo@ucsb.edu, yuehe@ucsb.edu