theta_est_l2_dqt_estAB {AIUQ}R Documentation

Minimize l2 loss for Dqt

Description

Minimize l2 loss function for dynamic image structure function(Dqt), and return estimated parameters and mean squared displacement(MSD).

Usage

theta_est_l2_dqt_estAB(
  param,
  A_ini,
  q,
  index_q,
  Dqt,
  d_input,
  model_name,
  msd_fn = NA,
  msd_grad_fn = NA
)

Arguments

param

a vector of natural logarithm of parameters

A_ini

initial value of A(q) to be optimized over. Note true A(q) is determined by the properties of the imaged material and imaging optics. See 'References'.

q

wave vector in unit of um^-1

index_q

selected index of wave number

Dqt

observed dynamic image structure function. See 'Details'.

d_input

sequence of lag times

model_name

model name for the fitted model, options from ('BM','OU', 'FBM',OU+FBM','user_defined')

msd_fn

msd_fn user defined mean squared displacement structure (MSD), a function of param parameters and d_input lag times

msd_grad_fn

user defined MSD gradient structure, a function of param and d_input

Details

Dynamic image structure function(Dqt) can be obtained from ensemble average of absolute values squared of Four transformed intensity difference:

D(q,\Delta t) = \langle |\Delta \hat{I}(q,t,\Delta t)|^2\rangle

See 'References'.

Value

A list of estimated parameters and MSD from minimizing the l2 loss function.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Cerbino, R., & Trappe, V. (2008). Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Physical review letters, 100(18), 188102.


[Package AIUQ version 0.5.3 Index]