theta_est_l2_dqt_fixedAB {AIUQ} | R Documentation |
Minimize l2 loss for Dqt with fixed A(q) and B
Description
Minimize l2 loss function for dynamic image structure function(Dqt) with fixed A(q) and B, and return estimated parameters and mean squared displacement(MSD).
Usage
theta_est_l2_dqt_fixedAB(
param,
q,
index_q,
Dqt,
A_est_q,
B_est,
d_input,
model_name,
msd_fn = NA,
msd_grad_fn = NA
)
Arguments
param |
a vector of natural logarithm of parameters |
q |
wave vector in unit of um^-1 |
index_q |
selected index of wave number |
Dqt |
observed dynamic image structure function. See 'Details'. |
A_est_q |
estimated value of A(q). This parameter is determined by the properties of the imaged material and imaging optics. See 'References'. |
B_est |
estimated value of B. This parameter is determined by the noise in the system. See 'References'. |
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 |
msd_grad_fn |
user defined MSD gradient structure, a function of
|
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.