Two Dimensional Arma Models and Parameter Adjustment to Estimate the Ctf of the Electron Microscope

A powerful parametric spectral estimation technique, 2D-ARMA (Auto Regressive Moving Average) modeling, has been applied to contrast transfer function (CTF) detection in electron microscopy. Parametric techniques such as AR (auto regressive) and ARMA models allow a more exact determination of the CTF than traditional methods based only on the Fourier Transform (FT). Previous works revealed that AR models can be used to improve the CTF estimation and the detection of its zeroes. ARMA models reduce the model order and the computing time, and more interestingly, increase the achieved accuracy. ARMA models are generated from electron microscopy (EM) images, and then a stepwise search algorithm is used to determine all the parameters of a theoretical CTF model in the ARMA model previously calculated. Furthermore, this adjustment is truly 2D in order to properly treat astigmatic images. The user only needs to know a few a priori parameters of the experimental conditions for his micrographs, which turns this technique into an automatic and very powerful tool.