Often a set of images is obtained from a heterogeneous mixture of particles of two or more different kinds or different conformations. It is therefore desirable to reconstruct not just a single averaged volume, but the entire set of 3D molecular conformations. We have developed a method for estimating the covariance matrix of the distribution of the 3D volumes directly from the 2D projection images.  At present, our package does not include this functionality, but it is certainly high on our todo list.

 

Further reading:

R. R. Lederman, A. Singer, A Representation Theory Perspective on Simultaneous Alignment and Classification, arXiv preprint.

J. Andén, E. Katsevich, A. Singer, Covariance estimation using conjugate gradient for 3D classification in Cryo-EM, in IEEE 12th International Symposium on Biomedical Imaging (ISBI 2015), pp. 200-204, 16-19 April 2015.

E. Katsevich, A. Katsevich, A. Singer, Covariance Matrix Estimation for the Cryo-EM Heterogeneity ProblemSIAM Journal on Imaging Sciences, 8 (1), pp. 126-185 (2015).