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Description

Molecules imaged using cryo-electron microscopy (cryo-EM) often exhibit a significant amount of variability, be it in conformation or composition. The molecules are typically represented as 3D volume maps of the electric potential as a function of space. In order to characterize the variability of these maps, the authors propose a method for fast and accurate estimation of the 3D covariance matrix. The estimator is given by the least-squares solution to a linear inverse problem and is efficiently calculated by exploiting its 6D convolutional structure. Combining this with a circulant preconditioner, the solution is obtained using the conjugate gradient method. For $n$ images of size $N$-by-$N$, the computational complexity of the algorithm is $O(n N^4 + \sqrt{\kappa} N^6 \log N)$, where $\kappa$ is a condition number typically of the order $200$. The method is evaluated on simulated and experimental datasets, achieving results comparable to the state of the art at very short runtimes.