Cryo-EM reconstruction with traditional iterative algorithms is often split into two separate stages: ab initio, where an initial estimation of the volume and the pose variables are estimated, and high-resolution refinement, where a high-resolution volume is obtained using local optimization. While state-of-the-art results for high-resolution refinement are obtained using the Expectation-Maximization algorithm, this requires marginalization over the pose variables for all the 2D particle images at each iteration. In contrast, ab initio reconstruction is often performed using a variation of the stochastic gradient descent algorithm, which only uses a subset of the data at each iteration. In this talk, we present an approach that has the potential to enable the use of stochastic optimization algorithms for high-resolution refinement with improved running time. We present an analysis related to the conditioning of the problem that motivates our approach and show preliminary numerical results.

Principal component analysis (PCA) plays an important role in the analysis of cryo-EM images for various tasks such as classification, denoising, compression, and ab-initio modeling. We introduce a fast method for estimating a compressed representation of the 2-D covariance matrix of noisy cryo-electron microscopy projection images that enables fast PCA computation. Our method is based on a new algorithm for expanding images in the Fourier-Bessel basis (the harmonics on the disk), which provides a convenient way to handle the effect of the contrast transfer functions. For $N$ images of size $L$ by $L$, our method has much lower time and space complexities compared to the previous work. We demonstrate our approach on synthetic and experimental data and show acceleration by factors of up to two orders of magnitude.

Cryogenic electron microscopy (cryo-EM) is a powerful technique to obtain the 3D structure of macromolecules from thousands of noisy projection images. Since these macromolecules are flexible by nature, the areas where a protein moves yields in a local drop of resolution in the reconstruction. We propose a method named dynamight, that represents the molecule with gaussian basis functions and estimates deformation fields for every experimental image. We further use the estimated deformations to better resolve the flexible regions in the reconstruction using a filtered backprojection algorithm along curved lines. We present results on real data showing that we obtain improved 3D reconstruction