The mathematics of computerized tomography
The mathematics of computerized tomography
SIAM Journal on Imaging Sciences
Foundations of Computational Mathematics
Uniqueness of tomography with unknown view angles
IEEE Transactions on Image Processing
Feasibility of tomography with unknown view angles
IEEE Transactions on Image Processing
Graph Laplacian Tomography From Unknown Random Projections
IEEE Transactions on Image Processing
Computing Steerable Principal Components of a Large Set of Images and Their Rotations
IEEE Transactions on Image Processing
Sensor network localization by eigenvector synchronization over the euclidean group
ACM Transactions on Sensor Networks (TOSN)
Ranking and sparsifying a connection graph
WAW'12 Proceedings of the 9th international conference on Algorithms and Models for the Web Graph
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The cryo-electron microscopy (cryo-EM) reconstruction problem is to find the three-dimensional structure of a macromolecule given noisy versions of its two-dimensional projection images at unknown random directions. We introduce a new algorithm for identifying noisy cryo-EM images of nearby viewing angles. This identification is an important first step in three-dimensional structure determination of macromolecules from cryo-EM, because once identified, these images can be rotationally aligned and averaged to produce “class averages” of better quality. The main advantage of our algorithm is its extreme robustness to noise. The algorithm is also very efficient in terms of running time and memory requirements, because it is based on the computation of the top few eigenvectors of a specially designed sparse Hermitian matrix. These advantages are demonstrated in numerous numerical experiments.