Efficient high-resolution refinement in cryo-EM with stochastic gradient descent.

Area of Science:

• Structural Biology
• Biophysics
• Computational Biology

Background:

• Electron cryomicroscopy (cryo-EM) determines 3D structures of biomolecules from 2D projections.
• Efficient algorithms are vital for processing large cryo-EM datasets.
• Stochastic gradient descent (SGD) accelerates low-resolution cryo-EM reconstruction but struggles at high resolutions.

Purpose of the Study:

• To investigate the conditioning of the cryo-EM optimization problem.
• To develop a method enabling gradient descent-based algorithms for high-resolution cryo-EM.
• To improve the speed and flexibility of cryo-EM structure determination.

Main Methods:

• Theoretical analysis of the optimization problem's condition number.
• Development of a diagonal preconditioner using Hutchinson's diagonal estimator.
• Numerical experiments comparing preconditioned SGD with standard methods.

Main Results:

• Identified large condition numbers as a barrier to high-resolution gradient descent in cryo-EM.
• Demonstrated that the preconditioned SGD approach significantly improves convergence speed.
• Showcased enhanced performance in numerical experiments using the estimated preconditioner.

Conclusions:

• The preconditioned SGD method offers a promising solution for high-resolution cryo-EM.
• This approach could unify ab initio reconstruction and high-resolution refinement.
• Results represent a significant step towards faster and more flexible cryo-EM structure determination.