Improving the optimization landscape of cryo-EM high-resolution 3D reconstruction

What is it about?

This article tackles a computational bottleneck in cryo-electron microscopy (cryo-EM), a technique that determines 3D protein structures from thousands of 2D images. Currently, cryo-EM data processing uses two separate stages: fast stochastic gradient descent (SGD) for initial rough reconstructions, then slow expectation-maximization algorithms for high-resolution details. We study and illustrate why SGD fails at high resolution - the mathematical problem becomes "ill-conditioned", leading to slow convergence of the solution entries corresponding to high-resolution features. We developed a "preconditioner" that corrects this issue, essentially rescaling the dimensions that cause difficulties to the optimization algorithm. Testing in a simplified setting where particle orientations are known, we show the preconditioned SGD successfully captures high-resolution details that standard SGD misses, while maintaining speed advantages.

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Photo by Andy Dutton on Unsplash

Photo by Andy Dutton on Unsplash

Why is it important?

We address a fundamental problem in cryo-EM high-resolution reconstruction pipelines. The proposed solution enables stochastic gradient methods to achieve fast convergence not only for initial reconstruction but also at high resolution, leading to significant speed improvements. In addition, by unifying the traditional two-stage process into a single conceptually consistent framework with fewer modeling assumptions, this work enables more streamlined implementations while opening possibilities for incorporating advanced priors and learned regularization methods that better capture biological knowledge in the data.