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In cryo-electron microscopy (Cryo-EM) imaging, noise levels can often exceed the signal magnitude by 10 to 100 times, making 3-D structure determination a considerable challenge. Given the large number of images, swift denoising becomes a pivotal preprocessing step. In our work, we introduce an entirely unsupervised denoiser built on the estimated covariance matrix of clean images. However, the typically high dimensions of image covariance present both statistical and computational hurdles. A key observation is that if the image manifold is invariant under global in-plane rotations, this symmetry can be harnessed to markedly speed up computation and reduce dimensionality.

In this talk, I will detail how the latest progress on the fast expansion into harmonics on the disk enables us to utilize this rotational symmetry. This results in a surge in speed for covariance estimation - achieving a rate a thousand times faster than previously fastest methods. Additionally, I will explore the successful application of our approach to joint deconvolution and denoising of large-scale, real-world cryo-EM images.