Title: Manifold methods for image denoising in cryo-electron microscopy

Abstract: 
The Nobel Prize in Chemistry 2017 was awarded ``for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution''. In a nutshell, cryo-electron microscopy is a method to determine the three-dimensional structure of molecules from their two-dimensional images taken by an electron microscope. A key challenge in cryo-electron microscopy is that the two-dimensional images are extremely noisy, and must be denoised first to improve their quality (signal-to-noise ratio).

We present a method for denoising the two-dimensional images that exploits the fact that all (unknown) noiseless images lie on an (unknown) three-dimensional manifold. The method is based on constructing a ``Fourier-like'' basis on the manifold, followed by using a subset of the basis functions to "filter" the images.  We show that all the quantities required by the filtering procedure can be estimated using only the input two-dimensional images.  Moreover, the proposed approach allows using not only the given input images, but also all their infinitely many in-plane rotations.