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Manifold methods for cryo-EM image denoising

Banff International Research Station for Mathematical Innovation and Discovery

The goal in cryo-electron microscopy is to recover the three-dimensional structure of a molecule from many of its two-dimensional tomographic projection images. A key challenge in this imaging setup is that the two-dimensional images are extremely noisy. Thus, the process of reconstructing a three-dimensional model form the two-dimensional images typically requires some form of denoising, to improve the quality (signal-to-noise ratio) of the two-dimensional images. Such denoising is often implemented by one of the existing class averaging algorithms, or by other forms of statistical analysis, such as principal components analysis and its variants. We present an algorithm for denoising the entire set of two-dimensional images at once, by exploiting the geometrical property that all (unknown) clean images corresponding to the same underlying structure lie on a manifold of intrinsic dimension three. Thus, each image can be denoised by projecting it onto this (unknown) low-dimensional manifold of clean images. We show that all the quantities required to compute this projection can be estimated using only the two-dimensional projection images. In particular, no prior assumptions on the images nor the three-dimensional volume are required.

Mathematics; Numerical analysis; Approximations and expansions; Control/optimization/operation research

video/mp4

Author affiliation: Tel-Aviv University

2019-03-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68563

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/