Deblurring of Motionally Averaged Images with Applications to Single-Particle Cryo-Electron Microscopy

TL;DR

This paper presents methods for deblurring images affected by translational and rotational motion errors, with applications to cryo-electron microscopy, using Fourier-based and expansion techniques to improve image reconstruction accuracy.

Contribution

It introduces Fourier and expansion-based deblurring techniques for combined translational and rotational errors, tailored for cryo-EM image reconstruction.

Findings

Effective deblurring with Fourier-based methods demonstrated.

Hermite and Laguerre-Fourier expansions improve Fourier transform properties.

Applicable to cryo-EM for biomolecular complex imaging.

Abstract

This paper addresses the deconvolution of an image that has been obtained by superimposing many copies of an underlying unknown image of interest. The superposition is assumed to not be exact due to noise, and is described using an error distribution in position, orientation, or both. We assume that a good estimate of the error distribution is known. The most natural approach to take for the purely translational case is to apply the Fourier transform and use the classical convolution theorem together with a Weiner filter to invert. In the case of purely rotational deblurring, the similar Fourier analysis is applied. That is, for an blurred image function defined on polar coordinates, the Fourier series and the convolution theorem for the series can be applied. In the case of combinations of translational and rotational errors, the motion-group Fourier transform is used. In addition, for the three cases we present the alternative method using Hermite and Laguerre-Fourier expansion, which has a special property in Fourier transform. The problem that is solved here is motivated by one of the steps in the cryo-electron-tomographic reconstruction of biomolecular complexes such as viruses and ion channels.