Statistical modeling and removal of lipid membrane projections for cryo-EM structure determination of reconstituted membrane proteins.

This paper describes steps in the single-particle cryo-EM 3D structure determination of membrane proteins in their membrane environment. Using images of the Kv1.2 potassium-channel complex reconstituted into lipid vesicles, we describe procedures for the merging of focal-pairs of exposures and the removal of the vesicle-membrane signal from the micrographs. These steps allow 3D reconstruction to be performed from the protein particle images. We construct a 2D statistical model of the vesicle structure based on higher-order singular value decomposition (HOSVD), by taking into account the structural symmetries of the vesicles in polar coordinates. Non-roundness in the vesicle structure is handled with a non-linear shape alignment to a reference, which ensures a compact model representation. The results show that the learned model is an accurate representation of the imaged vesicle structures. Precise removal of the strong membrane signals allows better alignment and classification of images of small membrane-protein particles, and allows higher-resolution 3D reconstruction.

Multilinear Modelling of Faces and Expressions.

In this work, we present a new versatile 3D multilinear statistical face model, based on a tensor factorisation of 3D face scans, that decomposes the shapes into person and expression subspaces. Investigation of the expression subspace reveals an inherent low-dimensional substructure, and further, a star-shaped structure. This is due to two novel findings. (1) Increasing the strength of one emotion approximately forms a linear trajectory in the subspace. (2) All these trajectories intersect at a single point - not at the neutral expression as assumed by almost all prior works-but at an apathetic expression. We utilise these structural findings by reparameterising the expression subspace by the fourth-order moment tensor centred at the point of apathy. We propose a 3D face reconstruction method from single or multiple 2D projections by assuming an uncalibrated projective camera model. The non-linearity caused by the perspective projection can be neatly included into the model. The proposed algorithm separates person and expression subspaces convincingly, and enables flexible, natural modelling of expressions for a wide variety of human faces. Applying the method on independent faces showed that morphing between different persons and expressions can be performed without strong deformations.

Structure-from-motion without correspondence from tomographic projections by Bayesian inversion theory.

In conventional tomography, the interior of an object is reconstructed from tomographic projections such as X-ray or transmission electron microscope images. All the current reconstruction methods assume that projection geometry of the imaging device is either known or solved in advance by using e.g., fiducial or nonfiducial feature points in the images. In this paper, we propose a novel approach where the imaging geometry is solved simultaneously with the volume reconstruction problem while no correspondence information is needed. Our approach is a direct application of Bayesian inversion theory and produces the maximum likelihood or maximum a posteriori estimates for the motion parameters under the selected noise and prior distributions. In this paper, the method is implemented for a two-dimensional model problem with one-dimensional affine projection data. The performance of the method is tested with simulated and measured X-ray projection data.

Removal of Vesicle Structures From Transmission Electron Microscope Images.

In this paper, we address the problem of imaging membrane proteins for single-particle cryo-electron microscopy reconstruction of the isolated protein structure. More precisely, we propose a method for learning and removing the interfering vesicle signals from the micrograph, prior to reconstruction. In our approach, we estimate the subspace of the vesicle structures and project the micrographs onto the orthogonal complement of this subspace. We construct a 2D statistical model of the vesicle structure, based on higher order singular value decomposition (HOSVD), by considering the structural symmetries of the vesicles in the polar coordinate plane. We then propose to lift the HOSVD model to a novel hierarchical model by summarizing the multidimensional HOSVD coefficients by their principal components. Along with the model, a solid vesicle normalization scheme and model selection criterion are proposed to make a compact and general model. The results show that the vesicle structures are accurately separated from the background by the HOSVD model that is also able to adapt to the asymmetries of the vesicles. This is a promising result and suggests even wider applicability of the proposed approach in learning and removal of statistical structures.