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. (C) 2016 Elsevier Inc. All rights reserved.