A variant to the “random approximation” of the reference-free alignment algorithm

Abstract Single-particle averaging from electron microscope images strongly depends on alignment. Most alignment procedures are based on cross-correlation of an initial reference image with the rest of the population, leading to a clear pattern dependence. Among the different approaches that have been proposed to minimize this problem, one of the most widely used is the so-called iterative reference-free alignment algorithm (RFAA), proposed by Penczek et al. [Ultramicroscopy 40 (1992) 33]. To avoid the pattern dependence shown by the initial “random approximation” step of this method, we propose a variant of the algorithm that is more independent of the input order of the initial images and which could substitute the random initialization of the RFAA.