A new FFT-accelerated projection matching method is presented and tested. The electron microscopy images are represented by their Fourier - Bessel transforms and the 3D model by its expansion in spherical harmonics, or more specifically in terms of symmetry-adapted functions. The rotational and translational properties of these representations are used to quickly access all the possible 2D projections of the 3D model, which allow an exhaustive inspection of the whole five-dimensional domain of parameters associated to each particle. (c) 2008 Elsevier Inc. All rights reserved.