Cryo-electron microscopy has recently been recognized as a useful alternative to obtain three-dimensional density maps of macromolecular complexes, especially when crystallography and NMR techniques fail. The three-dimensional model is constructed from large collections of cryo-electron microscopy images of identical particles in random (and unknown) orientations. The major problem with cryo-electron microscopy is that the images are very noisy as the signal-to-noise ratio can be below one. Thus, standard filtering techniques are not directly applicable. Traditionally, the problem of immense noise in the cryo-electron microscopy images has been tackled by clustering the images and computing the class averages. However, then one has to assume that the particles have only few preferred orientations. In this paper we propose a sound method for denoising cryo-electron microscopy images using their Radon transforms. The method assumes only that the images are from identical particles but n...