This paper presents a novel algorithm for the 3D tomographic inversion problem that arises in single-particle electron cryo-microscopy (Cryo-EM). It is based on two key components: 1) a variational formulation that promotes sparsity in the wavelet domain and 2) the Toeplitz structure of the combined projection/back-projection operator. The first idea has proven to be very effective for the recovery of piecewise-smooth signals, which is confirmed by our numerical experiments. The second idea allows for a computationally efficient implementation of the reconstruction procedure, using only one circulant convolution per iteration.