In this paper, we consider the problem of reconstructing sources in a homogeneous viscoelastic medium from wavefield measurements. We first present a modified time-reversal imaging algorithm based on a weighted Helmholtz decomposition and justify mathematically that it provides a better approximation than by simply time reversing the displacement field, where artifacts due to the coupling betwe en the pressure and shear waves appear. Then, we investigate the source inverse problem in an elastic attenuating medium. We provide a regularized time-reversal imagin g which corrects the attenuation effect at the first order. The results of this paper yie ld the fundamental tools for solving imaging problems in elastic media using cross correl ation techniques