In focusing Kerr media, small- scale filamentation is the major obstacle to imaging at high light intensities. In this article, we experimentally and numerically demonstrate a method based on statistical averaging to reduce the detrimental effects of filamentation on the reconstructed images. The experiments are performed with femtosecond optical pulses propagating through a nonlinear liquid (toluene). We use digital holography to capture the transmitted optical image. The reverse propagation of the captured field is numerically performed using a numerical solution of the nonlinear Schrodinger equation. Because of their intrinsic sensitivity to measurement noise, filaments fail to propagate back on their initial trajectories and parasitic filaments form. The principle of the method is the introduction of artificial perturbations on the measurement, which spatially displace the parasitic filaments. By averaging the reconstruction over many realizations of the artificial perturbation, we show that the reconstruction improves the quality of the images. Finally, in order to identify the different regimes of optical power for which the filaments are time reversible, we also derive an analytical estimate for the condition number of the nonlinear propagator. (C) 2015 Optical Society of America