A novel variational algorithm is developed for video inpainting. Within a Bayesian framework, using standard maximum a posteriori to variational formulation rationale, we derive a minimum energy formulation for the estimation of a reconstructed sequence as well as motion recovery. From the EulerLagrange Equations, we propose a full multiresolution algorithm in order to compute a good local minimizer for our energy and discuss its numerical implementation. Experimental results for synthetic as well as real sequences are presented.