This paper introduces a sparsity based optical flow estimation method in digital video sequences. The method stems from the key observation that the gradient field of optical flow, in digital video sequences, is usually structured and sparse in spatial domain, provided there is a small number of multiple motions in the scene. The gradient field of motion vectors is formed by the pixels forming the edges of moving objects. We utilize this fact and formulate the optical flow estimation problem in sparse representation framework. We then use a minimization algorithm over ℓ1 norm of the gradient flow field to find the solution to this problem. The proposed algorithm has been evaluated on Middlebury's benchmark video sequence database.