Sparsity regularization has been drawn great attention towards ill-posed inverse problem. In that theory, data can be approximated by a linear combination of dictionary atoms (e.g. Curvelet) with only few non-zero coefficients that can present most information of data. To improve the fidelity, sparsity constraint term is usually involved in the object functional under the \emph{priori} assumption. Currently, the data-driven tight frame (DDTF) is widely used due to preserving more directional structures that adaptively learned from a dataset. Regarding to variational data assimilation (VDA) for 2D velocity reconstruction, however, insufficient estimation of background, error covariance matrix and scarce observation will lead to unreliable prediction. In this scenario, the learning-regularizer would be taken into account in view of the fact that features in image contribute to optimizing the flow. Herein, in this study, we develop the traditional VDA by a vortex structure dictionary sparsity regularization. The split Bregman iteration algorithm is utilized to solve this non-smooth convex optimization problem. Some test cases using real data will show the viability of the proposed approach and its numerical performance is discussed.