In this paper, we proposed a new edge-directed image interpolation algorithm which can preserve the edge features and natural appearance of images efficiently. In the proposed scheme, we first get a close-form solution of the optimal interpolation coefficients under the sense of minimal mean square error by exploiting autoregressive model (AR) and the geometric duality between the low-resolution and high-resolution images .Then the coefficients of the Nonlocal Edge-directed interpolation (NLEDI) are derived with structure similarity in images, which are solutions of weighted least square equations. The new image interpolation approach preserves spatial coherence of the interpolated images better than the existing methods and it outperforms the other methods in terms of objective and subjective image quality.