This paper proposes an iterative high-resolution image interpolation algorithm using spatially adaptive constraints and regularization functional. The proposed algorithm adapts adaptive constraints according to the direction of..edges in an image, and can restore high-resolution image by optimizing regularization functional at each iteration, which is suitable for edge directional regularization. The proposed algorithm outperforms the conventional adaptive interpolation methods as well as non-adaptive ones, which not only can restore high frequency components, but also effectively reduce undesirable effects such as noise. Finally, in order to evaluate the performance of the proposed algorithm, various experiments are performed so that the proposed algorithm can provide good results in the sense of subjective and objective views.