In this paper, a super resolution (SR) and an enhancement algorithm are put forward. The SR method is proposed by the assumption of local self example model with nonlocal constraints, and the detail enhancement method is raised by analyzing 2-order holomorphic complete differential kernel of a single image. For the inappropriate frequency component in the SR process, we design a nonlocal constraint to weaken it. Final super resolution result is given by solving the designed optimization functions, taking both SAD and nonlocal constraints into consideration. Moreover, detail information of the single image is modeled in mathematical way. 2-order holomorphic complete differential kernel is proposed to constrain such information. Analysis is given on the relations and the differences between the proposed approach and some other state-of-the-art SR and enhancement methods. Experimental results show that the proposed method can achieve better image quality as compared to other competitors.