Concerning the loss of weak edges and texture details of the second-order Partial Differential Equation (PDE) amplification algorithm, an image enlargement algorithm was proposed based on improved complex diffusion adaptively coupled nonlocal transform domain model. By utilizing the advantage of accurate edge location of the complex diffusion model, the improved complex diffusion coupled impulse filter to enhance strong edges better; by modeling the sparse characteristics of the transform coefficients coming from three dimensional transformation of the image group composed of similar image blocks, the nonlocal transform domain model could make good use of the nonlocal information of the similar image blocks and had better processing effects on weak edges and texture details. Finally, the second-order derivation of the image obtained by the complex diffusion was used as the parameter to realize the adaptive coupling of the improved complex diffusion model and the nonlocal transform domain model. Compared with partial differential equation amplification algorithm, nonlocal transformation domain amplification algorithm and partial differential equation coupled space domain nonlocal model amplification algorithm, the proposed algorithm has better amplification effect on strong edges, weak edges and detail textures, the mean structural similarity measures of weak edges and texture detail images are higher than those of improved complex diffusion magnification algorithm and the nonlocal transform domain amplification algorithm. The proposed algorithm also confirms the validity of the coupling between the space domain model and the transform domain model, local model and nonlocal model.