The performance of image interpolation depends on an image model that can adapt to nonstationary statistics of natural images when estimating the missing pixels. However, the construction of such an adaptive model needs the knowledge of every pixels that are absent. We resolve this dilemma by a new piecewise 2D autoregressive technique that builds the model and estimates the missing pixels jointly. This task is formulated as a non-linear optimization problem. Although computationally demanding, the new non-linear approach produces superior results than current methods in both PSNR and subjective visual quality. Moreover, in quest for a practical solution, we break the non-linear optimization problem into two subproblems of linear least-squares estimation. This linear approach proves very effective in our experiments.