Image extrapolation can be formulated as reconstructing a matrix from partial observations obtained under an edge-removal sampling scheme. To further improve the performance of image extrapolation, this paper explores this task from the perspective of compressive sensing. By integrating such hybrid priors as smoothness, sparsity and low-rank, this paper proposes a prior-guided augmented Lagrangian multiplier (PALM) algorithm for image extrapolation. By iteratively minimizing reweighted residuals and refining the parametric model built from the known samples, the method approximates the unknown samples within edge regions. Relative to existing approaches, experiments indicate that the proposed PALM algorithm attains superior reconstruction quality while maintaining moderate computational complexity for image extrapolation.