Superresolution image reconstruction produces a high-resolution image from a set of shifted, blurred, and decimated versions thereof. Previously published techniques perform well only for small magnifications but get worse either in computational complexity or ringing artifacts for large magnifications. We propose a hybrid algorithm to reduce both ringing artifacts and computational complexity of maximum a posteriori (MAP)-based superresolution algorithms. The proposed algorithm magnifies the low-resolution image in stages, and applies a new edge-adaptive postprocessing algorithm at early stages. Experiment results show that the new approach is more efficient and can provide much better reconstruction quality in comparison with normal MAP algorithms.