We describe a new algorithm for combining multiple low-resolution images to obtain a high-resolution object estimate. Each camera is treated as a communication channel and we exploit sub-pixel shifts to achieve significant resolution enhancement. The 2D4 algorithm is an iterative likelihood-based method that is computationally less expensive than the two-dimensional Viterbi algorithm. In this paper, we modify the 2D4 algorithm and apply it to the multiframe image restoration problem. We demonstrate the reconstruction of a high-resolution scene from multiple blurred, noisy, and shifted low-resolution image measurements. We discuss the modifications and approximations to the 2D4 algorithm that are required to reduce its complexity for this application. We present the performance of this algorithm and compare it with the performance of Iterative Back Projection and optimal linear methods.