Super-resolution image reconstruction is a process to reconstruct high-resolution images from shifted, low-resolution, degraded observations. In the last two decades, a variety of super-resolution methods have been proposed. These methods are usually very sensitive to their assumed model of data and noise, which limits their utility. This paper reviews some of these methods and addresses their shortcomings. We propose an alternate approach using 1norm minimization and robust regularization based on a bilateral prior to deal with different data and noise models. This computationally inexpensive method is robust to errors in motion and blur estimation and results in images with sharp edges. Experimental results confirm the effectiveness of our method and demonstrate its superiority to other super-resolution methods.