Fast Single Image Super-Resolution

This paper addresses the problem of single image super-resolution, which consists of recovering a high resolution image from its blurred, decimated and noisy version. Given the well-known ill-posedness of image super-resolution, prior information is used for regularization purpose in order to obtain a well-posed problem. Among the existing algorithms, the alternating direction method of multipliers (ADMM) has been used intensively because of its effective implementation due to the possibility of splitting the super-resolution problem into up-sampling and deconvolution problems, which all can be easily solved. Instead of following this splitting strategy, we propose to consider the decimation and blurring operators simultaneously by taking advantage of their particular properties, leading to a new fast super-resolution approach. Based on this new scheme, different types of priors or regularizations are considered following the Bayesian framework. For a Gaussian prior, an analytical solution is easily obtained, which can be implemented in a very efficient way. In the case of non-Gaussian priors, we show that this analytical solution derived from the Gaussian case can be embedded into the ADMM framework, which accelerates the existing algorithms significantly. Simulation results on several images show the effectiveness of our fast scheme compared with the traditional ADMM implementation.