Huber Markov Random Field for Joint Super Resolution

Super Resolution (SR) technique takes a sequence of blurred noisy Low Resolution (LR) images of a scene and fuses them to produce a High Resolution (HR) image with better quality. The LR images should be aligned first. The most important SR methods are iterative simultaneous methods in which image fusion and image alignment are performed, simultaneously. In these methods, the SR problem is converted to an optimization problem in terms of the HR image and motion parameters. There are two major groups of simultaneous methods, i.e. joint methods and Alternating Minimization (AM) methods. The main difference between these two groups is that in the joint methods the correlation between HR image and motion parameters is fully considered in each iteration but in the AM methods this is not the case. Because the SR problem is ill-posed, to obtain unique solution, prior term is required for HR image. The most famous image priors are Gaussian Markov random field (GMRF), Total Variation (TV) and their mixture, i.e. Huber Markov random field (HMRF) which inherits the advantages of both GMRF and TV priors. But this new prior is non-quadratic, so can only used in AM methods. In this paper, after proposing a modified form for Huber potential function, a quasi-quadratic shape for HMRF prior is developed. Then using this new shape of HMRF a joint SR method is proposed. The experimental results on the synthetic and real sequences of LR images show the superiority of the proposed SR method.