In this thesis, we firstly introduce the application of the Generalized Gaussian Markov Random Field (GGMRF) to the problem of video super-resolution. The GGMRF prior is employed to perform a maximum a posteriori (MAP) estimation of the desired high-resolution image. Compared with traditional prior models, the GGMRF can describe the distribution of the high-resolution image much better and can also preserve better the discontinuities (edges) of the original image. Previous work had used GGMRF for image restoration in which the temporal dependencies among video frames are not considered. Since the corresponding energy function is convex, gradient descent optimisation techniques are used to solve the MAP estimation. Results show the super-resolved images using the GGMRF prior not only offers a good visual quality enhancement, but also contain a significantly smaller amount of noise. We then propose a Bayesian-based super resolution algorithm that uses approximations of symmetric alpha-stable (SaS) Markov Random Fields (MRF) as prior. The approximated SaS prior is employed to perform MAP estimation for the high-resolution (RR) image reconstruction process. Compared with other state-of-the-art prior models, the proposed prior can better capture the heavy tails of the distribution of the HR image. Thus, the edges of the reconstructed HR image are preserved better in our method. Since the corresponding energy function is non-convex, the graduated nonconvexity (GNC) method is used to solve the MAP estimation. Experiments confirm the better fit achieved by the proposed model to the actual data distribution and the consequent improvement in terms of visual quality over previously proposed super resolution algorithms . . A joint video fusion and super-resolution algorithm is also proposed in this thesis. The method addresses the problem of generating a high-resolution HR image from infrared (IR) and visible (VI) low-resolution (LR) images, in a Bayesian framework. In order to preserve better the discontinuities, a Generalized Gaussian Markov Random Field (MRF) is used to formulate the prior. Experimental results demonstrate that information from both visible and infrared bands is recovered from the LR frames in an effective way. Finally, a novel video super-resolution image reconstruction algorithm that based on low rank matrix completion algorithm is presented. The proposed algorithm addresses the problem of generating a HR image from several LR images, based on sparse representation and low-rank matrix completion. The approach represents observed LR frames in the form of sparse matrices and rearranges those frames into low dimensional constructions. Experimental results demonstrate that, high-frequency details in the super resolved images are recovered from the LR frames .