Mats Matsson, presents his master thesis Image Super-Resolution using Gaussian Markov Random Fields Abstract There are many scenarios where greater detail in an image is desired than what is possible with the available equipment, e.g. in video surveillance. A super-resolution image is an image with greater resolution estimated from images with lower resolution. In this thesis we examine the use of Intrinsic Gaussian Markov Random Fields (IGMRF) to construct a super-resolution image from a number of low- resolution images. We describe an approach to this based on the EM-Algorithm with stationary registration noise for the low-resolution images and a stationary IGMRF prior distribution for the super-resolution image, and then try to extend this to a non-stationary model for both. A non- stationary image prior has been tried by others. The non-stationary registration noise is something we believe is a novel approach. The methods have been evaluated with simulated images, with good results, and real images, with no improvements in detail. We found that a non-stationary registration noise approach work, but had unpredictable results using a non-stationary prior distribution. The lack of improvement in detail for the real images may be due to that we model the camera as a pin-hole camera, i.e. assume the lens is perfect. Our limited modeling of color images is also something that may improve future results.