Patch-based image representation and restoration

This thesis strives to familiarize the ideas behind the success of patch-based image representations in image processing applications in recent years. Furthermore we show how to restore images using the idea of patch-based dictionary learning and the k-means clustering algorithm. In chapter 1 we introduce the notion of patch-based image processing and take a look at why dictionary learning using sparsity is a hot topic and useful in processing natural images. The second chapter aims to formulate the different methods and approaches used in this thesis mathematically. Dictionary learning, the k-means algorithm and the Structural similarity index (SSIM) are in the main focus. Chapter 3 goes into the details of the experiments. We present and discuss the results as well. The fourth and final chapter summarizes the main ideas of the thesis and introduces development suggestions for further investigation based on the methods used. Using a fairly simplistic patch-based image processing method we manage to reconstruct images from a set of similar images to a reasonable extent. As the main result we see how the size of the patches as well as the size of the learned dictionary effects the quality of the restored image. We also detect the limitations and problems of this approach such as the appearance of patch artifacts which is an issue to attack and resolve in following studies.