(18.6 MB) Abstract
The development pace of high-resolution displays has been so fast in the recent years that many images acquired with low-end capture devices are already outdated or will be shortly in time. Super Resolution is central to match the resolution of the already existing image content to that of current and future high resolution displays and applications. This dissertation is focused on learning how to upscale images from the statistics of natural images. We build on a sparsity model that uses learned coupled low- and high-resolution dictionaries in order to upscale images.
Firstly, we study how to adaptively build coupled dictionaries so that their content is semantically related with the input image. We do so by using a Bayesian selection stage which finds the best-fitted texture regions from the training dataset for each input image. The resulting adapted subset of patches is compressed into a coupled dictionary via sparse coding techniques.
We then shift from l1 to a more efficient l2 regularization, as introduced by Timofte et al. Instead of using their patch-to-dictionary decomposition, we propose a fully collaborative neighbor embedding approach. In this novel scheme, for each atom in the dictionary we create a densely populated neighborhood from an extensive training set of raw patches (i.e. in the order of hundreds of thousands). This generates more accurate regression functions.
We additionally propose using sublinear search structures such as spherical hashing and trees to speed up the nearest neighbor search involved in regression-based Super Resolution. We study the positive impact of antipodally invariant metrics for linear regression frameworks, and we propose two efficient solutions: (a) the Half Hypersphere Confinement, which enables antipodal invariance within the Euclidean space, and (b) the bimodal tree, whose split functions are designed to be antipodally invariant and which we use in the context of a Bayesian Super Resolution forest.
In our last contribution, we extend antipodal invariance by also taking into consideration the dihedral group of transforms (i.e. rotations and reflections). We study them as a group of symmetries within the high-dimensional manifold. We obtain the respective set of mirror-symmetry axes by means of a frequency analysis, and we use them to collapse the redundant variability, resulting in a reduced manifold span which, in turn, greatly improves quality performance and reduces the dictionary sizes.
