Algorithms for Super-resolution of Images based on Sparse Representation and Manifolds. (Algorithmes de super-résolution d'ilmages basés sur représentations parcimonieuses et variétés)

Image super-resolution is defined as a class of techniques that enhance the spatialresolution of images. Super-resolution methods can be subdivided in single and multiimage methods. This thesis focuses on developing algorithms based on mathematicaltheories for single image super-resolution problems. Indeed, in order to estimate anoutput image, we adopt a mixed approach: i.e., we use both a dictionary of patcheswith sparsity constraints (typical of learning-based methods) and regularization terms(typical of reconstruction-based methods). Although the existing methods already per-form well, they do not take into account the geometry of the data to: regularize thesolution, cluster data samples (samples are often clustered using algorithms with theEuclidean distance as a dissimilarity metric), learn dictionaries (they are often learnedusing PCA or K-SVD). Thus, state-of-the-art methods still suffer from shortcomings.In this work, we proposed three new methods to overcome these deficiencies. First, wedeveloped SE-ASDS (a structure tensor based regularization term) in order to improve the sharpness of edges. SE-ASDS achieves much better results than many state-of-theart algorithms. Then, we proposed AGNN and GOC algorithms for determining a localsubset of training samples from which a good local model can be computed for reconstructing a given input test sample, where we take into account the underlying geometry of the data. AGNN and GOC methods outperform spectral clustering, soft clustering, and geodesic distance based subset selection in most settings. Next, we proposed aSOB strategy which takes into account the geometry of the data and the dictionary size. TheaSOB strategy outperforms both PCA and PGA methods. Finally, we combine all our methods in a unique algorithm, named G2SR. Our proposed G2SR algorithm shows better visual and quantitative results when compared to the results of state-of-the-art