Multi-frame image super-resolution focuses on reconstructing a high-resolution image from a set of low-resolution images with high similarity. Since super-resolution is an ill-posted problem, regularization techniques are widely used to constrain the minimization function. Combining image prior knowledge with fidelity model, Bayesian-based methods can effectively solve this ill-posed problem, which makes this kind of methods more popular than other methods. Our proposed model is based on maximum a posteriori probability (MAP) estimation. In this thesis, we propose a novel initialization method based on median operator to initialize our estimated high-resolution image. For the fidelity term in our proposed algorithm, the half-quadratic estimation is used to choose error norm adaptively instead of using fixed L1 or L2 norm. Furthermore, for our regularization term, we propose a novel regularization method based on Difference Curvature (DC) and Bilateral Total Variation (BTV) to suppress mixed noises and preserve image edges simultaneously. In our experimental results, synthetic data and real data are both tested to demonstrate the superiority of our proposed method in terms of clearer texture and less noise over other state-of-the-art methods.

Face recognition is a challenging problem in computer vision. Difficulties such as slight differences between similar faces of different people, changes in facial expressions, light and illumination condition, and pose variations add extra complications to the face recognition research. Many algorithms are devoted to solving the face recognition problem, among which the family of nonnegative matrix factorization (NMF) algorithms has been widely used as a compact data representation method. Different versions of NMF have been proposed. Wang et al. proposed the graph-based semi-supervised nonnegative learning (S2N2L) algorithm that uses labeled data in constructing intrinsic and penalty graph to enforce separability of labeled data, which leads to a greater discriminating power. Moreover the geometrical structure of labeled and unlabeled data is preserved through using the smoothness assumption by creating a similarity graph that conserves the neighboring information for all labeled and unlabeled data. However, S2N2L is sensitive to light changes, illumination, and partial occlusion. In this thesis, we propose a Semi-Supervised Half-Quadratic NMF (SSHQNMF) algorithm that combines the benefits of S2N2L and the robust NMF by the half- quadratic minimization (HQNMF) algorithm.Our algorithm improves upon the S2N2L algorithm by replacing the Frobenius norm with a robust M-Estimator loss function. A multiplicative update solution for our SSHQNMF algorithmis driven using the half- 4 quadratic (HQ) theory. Extensive experiments on ORL, Yale-A and a subset of the PIE data sets for nine M-estimator loss functions for both SSHQNMF and HQNMF algorithms are investigated, and compared with several state-of-the-art supervised and unsupervised algorithms, along with the original S2N2L algorithm in the context of classification, clustering, and robustness against partial occlusion. The proposed algorithm outperformed the other algorithms. Furthermore, SSHQNMF with Maximum Correntropy (MC) loss function obtained the best results for most test cases.