Algorithms for super-resolution of images based on Sparse Representation and Manifolds

lmage super-resolution is defined as a class of techniques that enhance the spatial resolution of images. Super-resolution methods can be subdivided in single and multi image methods. This thesis focuses on developing algorithms based on mathematical theories for single image super­ resolution problems. lndeed, in arder to estimate an output image, we adopta mixed approach: i.e., we use both a dictionary of patches with 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 the solution, cluster data samples (samples are often clustered using algorithms with the Euclidean distance as a dissimilarity metric), learn dictionaries (they are often learned using 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, we developed SE-ASDS (a structure tensor based regularization term) in arder to improve the sharpness of edges. SE-ASDS achieves much better results than many state-of-the- art algorithms. Then, we proposed AGNN and GOC algorithms for determining a local subset of training samples from which a good local model can be computed for recon- structing 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. The aSOB 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 methods.

Contradições como força de mudança: o processo de formação continuada de professores do ensino médio enquanto potencializador da práxis transformadora à luz da teoria histórico-cultural

The intervention research proposed was based on the Cultural-Historical Theory based on the laws and logic of materialism historical-dialectical. Therefore, we tried to design a research process that involved all as responsible for the process. In the field of continuous teacher's training usually has been found dualistic relationship / paradoxical processes as a result of the adopted training models which are characterized by individualist human processes. The teacher training work sought to overcome this dualism, to promote the unveiling of the contradictions with regard to teaching models. As a hypothesis, we imagined that immersed in this process, teachers recognize such contradictions, and this recognition would make the contradictions become the driving force of change in teaching practice, realizing the teaching-learning-development triad as the basis of praxis. Aiming to develop a process of continuing education to bring results to the professional teachers development looking for answer the following research question: How and what the changes of teachers who participated in the Didactic-Formative Intervention process raised the quality of their teaching practices? In this context, the objective of the research was to develop a process of Didactic-Formative Intervention from the perspective of Cultural-Historical Theory with high school teachers in order to theorize about the changes in pedagogical practices of teachers and learn aspects that transform the essence teaching practice. The research involved two high school teachers of a public school in Uberlândia-MG. The training meetings took place at the school through a collective study group between the years 2013 and 2015. As procedures were used two interconnected aspects: classes observations, and a theoretical and methodological training, both for diagnosis and for the process evaluation, the second aspect has a formative dimension, and a didactic dimension (double meaning) to form didactically the teacher and to elaborate didactic procedures. The collected data were analyzed by observing the assumptions of the method, analysis by units and the processuality. As results teachers showed changes in their teaching practices regarding the organization of the pedagogical work and also centered their design educational actions based on learning and development of the students. The presence of continuous diagnosis during the classes, work with a systems of concepts and their conceptual links, problematization as a teaching method can be pointed as meaningful changes in their praxis. Regarding the training activities that emerged from the analysis of the compiled materials and analyzed throughout the process can be emphasized: forming a collective group of school teachers continuous training, diagnostics, development of practical activities, increase relationships among participants, the choice of scientific material used should have direct relation to the needs of the participants, promoting conditions that enable the emergence of contradictions between the pedagogical practice of teachers and teaching based on the perspective of the Cultural-Historical Theory. This research craved to develop and design a teachers' training processes that increase the quality of teachers life and ways of teaching in the Brazilian public school.