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.

Data-driven Automatic Edge Sharpening

Sharpening is a powerful image transformation because sharp edges can bring out image details. Sharpness is achieved by increasing local contrast and reducing edge widths. We present a method that enhances sharpness of images and thereby their perceptual quality. Most existing enhancement techniques require user input to improve the perception of the scene in a manner most pleasing to the particular user. Our goal of image enhancement is to improve the perception of sharpness in digital images for human viewers. We consider two parameters in order to exaggerate the differences between local intensities. The two parameters exploit local contrast and widths of edges. We start from the assumption that color, texture, or objects of focus such as faces affect the human perception of photographs. When human raters are presented with a collection of images with different sharpness and asked to rank them according to perceived sharpness, the results have shown that there is a statistical consensus among the raters. We introduce a ramp enhancement technique by modifying the optimal overshoot in the ramp for different region contrasts as well as the new ramp width. Optimal parameter values are searched to be applied to regions under the criteria mentioned above. In this way, we aim to enhance digital images automatically to create pleasing image output for common users.

Atomic resolution studies of oxide superlattices and ultrathin films

The ability to grow ultrathin films layer-by-layer with well-defined epitaxial relationships has allowed research groups worldwide to grow a range of artificial films and superlattices, first for semiconductors, and now with oxides. In the oxides thin film research community, there have been concerted efforts recently to develop a number of epitaxial oxide systems grown on single crystal oxide substrates that display a wide variety of novel interfacial functionality, such as enhanced ferromagnetic ordering, increased charge carrier density, increased optical absorption, etc, at interfaces. The magnitude of these novel properties is dependent upon the structure of thin films, especially interface sharpness, intermixing, defects, and strain, layering sequence in the case of superlattices and the density of interfaces relative to the film thicknesses. To understand the relationship between the interfacial thin film oxide atomic structure and its properties, atomic scale characterization is required. Transmission electron microscopy (TEM) offers the ability to study interfaces of films at high resolution. Scanning transmission electron microscopy (STEM) allows for real space imaging of materials with directly interpretable atomic number contrast. Electron energy loss spectroscopy (EELS), together with STEM, can probe the local chemical composition as well as local electronic states of transition metals and oxygen. Both techniques have been significantly improved by aberration correctors, which reduce the probe size to 1 Å, or less. Aberration correctors have thus made it possible to resolve individual atomic columns, and possibly probe the electronic structure at atomic scales. Separately, using electron probe forming lenses, structural information such as the crystal structure, strain, lattice mismatches, and superlattice ordering can be measured by nanoarea electron diffraction (NED). The combination of STEM, EELS, and NED techniques allows us to gain a fundamental understanding of the properties of oxide superlattices and ultrathin films and their relationship with the corresponding atomic and electronic structure. In this dissertation, I use the aforementioned electron microscopy techniques to investigate several oxide superlattice and ultrathin film systems. The major findings are summarized below. These results were obtained with stringent specimen preparation methods that I developed for high resolution studies, which are described in Chapter 2. The essential materials background and description of electron microscopy techniques are given in Chapter 1 and 2. In a LaMnO3-SrMnO3 superlattice, we demonstrate the interface of LaMnO3-SrMnO3 is sharper than the SrMnO3-LaMnO3 interface. Extra spectral weights in EELS are confined to the sharp interface, whereas at the rougher interface, the extra states are either not present or are not confined to the interface. Both the structural and electronic asymmetries correspond to asymmetric magnetic ordering at low temperature. In a short period LaMnO3-SrTiO3 superlattice for optical applications, we discovered a modified band structure in SrTiO3 ultrathin films relative to thick films and a SrTiO3 substrate, due to charge leakage from LaMnO3 in SrTiO3. This was measured by chemical shifts of the Ti L and O K edges using atomic scale EELS. The interfacial sharpness of LaAlO3 films grown on SrTiO3 was investigated by the STEM/EELS technique together with electron diffraction. This interface, when prepared under specific conditions, is conductive with high carrier mobility. Several suggestions for the conductive interface have been proposed, including a polar catastrophe model, where a large built-in electric field in LaAlO3 films results in electron charge transfer into the SrTiO3 substrate. Other suggested possibilities include oxygen vacancies at the interface and/or oxygen vacancies in the substrate. The abruptness of the interface as well as extent of intermixing has not been thoroughly investigated at high resolution, even though this can strongly influence the electrical transport properties. We found clear evidence for cation intermixing through the LaAlO3-SrTiO3 interface with high spatial resolution EELS and STEM, which contributes to the conduction at the interface. We also found structural defects, such as misfit dislocations, which leads to increased intermixing over coherent interfaces.

Discontinuous Galerkin Methods for the Biharmonic Problem

This work is concerned with the design and analysis of hp-version discontinuous Galerkin (DG) finite element methods for boundary-value problems involving the biharmonic operator. The first part extends the unified approach of Arnold, Brezzi, Cockburn & Marini (SIAM J. Numer. Anal. 39, 5 (2001/02), 1749-1779) developed for the Poisson problem, to the design of DG methods via an appropriate choice of numerical flux functions for fourth order problems; as an example we retrieve the interior penalty DG method developed by Suli & Mozolevski (Comput. Methods Appl. Mech. Engrg. 196, 13-16 (2007), 1851-1863). The second part of this work is concerned with a new a-priori error analysis of the hp-version interior penalty DG method, when the error is measured in terms of both the energy-norm and L2-norm, as well certain linear functionals of the solution, for elemental polynomial degrees $p\ge 2$. Also, provided that the solution is piecewise analytic in an open neighbourhood of each element, exponential convergence is also proven for the p-version of the DG method. The sharpness of the theoretical developments is illustrated by numerical experiments.

FAULT MORPHOLOGY WITHIN THE SOUTHERN KENYAN PORTION OF THE EAST AFRICAN RIFT VALLEY

Faults form quickly, geologically speaking, with sharp, crisp step-like profiles. Logic dictates that erosion wears away this "sharpness" or angularity creating more rounded features. As erosion occurs, debris accumulates at the base of the scarp slope. The stable end point of this process is when the scarp slope approaches an ideal sigmoid shape. This theory of fault end process, in combination with a new method developed in this report for fault profile delineation, has the potential to enable observation and categorization of fault profiles over large, diverse swaths of fault formation-- in remote areas such as the Southern Kenyan Rift Valley. This up-to date method uses remote sensing data and the digitizer tool in Global Mapper to create shape files of fault segments. This method can provide further evidence to support the notion that sigmoidal- shaped profiles represent a natural endpoint of the erosional process of fault scarps. Over time, faults of many different ages would exist in this similar shape over a wide region. However, keeping in mind that other processes can be at work on scarps-- most notably drainage patterns, when anomalies in profiles are observed, reactivation in some form possibly has occurred.

Humor político audiovisual en Colombia: de los gloriosos años noventa en televisión a internet como alternativa

El humor político alrededor del mundo ha sido un recurso para criticar el poder y la esfera política con la mordacidad que otros escenarios no permiten y con lenguajes que generan empatía con el público. En la capacidad de criticar a todos los poderes –y poderosos- por igual, sin condescendencias, recae la credibilidad de esa crítica, la cual se debe poder hacer sin censura en una sociedad pluralista y democrática. En Colombia, el humor político en televisión emergió y vivió su época dorada en la década de los noventa, hasta que su principal exponente, Jaime Garzón, fue asesinado. Este trabajo de grado buscó indagar por qué, a pesar de que nuevos productos de crítica política con humor surgieron en el país, hoy no hay ese tipo de oferta en la televisión abierta nacional. La respuesta a ese interrogante se pudo encontrar en múltiples factores, como un nuevo modelo económico en la industria de la televisión, un ambiente político polarizado y la ausencia o falta de promoción de talentos detrás de los libretos. Asimismo, en medio de esta coyuntura, se plantea que internet ha sido un vehículo para expresar, incluso de manera anónima, lo que miembros de la sociedad creen que anda mal con el poder y la política.