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.

Mineralogical, geochemical and magnetic signatures of surface sediments from the Canadian Beaufort Shelf and Amundsen Gulf (Canadian Arctic)

Mineralogical, geochemical, magnetic, and siliciclastic grain-size signatures of 34 surface sediment samples from the Mackenzie-Beaufort Sea Slope and Amundsen Gulf were studied in order to better constrain the redox status, detrital particle provenance, and sediment dynamics in the western Canadian Arctic. Redox-sensitive elements (Mn, Fe, V, Cr, Zn) indicate that modern sedimentary deposition within the Mackenzie-Beaufort Sea Slope and Amundsen Gulf took place under oxic bottom-water conditions, with more turbulent mixing conditions and thus a well-oxygenated water column prevailing within the Amundsen Gulf. The analytical data obtained, combined with multivariate statistical (notably, principal component and fuzzy c-means clustering analyses) and spatial analyses, allowed the division of the study area into four provinces with distinct sedimentary compositions: (1) the Mackenzie Trough-Canadian Beaufort Shelf with high phyllosilicate-Fe oxide-magnetite and Al-K-Ti-Fe-Cr-V-Zn-P contents; (2) Southwestern Banks Island, characterized by high dolomite-K-feldspar and Ca-Mg-LOI contents; (3) the Central Amundsen Gulf, a transitional zone typified by intermediate phyllosilicate-magnetite-K-feldspar-dolomite and Al-K-Ti-Fe-Mn-V-Zn-Sr-Ca-Mg-LOI contents; and (4) mud volcanoes on the Canadian Beaufort Shelf distinguished by poorly sorted coarse-silt with high quartz-plagioclase-authigenic carbonate and Si-Zr contents, as well as high magnetic susceptibility. Our results also confirm that the present-day sedimentary dynamics on the Canadian Beaufort Shelf is mainly controlled by sediment supply from the Mackenzie River. Overall, these insights provide a basis for future studies using mineralogical, geochemical, and magnetic signatures of Canadian Arctic sediments in order to reconstruct past variations in sediment inputs and transport pathways related to late Quaternary climate and oceanographic changes.

Enviromagnetic, major element, and grain-size analyses of surface sediment samples along the continental margin between East Brazil and Patagonia

Continental margin sediments of SE South America originate from various terrestrial sources, each conveying specific magnetic and element signatures. Here, we aim to identify the sources and transport characteristics of shelf and slope sediments deposited between East Brazil and Patagonia (20°-48°S) using enviromagnetic, major element, and grain-size data. A set of five source-indicative parameters (i.e., chi-fd%, ARM/IRM, S0.3T, SIRM/Fe and Fe/K) of 25 surface samples (16-1805 m water depth) was analyzed by fuzzy c-means clustering and non-linear mapping to depict and unmix sediment-province characteristics. This multivariate approach yields three regionally coherent sediment provinces with petrologically and climatically distinct source regions. The southernmost province is entirely restricted to the slope off the Argentinean Pampas and has been identified as relict Andean-sourced sands with coarse unaltered magnetite. The direct transport to the slope was enabled by Rio Colorado and Rio Negro meltwaters during glacial and deglacial phases of low sea level. The adjacent shelf province consists of coastal loessoidal sands (highest hematite and goethite proportions) delivered from the Argentinean Pampas by wave erosion and westerly winds. The northernmost province includes the Plata mudbelt and Rio Grande Cone. It contains tropically weathered clayey silts from the La Plata Drainage Basin with pronounced proportions of fine magnetite, which were distributed up to ~24° S by the Brazilian Coastal Current and admixed to coarser relict sediments of Pampean loessoidal origin. Grain-size analyses of all samples showed that sediment fractionation during transport and deposition had little impact on magnetic and element source characteristics. This study corroborates the high potential of the chosen approach to access sediment origin in regions with contrasting sediment sources, complex transport dynamics, and large grain-size variability.

Parcellation of fMRI datasets with ICA and PLS: a data driven approach

Inter-subject parcellation of functional Magnetic Resonance Imaging (fMRI) data based on a standard General Linear Model (GLM) and spectral clustering was recently proposed as a means to alleviate the issues associated with spatial normalization in fMRI. However, for all its appeal, a GLM-based parcellation approach introduces its own biases, in the form of a priori knowledge about the shape of Hemodynamic Response Function (HRF) and task-related signal changes, or about the subject behaviour during the task. In this paper, we introduce a data-driven version of the spectral clustering parcellation, based on Independent Component Analysis (ICA) and Partial Least Squares (PLS) instead of the GLM. First, a number of independent components are automatically selected. Seed voxels are then obtained from the associated ICA maps and we compute the PLS latent variables between the fMRI signal of the seed voxels (which covers regional variations of the HRF) and the principal components of the signal across all voxels. Finally, we parcellate all subjects data with a spectral clustering of the PLS latent variables. We present results of the application of the proposed method on both single-subject and multi-subject fMRI datasets. Preliminary experimental results, evaluated with intra-parcel variance of GLM t-values and PLS derived t-values, indicate that this data-driven approach offers improvement in terms of parcellation accuracy over GLM based techniques.

Generalized fuzzy clustering for segmentation of multi-spectral magnetic resonance images.

An integrated approach for multi-spectral segmentation of MR images is presented. This method is based on the fuzzy c-means (FCM) and includes bias field correction and contextual constraints over spatial intensity distribution and accounts for the non-spherical cluster's shape in the feature space. The bias field is modeled as a linear combination of smooth polynomial basis functions for fast computation in the clustering iterations. Regularization terms for the neighborhood continuity of intensity are added into the FCM cost functions. To reduce the computational complexity, the contextual regularizations are separated from the clustering iterations. Since the feature space is not isotropic, distance measure adopted in Gustafson-Kessel (G-K) algorithm is used instead of the Euclidean distance, to account for the non-spherical shape of the clusters in the feature space. These algorithms are quantitatively evaluated on MR brain images using the similarity measures.

Fuzzy clustering applied to a demand response model in a smart grid contingency scenario

This paper focus on a demand response model analysis in a smart grid context considering a contingency scenario. A fuzzy clustering technique is applied on the developed demand response model and an analysis is performed for the contingency scenario. Model considerations and architecture are described. The demand response developed model aims to support consumers decisions regarding their consumption needs and possible economic benefits.

Fuzzy clustering applied to a demand response model in a smatr grid contingency scenario

This paper focus on a demand response model analysis in a smart grid context considering a contingency scenario. A fuzzy clustering technique is applied on the developed demand response model and an analysis is performed for the contingency scenario. Model considerations and architecture are described. The demand response developed model aims to support consumers decisions regarding their consumption needs and possible economic benefits.

Fuzzy clustering não supervisionado na detecção automática de regiões de upwelling a partir de mapas de temperatura da superfície oceânica

Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia Informática

Objective function based fuzzy clustering in air traffic management

Data analysis, fuzzy clustering, fuzzy rules, air traffic management

A Homogeneous Set-Theoretical Frame for Clustering Fuzzy Relational Data

Our purpose is to provide a set-theoretical frame to clustering fuzzy relational data basically based on cardinality of the fuzzy subsets that represent objects and their complementaries, without applying any crisp property. From this perspective we define a family of fuzzy similarity indexes which includes a set of fuzzy indexes introduced by Tolias et al, and we analyze under which conditions it is defined a fuzzy proximity relation. Following an original idea due to S. Miyamoto we evaluate the similarity between objects and features by means the same mathematical procedure. Joining these concepts and methods we establish an algorithm to clustering fuzzy relational data. Finally, we present an example to make clear all the process

Identification of different heart tissues from MRI C-SENC images using an unsupervised multi-stage fuzzy clustering technique.

PURPOSE: To objectively characterize different heart tissues from functional and viability images provided by composite-strain-encoding (C-SENC) MRI. MATERIALS AND METHODS: C-SENC is a new MRI technique for simultaneously acquiring cardiac functional and viability images. In this work, an unsupervised multi-stage fuzzy clustering method is proposed to identify different heart tissues in the C-SENC images. The method is based on sequential application of the fuzzy c-means (FCM) and iterative self-organizing data (ISODATA) clustering algorithms. The proposed method is tested on simulated heart images and on images from nine patients with and without myocardial infarction (MI). The resulting clustered images are compared with MRI delayed-enhancement (DE) viability images for determining MI. Also, Bland-Altman analysis is conducted between the two methods. RESULTS: Normal myocardium, infarcted myocardium, and blood are correctly identified using the proposed method. The clustered images correctly identified 90 +/- 4% of the pixels defined as infarct in the DE images. In addition, 89 +/- 5% of the pixels defined as infarct in the clustered images were also defined as infarct in DE images. The Bland-Altman results show no bias between the two methods in identifying MI. CONCLUSION: The proposed technique allows for objectively identifying divergent heart tissues, which would be potentially important for clinical decision-making in patients with MI.

Fuzzy tolerance/equivalence relations from intersection, union and complement operators and their application to a clustering method

This master thesis work introduces the fuzzy tolerance/equivalence relation and its application in cluster analysis. The work presents about the construction of fuzzy equivalence relations using increasing generators. Here, we investigate and research on the role of increasing generators for the creation of intersection, union and complement operators. The objective is to develop different varieties of fuzzy tolerance/equivalence relations using different varieties of increasing generators. At last, we perform a comparative study with these developed varieties of fuzzy tolerance/equivalence relations in their application to a clustering method.

A Homogeneous Set-Theoretical Frame for Clustering Fuzzy Relational Data

Our purpose is to provide a set-theoretical frame to clustering fuzzy relational data basically based on cardinality of the fuzzy subsets that represent objects and their complementaries, without applying any crisp property. From this perspective we define a family of fuzzy similarity indexes which includes a set of fuzzy indexes introduced by Tolias et al, and we analyze under which conditions it is defined a fuzzy proximity relation. Following an original idea due to S. Miyamoto we evaluate the similarity between objects and features by means the same mathematical procedure. Joining these concepts and methods we establish an algorithm to clustering fuzzy relational data. Finally, we present an example to make clear all the process

Dynamic Niche Clustering: a fuzzy variable radius niching technique for multimodal optimisation in GAs

This paper describes the recent developments and improvements made to the variable radius niching technique called Dynamic Niche Clustering (DNC). DNC is fitness sharing based technique that employs a separate population of overlapping fuzzy niches with independent radii which operate in the decoded parameter space, and are maintained alongside the normal GA population. We describe a speedup process that can be applied to the initial generation which greatly reduces the complexity of the initial stages. A split operator is also introduced that is designed to counteract the excessive growth of niches, and it is shown that this improves the overall robustness of the technique. Finally, the effect of local elitism is documented and compared to the performance of the basic DNC technique on a selection of 2D test functions. The paper is concluded with a view to future work to be undertaken on the technique.

Evolutionary fuzzy clustering of relational data

This paper is concerned with the computational efficiency of fuzzy clustering algorithms when the data set to be clustered is described by a proximity matrix only (relational data) and the number of clusters must be automatically estimated from such data. A fuzzy variant of an evolutionary algorithm for relational clustering is derived and compared against two systematic (pseudo-exhaustive) approaches that can also be used to automatically estimate the number of fuzzy clusters in relational data. An extensive collection of experiments involving 18 artificial and two real data sets is reported and analyzed. (C) 2011 Elsevier B.V. All rights reserved.