Browsing by Author "Papadakis, Emanuel I."
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Item A Smoothing Model and Its Asymptotics with Applications to Health Studies and Social Research(2016-12) Huang, Shujiao 1989-; Fu, Wenjiang; Azencott, Robert; Papadakis, Emanuel I.; Yang, YipengSmoothing is a data-driven technique in statistical modeling. It has many desirable properties, and can be applied to modeling complex data. In this dissertation, a smoothing cohort model is considered as an effective alternative to address the identifiability problem in age-period-cohort analysis, in which multiple estimators are induced by a linear dependence of covariates: Period - Age = Cohort in the regression model of APC analysis. The smoothing cohort model yields consistent estimation of age and period effects, but cohort effect estimation is biased. Hence, the second stage model aims to correct the bias by setting a constraint using the consistent estimation of age or period effect from the first stage. Selection of constraints in the second stage is studied through simulations. The large sample behavior of the model parameter estimation is examined. The method is applied to cancer-incidence rate, mortality rate, and homicide-arrest rate data and yields sensible trend estimation in age, period, and cohort.Item Almost Parseval Frame Wavelets with Prescribed Anisotropy, Orientations, and Compact Support(2023-08) Thacker, Stephen Phillip; Papadakis, Emanuel I.; Sun, Qiyu; Vershynina, Anna; Labate, DemetrioIn the context of multi-wavelet frame filter design, good spatial localization of filters is desirable for fast algorithms to avoid the introduction of ringing artifacts associated with the poor spatial localization of filters. While shearlets obtain nearly optimal reconstruction of cartoon-like images, they are not compactly supported in the time domain. In 2019, Karantzas, Atreas, Papadakis and Stavropoulos published a paper detailing a new technique that allowed for the construction of multi-wavelet Parseval frames that contain hand selected elements, which can include anisotropic atoms. A key consequence of their work is the ability to algorithmically construct compactly supported Parseval frames of dyadic wavelets that contain elements defined by high-pass filters which can have a variety of properties such as acting as differential operators with prescribed orientations, e.g., Prewitt and Sobel operators. The key limitation of their work is that, unlike shearlets, these Parseval frames wavelets can only achieve limited degrees of orientation. In an effort to address these design problems we derived a number of results. Our first main result gives, for the class of bandlimited functions, the reconstruction error from multi-wavelet systems constructed from handpicked filterbanks, which can include differential operators of prescribed anisotropy. Our second main result is a new construction attempting to overcome the 2019 paper's gap in the study of the error resulting from the removal of the additional frame wavelets. In fact, we show that the frame wavelets of the Parseval frame can be combined with additional atoms of different length, and then scaled by constants to create a multi-wavelet frame with good frame bounds that can be close to 1. This allows us to modify constructions from the 2019 paper to contain atoms from higher resolution systems, obtaining greater degrees of anisotropy while maintaining good frame bounds for the class of bandlimited functions. These results are generalizable for any square-integrable function but under certain constraints.Item Compactly Supported Frame Wavelets and Applications(2019-08) Karantzas, Nikolaos 1986-; Papadakis, Emanuel I.; Labate, Demetrio; Bodmann, Bernhard G.; Prasad, SaurabhSignal processing has been at the forefront of modern information technology as the need for storing, analyzing, and interpreting data gathered all around us is ever growing. Multi-dimensional sparse signal representations occupy a significant part of the literature on multi-scale decompositions. The interest in such representations arises from their ability to analyze, synthesize, and modify signals carrying information about the behavior of specific phenomena. This work is devoted to the development and design of application-targeted tools for the multi-variable analysis of image data. Our main interests revolve around both the theoretical and practical aspects of signal processing, machine learning, and deep neural networks. In Chapter $1$ we present the necessary mathematical background this work is based on. In Chapter $2$ we develop a theoretical base for the construction of a specific class of compactly supported Parseval Framelets with directional characteristics. The framelets we construct arise from readily available refinable functions and their filters have few non-zero coefficients, custom-selected orientations and can act as finite-difference operators. We present explicit examples related to well-known directional representations (directional filter banks). Finally, in Chapter $3$ we explore the capabilities of our construction in the growing field of deep convolutional neural networks.Item Converting a Neuron-Morphology Reconstruction System: Open-Science Design and Implementation(2016-05) Mughal, Zakariyya 1990-; Kakadiaris, Ioannis A.; Papadakis, Emanuel I.; Shah, Shishir KiritThe thesis describes the conversion of the Online Reconstruction and functional Imaging Of Neurons (ORION) system for neuron-morphology reconstruction from an interpreted language to a compiled language. The motivation of this conversion is to provide a tool that can be used by neuroscience researchers to analyze their own neuron data and compare the output against both manual and automated tracings. This is in line with the goals of open science: a movement that seeks to make the findings and processes of research more widely available for peer review and reproducibility. By collaboratively sharing both neuron-imaging data and code between organizations, it is possible to compare the results of multiple methods without reimplementing all the stages of the reconstruction pipeline. In order to release the existing algorithm so that it can easily be incorporated into other tools, the implementation must be rewritten in a different language. This presents a challenge because the languages have vastly different paradigms. As a result, much of the existing code needs to be analyzed to determine any changes needed to the design. Creating a new implementation also means that the new system can be designed with modifiability in mind so that future changes can be easily incorporated. The specific objectives are to (i) analyze the ORION algorithm and implementation to determine the architecture for the new system that is efficient and extensible; (ii) integrate the system into a popular toolkit for biomedical image analysis for ease-of-use and visualization; (iii) develop a test suite of both the individual components (unit testing) and across the whole system (integration tests); and (iv) ensure that the software gives reproducible results by making it easy to build and distribute. The reconstruction of neuron morphology from microscopy imaging data is an invaluable method for understanding neuron characteristics. However, due to the cost in time and effort, manual neuron reconstruction is not feasible for large-scale analysis of neuron datasets. This implementation provides a working method for determining neuron morphology that can be used to collect statistical properties from various neuron data that can also be extended by the community.Item DIRECTIONAL MULTISCALE ANALYSIS USING SHEARLET THEORY AND APPLICATIONS(2012-08) Negi, Pooran 1978-; Labate, Demetrio; Papadakis, Emanuel I.; Bodmann, Bernhard G.; Azencott, Robert; Prasad, SaurabhShearlets emerged in recent years in applied harmonic analysis as a general framework to provide sparse representations of multidimensional data. This construction was motivated by the need to provide more efficient algorithms for data analysis and processing, overcoming the limitations of traditional multiscale methods. Particularly, shearlets have proved to be very effective in handling directional features compared to ideas based on separable extension, used in multi-dimensional Fourier and wavelet analysis. In order to efficiently deal with the edges and the other directionally sensitive (anisotropic) information, the analyzing shearlet elements are defined not only at various locations and scales but also at various orientations. Many important results about the theory and applications of shearlets have been derived during the past 5 years. Yet, there is a need to extend this approach and its applications to higher dimensions, especially 3D, where important problems such as video processing and analysis of biological data in native resolution require the use of 3D representations. The focus of this thesis is the study of shearlet representations in 3D, including their numerical implementation and application to problems of data denoising and enhancement. Compared to other competing methods like 3D curvelet and surfacelet, our numerical experiments show better Peak Signal to Noise Ratio (abbreviated as PSNR) and visual quality. In addition, to further explore the ability of shearlets to provide an ideal framework for sparse data representations, we have introduced and analyzed a new class of smoothness spaces associated with the shearlet decomposition and their relationship with Besov and curvelet spaces. Smoothness spaces associated to a multi-scale representation system are important for analysis and design of better image processing algorithms.Item Discriminative Semi-coupled Dictionary Learning for Face Recognition(2012-12) Chu, Dat 1985-; Kakadiaris, Ioannis A.; Shah, Shishir Kirit; Papadakis, Emanuel I.Performing 3D face recognition when only partial 3D data are present in the gallery and probe is a very challenging task. The task is even more challenging when the gallery dataset originates from one side of the face while the probe dataset originates from the other. We present a new method for computing the similarity of partial 3D data for the purpose of face recognition. This method improves upon an existing Semi-Coupled Dictionary Learning method by computing a jointly-optimized solution that incorporates the reconstruction cost, the discrimination cost and the semi-coupling cost. Our experiments show that this method can improve upon recognition performance of existing state-ofthe- art wavelet signatures used in 3D face recognition. The use of a semi-coupling term allows our method to handle partial face meshes with a possible extension to other types of signatures.Item Extraction and Normalization of Directional Characteristics of Images and Textures using Multiscale Transforms(2014-12) Upadhyay, Sanat Kumar 1988-; Papadakis, Emanuel I.; Azencott, Robert; Gladish, Gregory W.; Kakadiaris, Ioannis A.; Labate, DemetrioThis dissertation consists of two projects, one of which is on illumination normalization in monochromatic images that form Chapter 1 of this dissertation. The second project is on Texture analysis and application in cancer detection, which is given in Chapter 2. Illumination normalization is an important problem in the field of computer vision and pattern recognition. Often we require to build a system that could match an image of some object against another image of the same object, but acquired under different lighting conditions. In such applications, it becomes necessary to obtain light neutral surrogate of original images, for better comparison. The problem is known to be ill-posed, and therefore existing methods have to make a compromise between speed and output quality. We present a new wavelet based technique for normalizing illuminations in monochromatic images. We give a mathematical definition for Illumination normalization operator and show that this operator preserves structures of a scene while neutralizing changes in illumination. Practical implementation inherits high speed due to fast DWT algorithms. We demonstrate theoretically and experimentally that edges are preserved by preserving singularities at each point. The mathematical signature of structures is given by an ensemble of descriptors, in the form of various singularity exponents. In the second project, we implement a method for the 3D-rigid motion invariant texture discrimination and binary classification for discrete 3D-textures by modeling them as stationary Gaussian markov random fields. This method was first proposed by S. Jain, et al. The 'distance' between 3D-textures that remains invariant under all 3D-rigid motions of the texture to develop rules for 3D-rigid motion invariant texture discrimination and binary classification of textures. We experimentally establish that when they are combined with mean attenuation intensity differences the new augmented features are capable of discriminating between normal and abnormal liver tissue in arterial phase contrast enhanced X-ray CT–scans with high sensitivity and specificity. To extract these features CT-scans are processed in their native dimensionality. We experimentally observe that the 3D-rotational invariance of the proposed features improves the clustering of the feature vectors extracted from normal liver tissue samples.Item Fast Illumination Normalization for Face Recognition(2017) Mitsakos, Nikolaos; Upadhyay, Sanat; Papadakis, Emanuel I.Many applications of computer vision, security and surveillance require an accurate and realtime method for illumination neutralization and contrast enhancement. We present a new mathematical framework, with a real time implementation performing the task efficiently across multiple image modalities.Item Gaussian Polynomial Filters and Generalized Shift-Invariant Frames(2015-12) Maxwell, Nicholas 1985-; Bodmann, Bernhard G.; Kouri, Donald J.; Papadakis, Emanuel I.; Labate, Demetrio; Nammour, RamiWe present and study a family of filters on $L^2(\mathbb{R}^d)$ consisting of Gaussian polynomials. That is, multipliers in the frequency domain that are products of polynomials and Gaussians. These filters are constructed to approximate the characteristic functions of fairly general sets in $\mathbb{R}^d$, in an almost-uniform sense. We also study generalized shift-invariant (GSI) frames for $L^2(\mathbb{R}^d)$. These are frames consisting of regular lattice translations of countably many functions, which we call generators. GSI frames are fundamental to sampling theory and many areas of applied mathematics and engineering, in particular, signal and image analysis. Their distinguishing feature is an accommodation for generators which may be un- related to one another, and for general lattices of translations, which may vary with the generators. GSI frames generalize systems such as wavelets, Gabor systems, shearlets, curvelets, filter banks, etc. We discuss very general conditions on the generators under which one can determine lattice spacings, or sampling rates, so as to meet the frame condition. We develop a fast and numerically stable method for inverting the frame operator, and we give a detailed analysis of this method, as well as of the fast numerical implementation of the synthesis and analysis operators associated with GSI frames. We give a careful analysis of two methods for obtaining approximate dual GSI frames for general GSI frames. We apply this GSI system framework to the the Gaussian polynomial filters developed in this dissertation to obtain frames of translated Gaussian polynomials.Item Geometric Multiscale Analysis and Applications to Neuroscience Imaging(2017-08) Kayasandik, Cihan Bilge 1989-; Labate, Demetrio; Laezza, Fernanda; Josić, Krešimir; Papadakis, Emanuel I.This thesis is concerned with the development of quantitative methods for the analysis of neuronal images. Automated detection and segmentation of components of neurons in fluorescent images is a major goal in quantitative studies of neuronal networks, including applications of high-content-screenings where one needs to compute multiple morphological properties of neurons. Despite recent advances in image processing targeted to neurobiological applications, existing algorithms of soma detection and neurite tracing still have significant limitations which are more severe when processing fluorescence image stacks of neuronal cultures. To address such challenges, in this dissertation, we develop several novel methods and algorithms aimed at extracting quantitative information in fluorescent images of neuronal cultures or brain tissue, including methods for the automated detection of the soma and other subcellullar structures of interest, and algorithms for cell classification. Our methods rely on technique from harmonic analysis, especially wavelets and more advanced multiscale representation systems. Using these techniques, we are able to extract highly informative image characteristics with high geometric sensitivity and computational efficiency. As part of our work, we include a theoretical justification and an extensive numerical validation on microscopy imaging data provided by our collaborators in neuriscience. An extensive comparison with state-of-the-art existing methods demonstrate that our algorithms are highly competitive in terms of accuracy, reliability and computational efficiency.Item Geometric Multiscale Representations and Applications to the Analysis to Retinal Fundus Images(2020-05) Assi, Sabrine Hoteit; Labate, Demetrio; Laezza, Fernanda; Papadakis, Emanuel I.; Mang, AndreasSystematic diseases, such as diabetes, are known to cause quantifiable changes to the geometry of the retinal microvasculature. This microvasculature is the only part of the human circulation that can be visualized non-invasively in vivo so that it can be readily photographed and processed with the tools of digital image analysis. As the treatment of serious pathological conditions such as diabetic retinopathy can be significantly improved with early detection, retinal image analysis has been the subject of extensive studies. Thanks to the advances in image processing and machine learning during the last decade, a remarkable progress is being made towards developing automated diagnostic systems for diabetic retinopathy and related conditions. Despite this progress though, significant challenges remain. In this thesis, we develop and apply a novel method based on directional multiscale representations to the analysis of retinal fundus images. Namely, we construct a multiscale geometric feature descriptor to quantify the morphology of retinal vascularization and apply this descriptor within a supervised machine learning environment for problems of retinal image classification. By combining multiscale analysis and geometric sensitivity, our method provide a very competitive for the quantification of changes to the geometry of the retinal microvasculature. With respect to state-of-the-art methods based on deep learning, our approach is easily interpretable since the features we compute are morphological descriptors of retinal vascularization.Item Image Analysis Using Directional Multiscale Representations and Applications for Characterization of Neuronal Morphology(2015-12) Ozcan, Burcin 1987-; Papadakis, Emanuel I.; Labate, Demetrio; Bodmann, Bernhard G.; Laezza, FernandaRecent advances in high-resolution fluorescence microscopy have enabled the system- atic study of morphological changes in large populations of cells induced by chemical and genetic perturbations, facilitating the discovery of signaling pathways underlying diseases and the development of new pharmacological treatments. In these studies, though, quantifi- cation and analysis of morphological features are for the vast majority processed manually, slowing data processing significantly and limiting the information gained to a descriptive level. As an example, automated identification of the primary components of a neuron and extraction of its features are essential steps in many quantitative studies of neuronal net- works. Recent advances in applied harmonic analysis, especially in the area of multiscale representations, offer a variety of techniques and ideas which have potential to impact this field of scientific investigation. Motivated by the properties of directional multiscale rep- resentations, the focus of this thesis is to introduce a new notion, directional ratio, which is a multiscale quantitative measure, capable of distinguishing isotropic from anisotropic structures and the characterization of local isotropy. Another part of the dissertation illustrates the application of directional ratio. In partic- ular, we present an algorithm for automated soma extraction and separation of contiguous somas. Our numerical experiments show that this approach is reliable and efficient to detect and segment somas.Item Improving the Stability of the Recovery of Algebraic Curves via Bernstein Basis Polynomials and Neural Networks(2020-08) Molina, Wilfredo; Labate, Demetrio; Mang, Andreas; Papadakis, Emanuel I.; Guillén-Rondón, PabloWe present new methods for the stable reconstruction of a class of binary images from sparse measurements. The images that we consider are characteristic functions of algebraic shapes, that is, interiors of zero sets of bivariate polynomials, and we assume that we only know a finite set of samples of these images. A solution to this problem can be formulated in terms of a system of linear equations of moments. Although it was shown in the literature that one can improve the stability of the reconstruction by increasing the number of moments, the recovery of an algebraic shape remains unstable in the sense that small errors in the computation of the moments may have a catastrophic impact on the recovery algorithm. To address this numerical and theoretical instability, we introduce a novel approach where we represent bivariate polynomials and moments in terms of Bernstein basis polynomials and use them in combination with a polynomial-reproducing, refinable sampling kernel. We show that this is approach is very robust, straightforward to implement, and fast to compute. We also address the same reconstruction problem using an alternative approach that combines a convolutional neural network with a model-based constraint supported by our prior theoretical study. This approach also yields very competitive results and is even more robust to noise. We illustrate the performance of our algorithms on noisy samples through extensive experiments. Our code is publicly accessible on GitHub at github.com/wjmolina/AlgebraicCurves.Item LUMEN SEGMENTATION IN INTRAVASCULAR ULTRASOUND DATA(2012-12) Mendizabal Ruiz, Eduardo 1980-; Kakadiaris, Ioannis A.; Shah, Shishir Kirit; Vilalta, Ricardo; Papadakis, Emanuel I.; Biros, GeorgeIntravascular ultrasound (IVUS) is a catheter-based medical imaging technique that is capable of producing high resolution cross-sectional images of interior of blood vessels and it is currently the gold standard technique for the study of the characteristics of the atherosclerotic plaques. Segmentation of IVUS images refers to the delineation of the lumen/ intima and media/adventitia interfaces of the vessel. This process is necessary for assessing morphological characteristics of the vessel such as lumen diameter, minimum lumen cross-section area, and total atheroma volume. This information is crucial for making decisions such as whether a stent is needed to restore blood flow in an artery and to determine the characteristics of the stent. Other applications of IVUS include the study of mechanical properties of the vessel wall, characteristics of the plaque, and 3D reconstruction of the vessel. Segmentation of IVUS images may be performed manually by an observer. However, depending on the type of analysis, the number of frames to be segmented can range from a few frames to hundreds of frames. In this dissertation, we present a unified computational method for the semi-automatic segmentation of the luminal/wall interface in IVUS data. The method can be used with either B-mode or RF-data and it is based on the deformation of a curve by optimizing a probabilistic cost function. The main contribution is the development of a physicsbased inverse method for the segmentation of the lumen employing the IVUS RF data as compared with previous method which employs the B-mode reconstruction. Experimental results demonstrate the robustness and accuracy of the method. These results pave the way for the automation of the analysis of contrast-enhanced IVUS images to assess extraluminal perfusion.Item QUANTITATIVE ANALYSIS OF FLUORESCENT IMAGES OF GLIA CELLS USING DEEP NEURAL NETWORKS(2023-08) Huang, Yewen; Labate, Demetrio; Papadakis, Emanuel I.; Mang, Andreas; Kruyer, AnnaThe human brain is an incredibly intricate system comprising not only neurons but also another diverse group of cells known as glia. In recent years, there has been a remarkable surge in interest among neuroscientists regarding glia cells due to their crucial role in brain function. Among the various glia cell types, astrocytes, the most abundant, actively participate in numerous aspects of brain physiology, while microglia, a different subgroup of glia, serve as the brain's immune cells, protecting against infection and inflammation. Both astrocytes and microglia exhibit significant heterogeneity and complex morphological properties, which pose a considerable challenge for rigorous quantitative analysis. To address this challenge, my doctoral research aimed to develop a new class of computational methods that are accurate and efficient for the quantitative analysis of glia cells. To achieve this objective, I devised algorithms for the precise detection of astrocytes, microglia, and potentially other glia subfamilies in microscopy images of brain tissue. A notable innovation in my approach was the utilization of YOLO, an advanced deep learning platform for object detection, which I optimized to yield highly efficient cell detection models. Through extensive numerical experiments using multiple image datasets, I demonstrated that this method performs competitively compared to both conventional and state-of-the-art techniques, even in scenarios where cell density is high. Additionally, leveraging the outcomes of my glia detection pipeline, I developed an innovative method for the morphological analysis of astrocytes and microglia aimed to identify potential biological biomarkers in images of spinal cord injury.Item Receptive Field Convolutional Neural Networks and Applications in Image Classification(2020-08) Safaripoorfatide, Mohamadkazem; Labate, Demetrio; Mang, Andreas; Papadakis, Emanuel I.; Prasad, SaurabhConvolutional Neural Networks (CNN) have reached an impressive performance in object detection and classification tasks. However, such success requires massive amounts of high-quality labeled data and this is impractical in applications such as medical and hyperspectral imaging, where data annotation is labor-intensive and often requires domain experts. This dissertation presents a novel strategy to reduce the need for massive labeled data based on Receptive Field Convolutional Neural Network (RFCNN), a new class of CNNs, where convolutional filters are selected as linear combinations from a predefined dictionary and only the coefficients of this combination need to be learned. Our main contributions include the introduction of a sparsity constraint in combination with a recently introduced family of redundant framelets dictionary to reduce the number of parameters of the network while improving stability and generalization. To illustrate our approach, we consider problem of image classification using three challenging datasets: the UH 2013 hyperspectral dataset from the IEEE GRSS Data Fusion Contest, the Quick, Draw! Doodle Recognition Challenge dataset, and the Imagenet Large Scale Visual Recognition Challenge 2012 dataset. In addition, we propose a new deep learning strategy for a specific Hyperspectral Image classification task, namely the UH 2018 hyperspectral dataset from ”2018 IEEE GRSS Data Fusion Challenge”, where we integrate different deep learning strategies to efficiently learn joint spatial-spectral features over multiple scales.Item Shearlet-based Analysis of Image Inpainting and Convolutional Framelets(2020-08) Rodriguez Ayllon, Jose Pedro; Labate, Demetrio; Papadakis, Emanuel I.; Bodmann, Bernhard G.; Hebert, Thomas J.The main part of my dissertation deals with image inpainting - a classical problem in image analysis that I analyze from the point of view of microlocal analysis and the theory of sparse approximation. My most important result provides a new set of theoretical performance guarantees for the exact recovery of missing data in images where the information is dominated by curvilinear singularities. In fact, my study shows that a shearlet-based approach for the recovery of missing curvilinear edges in images is provably superior to methods based on conventional wavelets in a precises sense and gives a quantitative assessment on the size of the region that can reliably recovered. As a consequence, this result offers the theoretical underpinning for algorithms based on directional multiscale methods such as shearlets in applications to image inpainting. The arguments in my proofs rely on a new application of the microlocal properties of shearlets and techniques from oscillatory integrals that are inspired in part by a seminal paper by Donoho and Kutyniok, who first introduced methods from microlocal analysis in combination with ideas from sparse representations for problems of image analysis. The second part of my dissertation is a new study of convolutional framelets - a method recently introduced to provide a mathematical framework for the patch-based analysis of images - using tools from tensor analysis. This method gives an alternative approach to analyze framelets and a deeper insight into the mathematical properties of convolutional framelets. The first part of the dissertation follows rather closely some material published by the author in his first journal paper.Item Spectral Angle-Based Feature Extraction and Sparse Representation-Based Classification of Hyperspectral Imagery(2015-12) Cui, Minshan; Prasad, Saurabh; Roysam, Badrinath; Contreras-Vidal, Jose L.; Labate, Demetrio; Papadakis, Emanuel I.Remote sensing involves measuring and analyzing objects of interests through data collected by a remote imaging modality without physical contact with the objects. Hyperspectral sensors have become increasingly popular for a variety of remote sensing applications. Hyperspectral data are composed of densely sampled reflectance values over a wide range of the electromagnetic spectrum. Such a wealth of spectral information can provide unique spectral signatures of different materials present in a scene, which makes it especially suitable for classification tasks. In this dissertation, we present new dimensionality reduction (feature extraction) and classification algorithms for high-dimensional hyperspectral data. Specifically, we develop the theory and validate a new dimensionality reduction approach that maximizes angular separation in the lower dimensional subspace. We also propose and develop its ``local'' and ``nonlinear kernel'' variants for robust feature extraction of hyperspectral data. By preserving angular properties, the resulting subspaces demonstrate robustness to a variety of sources of variability that are commonly encountered in remote sensing applications. We also extend this approach to its ``spatial variant'' by incorporating spatial-contextual information along with spectral information from the hyperspectral images. We also optimize and develop a suitable sparse representation based classification framework for hyperspectral images. By extensive experiments on several real-world hyperspectral datasets, we demonstrate that the proposed algorithms significantly outperform the state-of-the-art methods. Further, we also demonstrate the applicability of the proposed methods for a practical environmental remote sensing task.Item Stable Phase Retrieval Using Low-Redundancy Frames of Polynomials(2015-12) Hammen, Nathaniel 1984-; Bodmann, Bernhard G.; Mixon, Dustin G.; Papadakis, Emanuel I.; Azencott, RobertIn many applications, measurements of a signal consist of the magnitudes of linear functionals while the phase information of these functionals is unavailable. Examples of these type of measurements occur in optics, quantum mechanics, speech recognition, and x-ray crystallography. The main topic of this thesis is the recovery of the phase information of a signal using a small number of these magnitude measurements. This is called phase retrieval. We provide a choice of 4d − 4 magnitude measurements that uniquely determines any d dimensional signal, up to a unimodular constant. Then we provide a choice of 6d − 3 magnitude measurements that admits a stable polynomial time algorithm to recover the signal under the influence of noise. We also explore the behavior of pathological signals in this algorithm, as well as the mean squared error. Finally, we show that if the signal is known to be s sparse, then we only need a suitable choice of O(s log d/s) such measurements for the stable algorithm to successfully recover the signal.Item TOWARDS IMPROVING MATCHING IN BIOMETRIC SYSTEMS(2015-12) Moutafis, Panagiotis 1988-; Kakadiaris, Ioannis A.; Papadakis, Emanuel I.; Shah, Shishir Kirit; Tsiamyrtzis, Panagiotis; Vilalta, RicardoThe integration of biometric technologies with authentication systems allows us to distinguish individuals easier, faster, and more accurately. As a result, biometric authentication is becoming increasingly important for various applications such as access control and financial transactions. However, despite the encouraging results obtained in controlled environments, biometric authentication remains a challenging problem in real-life conditions. Regardless of whether a biometric system relies on face, fingerprint, or any other biometric trait, it must perform (i) template matching to generate similarity scores that reflect the degree of similarity of the biometric samples matched and (ii) score-level processing to generate improved similarity scores. Depending on the biometric modality used, different challenges arise that degrade the recognition performance including: (i) distortions due to the different data acquisition conditions, (ii) artifacts introduced by pre-processing algorithms, (iii) incomplete utilization of the available information, and (iv) having to match data from different views. To address these challenges, we have developed new matching algorithms and score-processing methods that increase the recognition performance of biometric systems irrespective of the biometric trait used. Specifically, our contributions include: (i) a method that learns a non-linear distance metric for matching templates from the same view, (ii) a method that maps data from different views to a common discriminant space using non-linear projections, (iii) a score normalization framework that fully utilizes multiple samples per gallery subject, gallery-based information, and past experiences, and (iv) a score normalization framework for multimodal score fusion.