Dissertations / Theses on the topic 'Optimal embeddings'

Este proyecto hace referencia a estimaciones, en espacios funcionales, que relacionan la norma de una función y la de sus derivadas. Concretamente, nuestro principal objetivo es estudiar las estimaciones clásicas de las inclusiones de Sobolev, probadas por Gagliardo y Nirenberg, para derivadas de orden superior y espacios más generales. En particular, estamos interesados en describir el dominio y el rango óptimos para estas inclusiones entre los espacios invariantes por reordenamiento (r.i.) y espacios de normas mixtas.
This thesis project concerns estimates, in function spaces, that relate the norm of a function and that of its derivatives. Speci.cally, our main purpose is to study the classical Sobolev-type inequalities due to Gagliardo and Nirenberg for higher order derivatives and more general spaces. In particular, we concentrate on seeking the optimal domains and the optimal ranges for these embeddings between rearrangement-invariant spaces (r.i.) and mixed norm spaces.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 41-42).
In this thesis, we establish theoretical guarantees for several dimension reduction algorithms developed for applications in compressive sensing and signal processing. In each instance, the input is a point or set of points in d-dimensional Euclidean space, and the goal is to find a linear function from Rd into Rk , where k << d, such that the resulting embedding of the input pointset into k-dimensional Euclidean space has various desirable properties. We focus on two classes of theoretical results: -- First, we examine linear embeddings of arbitrary pointsets with the aim of minimizing distortion. We present an exhaustive-search-based algorithm that yields a k-dimensional linear embedding with distortion at most ... is the smallest possible distortion over all orthonormal embeddings into k dimensions. This PTAS-like result transcends lower bounds for well-known embedding teclhniques such as the Johnson-Lindenstrauss transform. -- Next, motivated by compressive sensing of images, we examine linear embeddings of datasets containing points that are sparse in the pixel basis, with the goal of recoving a nearly-optimal sparse approximation to the original data. We present several algorithms that achieve strong recovery guarantees using the near-optimal bound of measurements, while also being highly "local" so that they can be implemented more easily in physical devices. We also present some impossibility results concerning the existence of such embeddings with stronger locality properties.
by Elyot Grant.
S.M.

Pouvoir manipuler et de comparer de mesures de probabilité est essentiel pour de nombreuses applications en apprentissage automatique. Le transport optimal (TO) définit des divergences entre distributions fondées sur la géométrie des espaces sous-jacents : partant d'une fonction de coût définie sur l'espace dans lequel elles sont supportées, le TO consiste à trouver un couplage entre les deux mesures qui soit optimal par rapport à ce coût. Par son ancrage géométrique, le TO est particulièrement bien adapté au machine learning, et fait l'objet d'une riche théorie mathématique. En dépit de ces avantages, l'emploi du TO pour les sciences des données a longtemps été limité par les difficultés mathématiques et computationnelles liées au problème d'optimisation sous-jacent. Pour contourner ce problème, une approche consiste à se concentrer sur des cas particuliers admettant des solutions en forme close, ou pouvant se résoudre efficacement. En particulier, le TO entre mesures elliptiques constitue l'un des rares cas pour lesquels le TO admet une forme close, définissant la géométrie de Bures-Wasserstein (BW). Cette thèse s'appuie tout particulièrement sur la géométrie de BW, dans le but de l'utiliser comme outil de base pour des applications en sciences des données. Pour ce faire, nous considérons des situations dans lesquelles la géométrie de BW est tantôt utilisée comme un outil pour l'apprentissage de représentations, étendue à partir de projections sur des sous-espaces, ou régularisée par un terme entropique. Dans une première contribution, la géométrie de BW est utilisée pour définir des plongements sous la forme de distributions elliptiques, étendant la représentation classique sous forme de vecteurs de R^d. Dans une deuxième contribution, nous prouvons l'existence de transports qui extrapolent des applications restreintes à des projections en faible dimension, et montrons que ces plans "sous-espace optimaux" admettent des formes closes dans le cas de mesures gaussiennes. La troisième contribution de cette thèse consiste à obtenir des formes closes pour le transport entropique entre des mesures gaussiennes non-normalisées, qui constituent les premières expressions non triviales pour le transport entropique. Finalement, dans une dernière contribution nous utilisons le transport entropique pour imputer des données manquantes de manière non-paramétrique, tout en préservant les distributions sous-jacentes
Comparing and matching probability distributions is a crucial in numerous machine learning (ML) algorithms. Optimal transport (OT) defines divergences between distributions that are grounded on geometry: starting from a cost function on the underlying space, OT consists in finding a mapping or coupling between both measures that is optimal with respect to that cost. The fact that OT is deeply grounded in geometry makes it particularly well suited to ML. Further, OT is the object of a rich mathematical theory. Despite those advantages, the applications of OT in data sciences have long been hindered by the mathematical and computational complexities of the underlying optimization problem. To circumvent these issues, one approach consists in focusing on particular cases that admit closed-form solutions or that can be efficiently solved. In particular, OT between elliptical distributions is one of the very few instances for which OT is available in closed form, defining the so-called Bures-Wasserstein (BW) geometry. This thesis builds extensively on the BW geometry, with the aim to use it as basic tool in data science applications. To do so, we consider settings in which it is alternatively employed as a basic tool for representation learning, enhanced using subspace projections, and smoothed further using entropic regularization. In a first contribution, the BW geometry is used to define embeddings as elliptical probability distributions, extending on the classical representation of data as vectors in R^d.In the second contribution, we prove the existence of transportation maps and plans that extrapolate maps restricted to lower-dimensional projections, and show that subspace-optimal plans admit closed forms in the case of Gaussian measures.Our third contribution consists in deriving closed forms for entropic OT between Gaussian measures scaled with a varying total mass, which constitute the first non-trivial closed forms for entropic OT and provide the first continuous test case for the study of entropic OT. Finally, in a last contribution, entropic OT is leveraged to tackle missing data imputation in a non-parametric and distribution-preserving way

The abstract boundary construction of Scott and Szekeres has proven a practical classification scheme for boundary points of pseudo-Riemannian manifolds. It has also proved its utility in problems associated with the re-embedding of exact solutions containing directional singularities in space-time. Moreover it provides a model for singularities in space-time - essential singularities. However the literature has been devoid of abstract boundary results which have results of direct physical applicability.¶ This thesis presents several theorems on the existence of essential singularities in space-time and on how the abstract boundary allows definition of optimal em- beddings for depicting space-time. Firstly, a review of other boundary constructions for space-time is made with particular emphasis on the deficiencies they possess for describing singularities. The abstract boundary construction is then pedagogically defined and an overview of previous research provided.¶ We prove that strongly causal, maximally extended space-times possess essential singularities if and only if they possess incomplete causal geodesics. This result creates a link between the Hawking-Penrose incompleteness theorems and the existence of essential singularities. Using this result again together with the work of Beem on the stability of geodesic incompleteness it is possible to prove the stability of existence for essential singularities.¶ Invariant topological contact properties of abstract boundary points are presented for the first time and used to define partial cross sections, which are an generalization of the notion of embedding for boundary points. Partial cross sections are then used to define a model for an optimal embedding of space-time.¶ Finally we end with a presentation of the current research into the relationship between curvature singularities and the abstract boundary. This work proposes that the abstract boundary may provide the correct framework to prove curvature singularity theorems for General Relativity. This exciting development would culminate over 30 years of research into the physical conditions required for curvature singularities in space-time.

Cette thèse présente trois principaux sujets de recherche, les deux premiers étant indépendants et le dernier indiquant la relation des deux premières problématiques dans un cas concret.Dans la première partie nous nous intéressons au problème de transport optimal martingale dans l’espace de Skorokhod, dont le premier but est d’étudier systématiquement la tension des plans de transport martingale. On s’intéresse tout d’abord à la semicontinuité supérieure du problème primal par rapport aux distributions marginales. En utilisant la S-topologie introduite par Jakubowski, on dérive la semicontinuité supérieure et on montre la première dualité. Nous donnons en outre deux problèmes duaux concernant la surcouverture robuste d’une option exotique, et nous établissons les dualités correspondantes, en adaptant le principe de la programmation dynamique et l’argument de discrétisation initie par Dolinsky et Soner.La deuxième partie de cette thèse traite le problème du plongement de Skorokhod optimal. On formule tout d’abord ce problème d’optimisation en termes de mesures de probabilité sur un espace élargi et ses problèmes duaux. En utilisant l’approche classique de la dualité; convexe et la théorie d’arrêt optimal, nous obtenons les résultats de dualité. Nous rapportons aussi ces résultats au transport optimal martingale dans l’espace des fonctions continues, d’où les dualités correspondantes sont dérivées pour une classe particulière de fonctions de paiement. Ensuite, on fournit une preuve alternative du principe de monotonie établi par Beiglbock, Cox et Huesmann, qui permet de caractériser les optimiseurs par leur support géométrique. Nous montrons à la fin un résultat de stabilité qui contient deux parties: la stabilité du problème d’optimisation par rapport aux marginales cibles et le lien avec un autre problème du plongement optimal.La dernière partie concerne l’application de contrôle stochastique au transport optimal martingale avec la fonction de paiement dépendant du temps local, et au plongement de Skorokhod. Pour le cas d’une marginale, nous retrouvons les optimiseurs pour les problèmes primaux et duaux via les solutions de Vallois, et montrons en conséquence l’optimalité des solutions de Vallois, ce qui regroupe le transport optimal martingale et le plongement de Skorokhod optimal. Quand au cas de deux marginales, on obtient une généralisation de la solution de Vallois. Enfin, un cas spécial de plusieurs marginales est étudié, où les temps d’arrêt donnés par Vallois sont bien ordonnés
This PhD dissertation presents three research topics, the first two being independent and the last one relating the first two issues in a concrete case.In the first part we focus on the martingale optimal transport problem on the Skorokhod space, which aims at studying systematically the tightness of martingale transport plans. Using the S-topology introduced by Jakubowski, we obtain the desired tightness which yields the upper semicontinuity of the primal problem with respect to the marginal distributions, and further the first duality. Then, we provide also two dual formulations that are related to the robust superhedging in financial mathematics, and we establish the corresponding dualities by adapting the dynamic programming principle and the discretization argument initiated by Dolinsky and Soner.The second part of this dissertation addresses the optimal Skorokhod embedding problem under finitely-many marginal constraints. We formulate first this optimization problem by means of probability measures on an enlarged space as well as its dual problems. Using the classical convex duality approach together with the optimal stopping theory, we obtain the duality results. We also relate these results to the martingale optimal transport on the space of continuous functions, where the corresponding dualities are derived for a special class of reward functions. Next, We provide an alternative proof of the monotonicity principle established in Beiglbock, Cox and Huesmann, which characterizes the optimizers by their geometric support. Finally, we show a stability result that is twofold: the stability of the optimization problem with respect to target marginals and the relation with another optimal embedding problem.The last part concerns the application of stochastic control to the martingale optimal transport with a payoff depending on the local time, and the Skorokhod embedding problem. For the one-marginal case, we recover the optimizers for both primal and dual problems through Vallois' solutions, and show further the optimality of Vallois' solutions, which relates the martingale optimal transport and the optimal Skorokhod embedding. As for the two-marginal case, we obtain a generalization of Vallois' solution. Finally, a special multi-marginal case is studied, where the stopping times given by Vallois are well ordered

The analysis of signals stemming from a physical system is crucial for the experimental investigation of the underlying dynamics that drives the system itself. The field of time series analysis comprises a wide variety of techniques developed with the purpose of characterizing signals and, ultimately, of providing insights on the phenomena that govern the temporal evolution of the generating system. A renowned example in this field is given by spectral analysis: the use of Fourier or Laplace transforms to bring time-domain signals into the more convenient frequency space allows to disclose the key features of linear systems. A more complex scenario turns up when nonlinearity intervenes within a system's dynamics. Nonlinear coupling between a system's degrees of freedom brings about interesting dynamical regimes, such as self-sustained periodic (though anharmonic) oscillations ("limit cycles"), or quasi-periodic evolutions that exhibit sharp spectral lines while lacking strict periodicity ("limit tori"). Among the consequences of nonlinearity, the onset of chaos is definitely the most fascinating one. Chaos is a dynamical regime characterized by unpredictability and lack of periodicity, despite being generated by deterministic laws. Signals generated by chaotic dynamical systems appear as irregular: the corresponding spectra are broad and flat, prediction of future values is challenging, and evolutions within the systems' state spaces converge to strange attractor sets with noninteger dimensionality. Because of these properties, chaotic signals can be mistakenly classified as noise if linear techniques such as spectral analysis are used. The identification of chaos and its characterization require the assessment of dynamical invariants that quantify the complex features of a chaotic system's evolution. For example, Lyapunov exponents provide a marker of unpredictability; the estimation of attractor dimensions, on the other hand, highlights the unconventional geometry of a chaotic system's state space. Nonlinear time series analysis techniques act directly within the state space of the system under investigation. However, experimentally, full access to a system's state space is not always available. Often, only a scalar signal stemming from the dynamical system can be recorded, thus providing, upon sampling, a scalar sequence. Nevertheless, by virtue of a fundamental theorem by Takens, it is possible to reconstruct a proxy of the original state space evolution out of a single, scalar sequence. This reconstruction is carried out by means of the so-called embedding procedure: m-dimensional vectors are built by picking successive elements of the scalar sequence delayed by a lag L. On the other hand, besides posing some necessary conditions on the integer embedding parameters m and L, Takens' theorem does not provide any clue on how to choose them correctly. Although many optimal embedding criteria were proposed, a general answer to the problem is still lacking. As a matter of fact, conventional methods for optimal embedding are flawed by several drawbacks, the most relevant being the need for a subjective evaluation of the outcomes of applied algorithms. Tackling the issue of optimally selecting embedding parameters makes up the core topic of this thesis work. In particular, I will discuss a novel approach that was pursued by our research group and that led to the development of a new method for the identification of suitable embedding parameters. Rather than most conventional approaches, which seek a single optimal value for m and L to embed an input sequence, our approach provides a set of embedding choices that are equivalently suitable to reconstruct the dynamics. The suitability of each embedding choice m, L is assessed by relying on statistical testing, thus providing a criterion that does not require a subjective evaluation of outcomes. The starting point of our method are embedding-dependent correlation integrals, i.e. cumulative distributions of embedding vector distances, built out of an input scalar sequence. In the case of Gaussian white noise, an analytical expression for correlation integrals is available, and, by exploiting this expression, a gauge transformation of distances is introduced to provide a more convenient representation of correlation integrals. Under this new gauge, it is possible to test—in a computationally undemanding way—whether an input sequence is compatible with Gaussian white noise and, subsequently, whether the sequence is compatible with the hypothesis of an underlying chaotic system. These two statistical tests allow ruling out embedding choices that are unsuitable to reconstruct the dynamics. The estimation of correlation dimension, carried out by means of a newly devised estimator, makes up the third stage of the method: sets of embedding choices that provide uniform estimates of this dynamical invariant are deemed to be suitable to embed the sequence.The method was successfully applied to synthetic and experimental sequences, providing new insight into the longstanding issue of optimal embedding. For example, the relevance of the embedding window (m-1)L, i.e. the time span covered by each embedding vector, is naturally highlighted by our approach. In addition, our method provides some information on the adequacy of the sampling period used to record the input sequence.The method correctly distinguishes a chaotic sequence from surrogate ones generated out of it and having the same power spectrum. The technique of surrogate generation, which I also addressed during my Ph. D. work to develop new dedicated algorithms and to analyze brain signals, allows to estimate significance levels in situations where standard analytical algorithms are unapplicable. The novel embedding approach being able to tell apart an original sequence from surrogate ones shows its capability to distinguish signals beyond their spectral—or autocorrelation—similarities.One of the possible applications of the new approach concerns another longstanding issue, namely that of distinguishing noise from chaos. To this purpose, complementary information is provided by analyzing the asymptotic (long-time) behaviour of the so-called time-dependent divergence exponent. This embedding-dependent metric is commonly used to estimate—by processing its short-time linearly growing region—the maximum Lyapunov exponent out of a scalar sequence. However, insights on the kind of source generating the sequence can be extracted from the—usually overlooked—asymptotic behaviour of the divergence exponent. Moreover, in the case of chaotic sources, this analysis also provides a precise estimate of the system's correlation dimension. Besides describing the results concerning the discrimination of chaotic systems from noise sources, I will also discuss the possibility of using the related correlation dimension estimates to improve the third stage of the method introduced above for the identification of suitable embedding parameters. The discovery of chaos as a possible dynamical regime for nonlinear systems led to the search of chaotic behaviour in experimental recordings. In some fields, this search gave plenty of positive results: for example, chaotic dynamics was successfully identified and tamed in electronic circuits and laser-based optical setups. These two families of experimental chaotic systems eventually became versatile tools to study chaos and its possible applications. On the other hand, chaotic behaviour is also looked for in climate science, biology, neuroscience, and even economics. In these fields, nonlinearity is widespread: many smaller units interact nonlinearly, yielding a collective motion that can be described by means of few, nonlinearly coupled effective degrees of freedom. The corresponding recorded signals exhibit, in many cases, an irregular and complex evolution. A possible underlying chaotic evolution—as opposed to a stochastic one—would be of interest both to reveal the presence of determinism and to predict the system's future states. While some claims concerning the existence of chaos in these fields have been made, most results are debated or inconclusive. Nonstationarity, low signal-to-noise ratio, external perturbations and poor reproducibility are just few among the issues that hinder the search of chaos in natural systems. In the final part of this work, I will briefly discuss the problem of chasing chaos in experimental recordings by considering two example sequences, the first one generated by an electronic circuit and the second one corresponding to recordings of brain activity. The present thesis is organized as follows. The core concepts of time series analysis, including the key features of chaotic dynamics, are presented in Chapter 1. A brief review of the search for chaos in experimental systems is also provided; the difficulties concerning this quest in some research fields are also highlighted. Chapter 2 describes the embedding procedure and the issue of optimally choosing the related parameters. Thereupon, existing methods to carry out the embedding choice are reviewed and their limitations are pointed out. In addition, two embedding-dependent nonlinear techniques that are ordinarily used to characterize chaos, namely the estimation of correlation dimension by means of correlation integrals and the assessment of maximum Lyapunov exponent, are presented. The new approach for the identification of suitable embedding parameters, which makes up the core topic of the present thesis work, is the subject of Chapter 3 and 4. While Chapter 3 contains the theoretical outline of the approach, as well as its implementation details, Chapter 4 discusses the application of the approach to benchmark synthetic and experimental sequences, thus illustrating its perks and its limitations. The study of the asymptotic behaviour of the time-dependent divergent exponent is presented in Chapter 5. The alternative estimator of correlation dimension, which relies on this asymptotic metric, is discussed as a possible improvement to the approach described in Chapters 3, 4. The search for chaos out of experimental data is discussed in Chapter 6 by means of two examples of real-world recordings. Concluding remarks are finally drawn in Chapter 7.

The rapid increase in the demands for high bandwidth systems has motivated research in optoelectronic technologies and architectures. At McGill University, a five year five Major Project in Photonic Devices and Systems has been undertaken, with funding from the Canadian Institute for Telecommunications Research. One of the main goals of the project is to develop an optical backplane architecture capable of interconnecting several electronic printed circuit boards with an aggregate bandwidth on the order of 1 Terabit per second. Currently, the project is in its third year in which a representative subset of a Terabit Photonic Backplane is under development.
The objectives of this thesis are three fold. First, we motivate the study of optical backplanes by demonstrating that the interconnection network of a Cray T3D Supercomputer can be embedded onto the optical backplane. In particular, we demonstrate that the 3D mesh interconnect of the Cray T3D can be embedded into the "Dual Stream Linear HyperPlane" (9). Secondly, having established a motivation we then provide a detailed review of the functional specifications of an optical backplane. In particular, we provide a detailed review of the June 1995 backplane design (31). Thirdly, having established a motivation and a detailed design we then develop a executable software model of the June 1995 backplane using the VHDL hardware description language. The VHDL model is used to establish the functional correctness of the design. In addition, the VHDL model is used to develop a real-time simulator for the photonic backplane using 4013 Field Programmable Gate Arrays (FPGAs). The real time simulator can operate at a 4 MHz clock rate and can be used to test other electronic components such as the Message-Processors at realistic clock rates. (Abstract shortened by UMI.)

Currently a growing number of users depend on the Edge Cloud Computing Paradigm in a Metro Optical Network (MON). This has led to increased competition among the Cloud Service Providers (CPs) to supply incentives for the user through guaranteed Quality of Service (QoS). If the CP fails to guarantee the QoS for the accepted request, then the user will move to another CP. Making an informed decision dynamically in such a sensitive situation demands that the CP knows the user's application requirements. The Software Defined Networking (SDN) paradigm enabled the CP to achieve such desired requirement. Therefore, a framework called Virtual Network Embedding on SDN-based Metro Optical Network (VNE-MON) is proposed in this Thesis. The use of SDN paradigm in the framework guarantees profit to the CP as well as QoS to the user.\par The design concept of the SDN control plane, raises concerns regarding its scalability, reliability and performance compared to a traditionally distributed network. To justify concerns regarding the SDN, the performance of VNE-MON and its possible dependancy on the controller location is investigated. Several strategies are proposed and formulated using Integer Linear Programming to determine the controller location in a MON. Performance results from the assessment of the VNE-MON illustrates that it is more stable compare to GMPLS-based network. It is evident that the controller location's attributes have a significant effect on the efficacy of the accepted VN request.

The size and conformational complexity of proteins and other large systems represent major challenges for today's methods of quantum chemistry.This thesis is centered around the development of new computational tools to gain molecular-level insight into electronic transitions in such systems. To meet this challenge, we focus on the polarizable embedding (PE) model, which takes advantage of the fact that many electronic transitions are localized to a smaller part of the entire system.This motivates a partitioning of the large system into two regions that are treated at different levels of theory:The smaller part directly involved in the electronic process is described using accurate quantum-chemical methods, while the effects of the rest of the system, the environment, are incorporated into the Hamiltonian of the quantum region in an effective manner. This thesis presents extensions of the PE model with theaim of expanding its range of applicability to describe electronic transitions in large molecular systemsin the optical and X-ray regions. The developments cover both improvements with regardto the quantum region as well as the embedding potential representing the environment.Regarding the former, a damped linear response formulation has been implemented to allow for calculations of absorption spectra of large molecular systems acrossthe entire frequency range. A special feature of this development is its abilityto address core excitations that are otherwise not easily accessible.Another important development presented in this thesis is the coupling of the PE model to a multi-configuration self-consistent-field description of the quantum region and its further combination with response theory. In essence, this extends the PE model to the study of electronic transitions in large systems that are prone to static correlation --- a situation that is frequently encountered in biological systems. In addition to the direct environmental effects on the electronic structure of the quantum region, another important component of the description of electronic transitions in large molecular systems is an accurate account of the indirect effects of the environment, i.e., the geometrical distortions in the quantum region imposed by the environment. In thisthesis we have taken the first step toward the inclusion of geometry distortions in the PE frameworkby formulating and implementing molecular gradients for the quantum region. To identify critical points related to the environment description, we perform a theoretical analysis of the PE model starting from a full quantum-mechanicaltreatment of a composite system. Based on this, we present strategies for an accurate yet efficient construction of the embedding potentialcovering both the calculation of ground state and transition properties. The accurate representation of the environment makes it possible to reduce the size of the quantum region without compromising the overall accuracy of the final results. This further enables use of highly accurate quantum-chemical methods despite their unfavorable scaling with the size of the system. Finally, some examples of applications will be presented to demonstrate how the PE model may be applied as a tool to gain insight into and rationalize the factors influencing electronic transitions in large molecular systems of increasing complexity.

The dissertation was awarded the best PhD thesis prize 2016 by the Danish Academy of Natural Sciences.

QC 20170209

This thesis considers three separate but connected problems regarding energy networks: the load flow problem, the optimal power flow problem, and the islanding problem. All three problems are non-convex non linear problems, and so have the potential of returning local solutions. The goal of this thesis is to find solution methods to each of these problems that will minimize the chances of returning a local solution. The thesis first considers the load ow problem and looks into a novel approach to solving load flows, the Holomorphic Embedding Load Flow Method (HELM). The current literature does not provide any HELM models that can accurately handle general power networks containing PV and PQ buses of realistic sizes. This thesis expands upon previous work to present models of HELM capable of solving general networks efficiently, with computational results for the standard IEEE test cases provided for comparison. The thesis next considers the optimal power flow problem, and creates a framework for a load flow-based OPF solver. The OPF solver is designed with incorporating HELM as the load flow solver in mind, and is tested on IEEE test cases to compare it with other available OPF solvers. The OPF solvers are also tested with modified test cases known to have local solutions to show how a LF-OPF solver using HELM is more likely to find the global optimal solution than the other available OPF solvers. The thesis finally investigates solving a full AC-islanding problem, which can be considered as an extension of the transmission switching problem, using a standard MINLP solver and comparing the results to solutions obtained from approximations to the AC problem. Analysing in detail the results of the AC-islanding problem, alterations are made to the standard MINLP solver to allow better results to be obtained, all the while considering the trade-off between results and elapsed time.

Electrical and optical characterizations of heterostructures and thin films based on group III-V compound semiconductors are presented. Optical properties of GaMnN thin films grown by Metalorganic Chemical Vapor Deposition (MOCVD) on GaN/Sapphire templates were investigated using IR reflection spectroscopy. Experimental reflection spectra were fitted using a non - linear fitting algorithm, and the high frequency dielectric constant (ε∞), optical phonon frequencies of E1(TO) and E1(LO), and their oscillator strengths (S) and broadening constants (Γ) were obtained for GaMnN thin films with different Mn fraction. The high frequency dielectric constant (ε∞) of InN thin films grown by the high pressure chemical vapor deposition (HPCVD) method was also investigated by IR reflection spectroscopy and the average was found to vary between 7.0 - 8.6. The mobility of free carriers in InN thin films was calculated using the damping constant of the plasma oscillator. The terahertz detection capability of n-type GaAs/AlGaAs Heterojunction Interfacial Workfunction Internal Photoemission (HEIWIP) structures was demonstrated. A threshold frequency of 3.2 THz (93 µm) with a peak responsivity of 6.5 A/W at 7.1 THz was obtained using a 0.7 µm thick 1E18 cm−3 n - type doped GaAs emitter layer and a 1 µm thick undoped Al(0.04)Ga(0.96)As barrier layer. Using n - type doped GaAs emitter layers, the possibility of obtaining small workfunctions (∆) required for terahertz detectors has been successfully demonstrated. In addition, the possibility of using GaN (GaMnN) and InN materials for terahertz detection was investigated and a possible GaN base terahertz detector design is presented. The non - linear behavior of the Inter Pulse Time Intervals (IPTI) of neuron - like electric pulses triggered externally in a GaAs/InGaAs Multi Quantum Well (MQW) structure at low temperature (~10 K) was investigated. It was found that a grouping behavior of IPTIs exists at slow triggering pulse rates. Furthermore, the calculated correlation dimension reveals that the dimensionality of the system is higher than the average dimension found in most of the natural systems. Finally, an investigation of terahertz radiation efect on biological system is reported.

Novel polymer-enhanced photodefined through-silicon via (TSV) and passive technologies have been demonstrated for silicon interposers to obtain compact heterogeneous computing and mixed-signal systems. These technologies include: (1) Polymer-clad TSVs with thick (~20 µm) liners to help reduce TSV losses and stress, and obtain optical TSVs in parallel for interposer-to-interposer long-distance communication; (2) Polymer-embedded vias with copper vias embedded in polymer wells to significantly reduce the TSV losses; (3) Coaxial vias in polymer wells to reduce the TSV losses with controlled impedance; (4) Antennas over polymer wells to attain a high radiation efficiency; and (5) High-Q inductors over polymer wells. Cleanroom fabrication and characterization of the technologies have been demonstrated. For the fabricated polymer-clad TSVs, resistance and synchrotron x-ray diffraction (XRD) measurements have been demonstrated. High-frequency measurements up to 170 GHz and time-domain measurements up to 10 Gbps have been demonstrated for the fabricated polymer-embedded vias. For the fabricated coaxial vias and inductors, high-frequency measurements up to 50 GHz have been demonstrated. Lastly, for the fabricated antennas, measurements in the W-band have been demonstrated.

Avec l’avènement de l’ère intellectuelle et de l’Internet of Everything (IoE), les besoins de la communication mondiale et des applications diverses ont explosé. Cette révolution exige que les futurs réseaux de communication soient plus efficaces, intellectuels, agiles et évolutifs. De nombreuses technologies réseau sont apparues pour répondre à la tendance des réseaux de communication de nouvelle génération tels que les réseaux optiques élastiques (EONs) et la virtualisation de réseau. De nombreux défis apparaissent avec les apparences de la nouvelle architecture et de la nouvelle technologie, telles que le routage et l’allocation de ressource spectrale (RSA) dans les EONs et l’intégration de réseaux virtuels (Virtual Network Embedding ou VNE) dans la virtualisation de réseau.Cette thèse traite la conception et l’analyse d’algorithmes d’approximation dans trois problèmes d’optimation du RSA et du VNE : les impacts de la distribution du trafic et de la topologie du réseau sur le routage tout optique, de l’allocation de ressource spectrale, et du VNE dans les topologies des chemins et cycles. Pour le routage tout optique, le premier sous-problème du RSA, il y a toujours un problème en suspens concernant l’impact de la distribution du trafic et de la topologie EON. Comme le routage tout optique joue un rôle essentiel pour la performance globale de la RSA, cette thèse fournit une analyse approfondi théorique sur ces impacts. Pour le deuxième sous-problème du RSA, l’allocation de ressource spectrale, deux chemins optiques quelconques partageant des fibres optiques communes pourraient devoir être isolés dans le domaine spectral avec une bande de garde appropriée pour empêcher la diaphonie et / ou réduire les menaces de sécurité de la couche physique. Cette thèse considère le scénario dans lequel les exigences de bandes de garde réelles optiques sont différentes pour différentes paires de chemins, et étudie comment affecter les ressources spectrales efficacement dans une telle situation. L’hétérogénéité de la topologie des demandes de réseau virtuel (VNR) est un facteur important qui entrave les performances de la VNE. Cependant, dans de nombreuses applications spécialisées, les VNR ont des caractéristiques structurelles communes par exemple, des chemins et des cycles. Pour obtenir de meilleurs résultats, il est donc essentiel de concevoir des algorithmes dédiés pour ces applications en tenant compte des caractéristiques topologiques. Dans cette thèse, nous prouvons que les problèmes VNE dans les topologies de chemin et de cycle sont NP-difficiles. Afin de les résoudre, nous proposons des algorithmes efficaces également analysons leurs ratios d’approximation
With the coming of intellectual era and Internet of Everything (IoE), the needs of worldwide communication and diverse applications have been explosively growing. This information revolution requires the future communication networks to be more efficient, intellectual, agile and scalable. Many technologies have emerged to meet the requirements of next generation communication networks such as Elastic Optical Networks (EONs) and networking virtualization. However, there are many challenges coming along with them, such as Routing and Spectrum Assignment (RSA) in EONs and Virtual Network Embedding (VNE) in network virtualization. This dissertation addresses the algorithm design and analysis for these challenging problems: the impacts of traffic distribution and network topology on lightpath routing, the distance spectrum assignment and the VNE problem for paths and cycles.For lightpath routing, the first subproblem of the RSA, there is always a pending issue that how the changes of the traffic distribution and EON topology affect it. As the lightpath routing plays a critical role in the overall performance of the RSA, this dissertation provides a thoroughly theoretical analysis on the impacts of the aforementioned two key factors. To this end, we propose two theoretical chains, and derive the optimal routing scheme taking into account two key factors. We then treat the second subproblem of RSA, namely spectrum assignment. Any two lightpaths sharing common fiber links might have to be isolated in the spectrum domain with a proper guard-band to prevent crosstalk and/or reduce physical-layer security threats. We consider the scenario with diverse guard-band sizes, and investigate how to assign the spectrum resources efficiently in such a situation. We provide the upper and lower bounds for the optimal solution of the DSA, and further devise an efficient algorithm which can guarantee approximation ratios in some graph classes.The topology heterogeneity of Virtual Network Requests (VNRs) is one important factor hampering the performance of the VNE. However, in many specialized applications, the VNRs are of some common structural features e.g., paths and cycles. To achieve better outcomes, it is thus critical to design dedicated algorithms for these applications by accounting for topology characteristics. We prove the NP-Harness of path and cycle embeddings. To solve them, we propose some efficient algorithms and analyze their approximation ratios

For face identification, especially by human, it is desirable to render a high-resolution (HR) face image from the low-resolution (LR) one, which is called face hallucination or face super-resolution. A number of super-resolution techniques have been proposed in recent years. However, for face hallucination the utilization of the special properties of the faces is conductive to generate the HR face images.
In this thesis, we propose a new face hallucination framework based on image patches, which integrates two novel statistical super-resolution models. Considering that image patches reflect the combined effect of personal characteristics and patch-location, we first formulate a TensorPatch model based on multilinear analysis to explicitly model the interaction between multiple constituent factors. Motivated by Locally Linear Embedding, we develop an enhanced multilinear patch hallucination algorithm, which efficiently exploits the local distribution structure in the sample space. To better preserve face subtle details, we derive the Coupled PCA algorithm to learn the relation between HR residue and LR residue, which is utilized for compensate the error residue in hallucinated images. Experiments demonstrate that our framework not only well maintains the global facial structures, but also recovers the detailed facial traits in high quality. (Abstract shortened by UMI.)
In this thesis, we propose a novel dimensionality reduction algorithm called graph-regularized projection (GRP) to tackle the problem of semi-supervised dimensionality reduction that is rarely investigated in the literature. Given partially labeled data points, GRP aims at learning a not only smooth but also discriminative projection from high-dimensional data vectors to their latent low-dimensional representations. Motivated by recent semi-supervised learning process: graph regularization, we develop a graph-based regularization framework to enforce smoothness along the graph of the desired projection initiated by margin maximization. As a result, GRP has a natural out-of-sample extension to novel examples and thus can be generalized to the entire high-dimensional space. Extensive experiments on a synthetic dataset and several real databases demonstrate the effectiveness of our algorithm.
Next, this thesis addresses the problem of how to learn an appropriate feature representation from video to benefit video-based face recognition. By simultaneously exploiting the spatial and temporal information, the problem is posed as learning Spatio-Temporal Embedding (STE) from raw videos. STE of a video sequence is defined as its condensed version capturing the essence of space-time characteristics of the video. Relying on the co-occurrence statistics and supervised signatures provided by training videos, STE preserves the intrinsic temporal structures hidden in video volume, meanwhile encodes the discriminative cues into the spatial domain. To conduct STE, we propose two novel techniques, Bayesian keyframe learning and nonparametric discriminant embedding (NDE), for temporal and spatial learning, respectively. In terms of learned STEs, we derive a statistical formulation to the recognition problem with a probabilistic fusion model. On a large face video database containing more than 200 training and testing sequences, our approach consistently outperforms the state-of-the-art methods, achieving a perfect recognition accuracy.
Liu, Wei.
"August 2007."
Advisers: Xiaoou Tang; Jianzhuang Liu.
Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1110.
Thesis (Ph.D.)--Chinese University of Hong Kong, 2007.
Includes bibliographical references (p. 140-151).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstract in English and Chinese.
School code: 1307.

碩士
國立成功大學
資訊工程學系碩博士班
92
We propose a new family of Cayley graphs, named the k-valent graphs, for building interconnection networks. The k-valent graphs possess many valuable topological properties, such as regular with the node-degree k, logarithmic diameter subject to the number of nodes for some fxed k >= 6, and maximally fault tolerance. This new class also contains trivalent graphs (Vadapalli and Srimani, 1995) as its subclass of graphs. An algorithm is proposed to determine a shortest path between arbitrary two nodes. Besides, embedding of cycles or cliques on the k-valent graph is also discussed.

Meshes and hypercubes are two most important communication and computation structures used in parallel computing. Network embedding problems for meshes and hypercubes on traditional network architectures have been intensively studied during the past years. With the emergence of new network architectures, the traditional network embedding results are not enough to solve the new requirements. The main objective of this thesis is to design efficient network embedding schemes for realizing meshes and hypercubes on a group of future network architectures. This thesis is organized into two parts. The first part focuses on embedding meshes/tori on a group of double-loop networks by evaluating the traditional embedding metrics, since double-loop networks have been intensively studied and proven to have many desirable properties for future network architecture. We propose a novel tessellation approach to partition the geometric plane of double-loop networks into a set of parallelogram tiles, called P-shape. Based on the characteristics of P-shape, we design a simple embedding scheme, namely P-shape embedding, that embeds arbitrary-shape meshes and tori on double-loop networks in a systematic way. A main merit of P-shape embedding is that a large fraction of embedded mesh/torus edges have edge dilation 1, resulting in a low average dilation. These are the first results, to our knowledge, on embedding meshes and tori on general doubleloop networks which is of great significance due to the popularity of these architectures. Our P-shape construction bridges between regular graphs and double-loop networks, and provides a powerful tool for studying the topological properties of double-loop networks. In the second part, we study efficient embedding schemes for realizing hypercubes on a group of array-basedWDMoptical networks by analyzing the new embedding metric of wavelength requirement, as WDM optical networking is becoming a promising technology for deployment in many applications in advanced telecommunication and parallel computing. We first design routing and wavelength assignments of both bidirectional and unidirectional hypercubes on WDM optical linear arrays, rings, meshes and tori with the consideration of communication directions. For each case, we identify a lower bound on the number of wavelengths required, and design the embedding scheme and wavelength assignment algorithm that uses a provably near-optimal number of wavelengths. To further reduce the wavelength requirement, we extend the results to WDM ring networks with additional links, namely WDM chordal rings. Based on our proposed embedding schemes, we provide the analysis of chord length with optimal number of wavelengths to realize hypercubes on 3-degree and 4-degree WDM chordal rings. Furthermore, we propose an embedding scheme for realizing dimensional hypercubes on WDM optical arrays by considering the hypercubes dimension by dimension, called lattice embedding, instead of embedding hypercubes with all dimensions. Based on lattice embedding, the number of wavelengths required to realize dimensional hypercube on WDM arrays can been significantly reduced compared to the previous results. By our embedding schemes, many communications and computations, originally designed based on hypercubes, can be directly implemented in WDM optical networks, and the wavelength requirements can be easily derived using our obtained results.
http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1345349
Thesis (Ph.D.) - University of Adelaide, School of Computer Science, 2008

Kernel embedding methods have witnessed a great deal of practical success in the area of nonparametric hypothesis testing in recent years. But ever since its first proposal, there exists an inevitable problem that researchers in this area have been trying to answer--what kernel should be selected, because the performance of the associated nonparametric tests can vary dramatically with different kernels. While the way of kernel selection is usually ad hoc, we wonder if there exists a principled way of kernel selection so as to ensure that the associated nonparametric tests have good performance. As consistency results against fixed alternatives do not tell the full story about the power of the associated tests, we study their statistical performance within the minimax framework. First, focusing on the case of goodness-of-fit tests, our analyses show that a vanilla version of the kernel embedding based test could be suboptimal, and suggest a simple remedy by moderating the kernel. We prove that the moderated approach provides optimal tests for a wide range of deviations from the null and can also be made adaptive over a large collection of interpolation spaces. Then, we study the asymptotic properties of goodness-of-fit, homogeneity and independence tests using Gaussian kernels, arguably the most popular and successful among such tests. Our results provide theoretical justifications for this common practice by showing that tests using a Gaussian kernel with an appropriately chosen scaling parameter are minimax optimal against smooth alternatives in all three settings. In addition, our analysis also pinpoints the importance of choosing a diverging scaling parameter when using Gaussian kernels and suggests a data-driven choice of the scaling parameter that yields tests optimal, up to an iterated logarithmic factor, over a wide range of smooth alternatives. Numerical experiments are presented to further demonstrate the practical merits of our methodology.

碩士
國立彰化師範大學
物理學系
92
The purpose of this research was to explore the effects of concept mapping instruction on students’ conceptual change of optical concepts, and find out students’ attitudes toward concept mapping instruction. According to the purpose of this research, two intact classes were selected as experimental group and control group. The two groups received the same instructional contents on optical vision. The experimental group received concept mapping instruction, while the control group received traditional instruction. Data collection included written test, questionnaire and interviews. The research data was analyzed qualitatively and quantitatively. The results of the study were as follows: 一、Concept-mapping teaching strategy could help students catch concepts about the relation between light and color, but was helpless in the explanation of the images of lens by using reflective concept. 二、The best way to change concept and modify misconceptions with concept-mapping teaching strategy was by group discussion, practicing questions on the learning sheet, lab experiment, and multimedia demonstration. At the same time, asking students to draw concept maps and use them to solve problems could develop their ability of self-reflection, and clarify the concepts. 三、The achievement of students with concept mapping instruction were significantly higher than those without concept mapping instruction in their learning achievement. 四、87％ of the students felt that concept maps can raise their interests and confidence in learning optical concepts. 58％ of the students felt that it is hard to construct concept maps and were disturbed by the relation link . They preferred to construct concept maps and elaborate the concepts with the guidance of the teacher and through group discussion. 五、84％ of the students felt that concept maps can facilitate their learning in optical concepts, make the concepts clear, and enhance their confidence in problem-solving. 61％ of the students felt that concept maps can be applied to other subjects as a new teaching method. 37％ of the students were willing to keep on using concept maps to assist their learning.

碩士
國立高雄第一科技大學
電子工程系碩士在職專班
105
This thesis is to study how to promote the conversion efficiency of solar cells by integrating Archimedean solids with Fresnel lens. We have investigated the material of solar panels, compared the lens types, analyzed the focus distance and attempted different angles to find the best power generation performance of solar panels. This research focused on the commonly-used monocrystalline silicon solar cells and compared the performance difference between monocrystalline silicon solar cells and polycrystalline silicon solar cells. We experimented various lens combinations, including the daily-used glass lens, the single Fresnel lens, the array of single Fresnel lenses and the self-made 3D Fresnel lens, to find the optimal conditions for solar power generation. The experiment was conducted on the self-made multi-function garden lamps to find the optimal solar power conversion. We expect that this design principle will be applied in the daily life and popularized in many areas. Meanwhile, the future applications will result in more experimental data for us to study the economic benefits of solar power conversion performance.

Distribution networks are undergoing unprecedented challenges originated from the large-scale adoption of distributed energy resources, price responsive demand, electric storage resources, electric vehicles, etc. Power system analysis techniques such as Load Flow (LF) and Optimal Power Flow (OPF) are necessary to ensure secure and optimal operation in an increasingly active, distributed, and dynamic distribution grid operation. This dissertation presents robust and computationally efficient solution techniques for LF and OPF problems. In the first part of this dissertation, we utilize Riemannian optimization and present two solution methods. The first solution method is applicable to the LF problem and is shown to fall into the category of Riemannian approximate Newton methods, which guarantees descent at each iteration while maintaining a local superlinear convergence rate. The second solution method is a Riemannian Augmented Lagrangian Method (RALM) which applies to the OPF problem. The proposed solution approach exploits the geometrical properties of the power flow equations and ensures the physical feasibility of the solution. Computational experiments on several distribution networks provide encouraging results in terms of solution quality and speed. The second part of this dissertation employs Holomorphic embedding methods and presents two LF solution techniques. The first solution technique improves the computational efficiency of the Holomorphic Embedding Load flow Method (HELM). Numerical experimentation demonstrates overall time savings of up to 30% on IEEE radial distribution test cases. The second solution technique extends HELM to three-phase distribution networks with a generic topology and wye/delta connected ZIP load models. We demonstrate the efficacy of the proposed method through numerical results. The third part of this dissertation is focused on exploiting the existing network infrastructure to improve the system operation. We present an optimal line switching and bus splitting heuristic considering AC and N-1 contingency constraints and apply the proposed method to several IEEE standard test networks. We also provide directions for possible extensions to distribution networks. The proposed method identifies a network topology that reduces the operation cost while maintaining AC feasibility and initial system reliability level in the sense of N-1 contingency requirements.

博士
國立成功大學
電機工程學系碩博士班
92
A fundamental goal of image compression is to reduce the bit rate for transmission or data storage while maintaining an acceptable fidelity or image quality. Vector Quantization (VQ) is a popular method for image compression. The purpose of vector quantization is to create a codebook such that the average distortion between training vectors and their corresponding codevectors in the codebook is minimized. Neural networks are well suited to the problem of image compression due to their massively parallel and distributed architecture. The use of neural networks for vector quantization has a significant advantage, that is neural networks are highly parallel computing architecture and, thus, offer the potential for real-time VQ. 　　This dissertation describes the use of neural networks for vector quantization (VQ), two un-supervised neural network with grey relation and fuzzy clustering schemes for training the vector quantizer. A powerful feature of these new training algorithms is that the VQ codewords are determined in an adaptive manner, as compared to the popular LBG training algorithm, which requires that the entire training data be processed in a batch mode. In the first proposed grey-based neural network schemes, the grey theory is applied to a 2-D competitive Hopfield neural network (named GHNN) and two layer competitive learning network (named GCLN) in order to generate optimal solution for VQ. In accordance with the degree of similarity measure between training vectors and codevectors, the grey relational analysis is used to measure the relationship degree among them. 　　In most cases, unsupervised training algorithms attempt to “cluster” or average portions of the training data into representative groups. In the second proposed fuzzy neural network schemes, the codebook design is conceptually considered as a clustering problem. Here, it is a kind of neural network model imposed by the fuzzy clustering strategy working toward minimizing an objective function defined as the average distortion measure between any two training vectors within the same class. In order to generate feasible results, its implementation consists of neural networks and fuzzy clustering with penalty term methods (named FCLN and PFHNN). 　　While the GCLN, GHNN, FCLN and PFHNN algorithms converge to a local optimum, it is not guaranteed to reach the global optimum. The Genetic Algorithm (GA) is used in an attempt to optimize a specified objective function related to vector quantizer design. The physical processes of competition, selection and reproduction operating in populations are adopted in combination with GCLN and PFHNN and to produce a superior Genetic Grey-based Competitive Learning Network (GGCLN) and Genetic Fuzzy Hopfield Neural Network with penalty term (GFHNN) for codebook design in image compression. Simulation results illustrate that embedding GA, grey relation and fuzzy clustering techniques into neural networks provides an approach for search of globally optimal or near-optimum codebook to image compression. 　　Color images are widely used in our daily lives, and color image compression and cryptosystem are closed related for secure internet multimedia application. In this dissertation an invisible virtual color image system based on Interpolative Vector Quantization (IVQ) using a spread neural network with Penalized Fuzzy C-Means (PFCM) clustering technology (named SPFNN) is proposed. The goal is to offer safe exchange of a color stego-image in the internet. In the proposed scheme, is first compressed the secret color image by a spread-unsupervised neural network with PFCM based on IVQ, then the block cipher Data Encryption Standard (DES) and the Rivest, Shamir and Adleman (RSA) algorithms are hired to provide the mechanism of a hybrid cryptosystem for secure communication and convenient environment in the internet. In the SPFNN, the PFHNN algorithm is modified into spread neural network in order to generate optimal solution for color IVQ. Then we encrypted color IVQ indices and sorted codebooks of secret color image information and embedded into the frequency domain of the cover color image by Hadamard Transform (HT). Our proposed method has two benefits. One is the highly secure and convenience offered by the hybrid DES and RSA cryptosystems to exchange color image data in the internet. The other benefit is the excellent results can be obtained using our proposed color image compression scheme SPFNN method.

Many concrete problems, ranging from Portfolio selection to Water resource management, may be cast into a multiobjective programming framework. The simplistic way of superseding blindly conflictual goals by one objective function let no chance to the model but to churn out meaningless outcomes. Hence interest of discussing ways for tackling Multiobjective Programming Problems. More than this, in many real-life situations, uncertainty and imprecision are in the state of affairs. In this dissertation we discuss ways for solving Multiobjective Programming Problems with fixed and fuzzy coefficients. No preference, a priori, a posteriori, interactive and metaheuristic methods are discussed for the deterministic case. As far as the fuzzy case is concerned, two approaches based respectively on possibility measures and on Embedding Theorem for fuzzy numbers are described. A case study is also carried out for the sake of illustration. We end up with some concluding remarks along with lines for further development, in this field.
Operations Research
M. Sc. (Operations Research)

Every year, the number of applications relying on information extracted from high-resolution satellite imagery increases. In particular, the combined use of different data sources is rising steadily, for example to create high-resolution maps, to detect changes over time or to conduct image classification. In order to correctly fuse information from multiple data sources, the utilized images have to be precisely geometrically registered and have to exhibit a high absolute geo-localization accuracy. Due to the image acquisition process, optical satellite images commonly have an absolute geo-localization accuracy in the order of meters or tens of meters only. On the other hand, images captured by the high-resolution synthetic aperture radar satellite TerraSAR-X can achieve an absolute geo-localization accuracy within a few decimeters and therefore represent a reliable source for absolute geo-localization accuracy improvement of optical data. The main objective of this thesis is to address the challenge of image matching between high resolution optical and synthetic aperture radar (SAR) satellite imagery in order to improve the absolute geo-localization accuracy of the optical images. The different imaging properties of optical and SAR data pose a substantial challenge for a precise and accurate image matching, in particular for the handcrafted feature extraction stage common for traditional optical and SAR image matching methods. Therefore, a concept is required which is carefully tailored to the characteristics of optical and SAR imagery and is able to learn the identification and extraction of relevant features. Inspired by recent breakthroughs in the training of neural networks through deep learning techniques and the subsequent developments for automatic feature extraction and matching methods of single sensor images, two novel optical and SAR image matching methods are developed. Both methods pursue the goal of generating accurate and precise tie points by matching optical and SAR image patches. The foundation of these frameworks is a semi-automatic matching area selection method creating an optimal initialization for the matching approaches, by limiting the geometric differences of optical and SAR image pairs. The idea of the first approach is to eliminate the radiometric differences between the images trough an image-to-image translation with the help of generative adversarial networks and to realize the subsequent image matching through traditional algorithms. The second approach is an end-to-end method in which a Siamese neural network learns to automatically create tie points between image pairs through a targeted training. The geo-localization accuracy improvement of optical images is ultimately achieved by adjusting the corresponding optical sensor model parameters through the generated set of tie points. The quality of the proposed methods is verified using an independent set of optical and SAR image pairs spread over Europe. Thereby, the focus is set on a quantitative and qualitative evaluation of the two tie point generation methods and their ability to generate reliable and accurate tie points. The results prove the potential of the developed concepts, but also reveal weaknesses such as the limited number of training and test data acquired by only one combination of optical and SAR sensor systems. Overall, the tie points generated by both deep learning-based concepts enable an absolute geo-localization improvement of optical images, outperforming state-of-the-art methods.

博士
國立中正大學
電機工程所
98
Abstract There is widespread interest in the development of optical image encryption and data embedding systems. The advantages inherent in an optical approach to encryption and data embedding include such as a high-speed parallel data processing and the difficulty in data accessing, copying or falsification. Conventionally, optical image encryption is achieved by double random-phase encoding in the Fourier domain (also in the Fresnel or fractional Fourier domain), where two statistically independent random-phase masks placed at, the input and the Fourier (Fresnel or fractional Fourier) planes, are to be designed. While these two random-phase codes are generated traditionally by using an iterative algorithm, such as Projection Onto Constraint Sets Algorithm (POCSA), which is inefficient due to a long iterative process. How to develop a more efficient method than the previous works on creating two statistically independent random-phase masks, without losing the security of the system, is an important issue in this research. This is done by exploiting the modified Gerchberg-Saxton algorithm (MGSA) instead of traditional POCSA (Chapter 3). Similarly based on the proposed MGSA, we present a concealogram-based method for optical data embedding by using halftone encoding based on CGH technique (Chapter 4). A concealogram is generally created by encoding both the magnitude (intensity) and phase of a hidden image into a halftone host image, as a fashion of modifying the area and position of binary dots therein. The magnitude (intensity) and phase information for an image to be embedded, are generally obtained by using an iterative POCSA algorithm, which is inefficient due to a long iterative process. In the second important issue in this research is to develop a more efficient method than the prior works on creating concealograms for optical data embedding results. Actually, our research results show that the proposed MGSA-based method can not only achieve the data embedding purpose without losing the system security, but also provide a faster method than previous works. The final topic in this study is about optical multiple-image encryption (Chapter 5). Methods based on a single random-phase mask and double random-phase masks, are both proposed. They can also to be done by exploiting the MGSA instead of POCSA. Furthermore, the extension of the proposed algorithm to color-image encryption is also discussed. A crucial issue to this goal is to reduce the crosstalks between encrypted images, which accordingly increases the number of images that can be encrypted simultaneously (or, the multiplexing capacity). Our research results show that the crosstalks can be significantly reduced. In summary, the proposed MGSA is identified to be a powerful encoding tool in the development of both optical image encryption and data embedding.

Οι εμποτισμένες με φάρμακα μεταλλικές ενδοπροθέσεις (DES) έχει αποδειχθεί ότι ελαχιστοποιούν την υπερπλασία του ενδοθηλίου των στεφανιαίων αγγείων. Η υπερπλαστική αντίδραση του ουροθηλίου είναι το πιο συχνή επιπλοκή της χρήσης των μεταλλικών ενδοπροθέσεων στον ουρητήρα. Στην παρούσα μελέτη αξιολογήσαμε τις εμποτισμένες με zotarolimus μεταλλικές ενδοπροθέσεις (ZES- Endeavor Resolute, Medtronics Inc, USA) στον ουρητήρα χοίρων και κουνελιών. Μέθοδος: Μία ZES and μία συνήθης μεταλλική ενδοπρόθεση (BMS) τοποθετήθηκαν στον κάθε ουρητήρα 10 χοίρων και 6 κουνελιών. Η τοποθετήση έγινε κυστεοσκοπικά. Αξονική τομογραφία (CT) έγινε για την αξιολόγηση των ουρητήρων του χοίρου και ενδοφλέβιος πυελογραφία (IVP) έγινε για τον ίδιο σκοπό στα κουνέλια. Το πρόγραμμα παρακολούθησης περιλάμβανε CT ή IVP κάθε εβδομάδα για τις επόμενες 4 εβδομάδες για τους χοίρους και 8 εβδομάδες για τα κουνέλια. Σπινθηρογραφήματα νεφρών πριν την τοποθέτηση των ενδοπροθέσεων και κατά την 3 εβδομάδα παρακολούθησης έλαβε χώρα σε όλα τα ζώα. Οπτική τομογραφία συνοχής (OCT) χρησιμοποιήθηκε για την εκτίμηση της κατάστασης του αυλού και τοιχώματος των ουρητήρων που έφεραν τις ενδοπροθέσεις. Ιστοπαθολογική εξέταση των ουρητήρων με τις ενδοπρόθεσεις έγινε με τα παρασκευάσματα να έχουν στερεοποιηθεί σε glycol-methacrylate ρητίνη. Αποτελέσματα: Υπερπλαστική αντίδραση διαπιστώθηκε και στους δύο τύπους ενδοπροθέσεων. Οι BMS ενδοπροθέσεις αποφράχτηκαν πλήρως σε 7 ουρητήρες χοίρων ενώ οι ουρητήρες των ιδίων ζώων που έφεραν ZES ενδοπρόθεση έφεραν υπερπλαστική αντίδραση αλλά δεν κατέληγαν σε απόφραξη. Δύο ουρητήρες κουνελιών με BMS ενδοπροθέσεις αποφράχτηκαν τελείως ενώ όλες οι ZES ενδοπροθέσεις δε συσχετίστηκαν με απόφραξη του ουρητήρα. Διαπιστώθηκε έκπτωση της λειτουργίας 7 νεφρών χοίρων και 2 κουνελιών που είχαν ουρητήρες με αποφραγμένες ενδοπροθέσεις. Η OCT έδειξε αυξημένη υπερπλαστική αντίδραση σε ουρητήρες που έφεραν BMS ενδοπρόθεση σε σχέση με ZES. Παρόλα αυτά, η ιστοπαθολογική εξέταση έδειξε υπερπλαστική αντίδραση παρούσα σε όλες τις ενδοπροθέσεις αλλά σημαντικά περισσότερη υπερπλαστική αντίδραση στις BMS ενδοπροθέσεις. Συμπέρασμα: Οι ZES ενδοπροθέσεις στους ουρητήρες χοίρων και κουνελιών δε συσχετίστηκαν με υπερπλαστική αντίδραση που οδηγούσε σε απόφραξη της ενδοπρόθεσης. Αυτές οι ενδοπροθέσεις συσχετίστηκαν με σημαντικά μικρότερη υπερπλαστική αντίδραση συγκριτικά με τις BMS ενδοπροθέσεις ενώ η φλεγμονώδης αντίδραση ήταν παρόμοια και στους δύο τύπους ενδοπροθέσεων.
Drug eluting stents (DES) proved to minimize neointimal hyperplasia in coronary vessels. Hyperplastic reaction is the most common unwelcome event related to the use of metal mesh stents in the ureter. We evaluated the effect of zotarolimus eluting stent (ZES- Endeavor Resolute, Medtronics Inc, USA) in porcine and rabbit ureter. Methods: A ZES and a bare metal stent (BMS) were inserted in each ureter of 10 pigs and 6 rabbits. The insertion was performed by retrograde approach. Computerized tomography (CT) was used for the evaluation of porcine ureters while intraoperative intravenous pyelography (IVP) for rabbit ureters. The follow-up included CT or IVP every week for the following 4 weeks for pigs and 8 weeks for rabbits. Renal scintigraphies were performed prior to stent insertion and during the 3rd week in all animals. Optical coherence tomography (OCT) has been used for the evaluation of the luminal and intraluminal condition of the stented ureters. Histopathologic examination of the stented ureters embedded in glycol-methacrylate was performed. Results: Hyperplastic reaction was present in both stent types. BMSs in 7 porcine ureters were completely obstructed while porcine ureters stented with ZES had hyperplastic tissue which did not result in obstruction. Two rabbit ureters stented by BMS were occluded while no ZES was associated with ureteral obstruction. The function of the 7 porcine renal units and the two rabbit units with obstructed stented ureter was compromised. The OCT revealed increased hyperplastic reaction in the ureters stented by BMSs in comparison to ZESs. Although, hyperplastic reaction was present in all cases, pathology examination revealed significantly more hyperplastic reaction in BMSs. Conclusion: ZESs in the pig and rabbit ureter were not related to hyperplastic reaction resulting in stent occlusion. These stents were related to significantly lower hyperplastic reaction in comparison to BMSs while inflammation rates were similar for both stent types.