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Gustavsson, Oscar. "Inverse Halftoning Using Inverse Methods". Thesis, Linköpings universitet, Institutionen för teknik och naturvetenskap, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-96225.
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This Master´s thesis discusses the problems concerning inverse halftoning, which means converting a halftone image into a continuous tone one. The thesis evaluates the use of inverse methods, showing promising results. The algorithm is implemented and tested using Matlab and serves as a prototype for possible full scale applications. The work is based upon previously published articles on the subject, along with basic halftoning and printing theory. This serves as a starting point from which the proposed method is developed, and the results are in some areas competitive against other, previously published approaches.
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Lopez, Rincon Alejandro. "Le problème inverse en l'électrocardiographie". Thesis, Bordeaux 1, 2013. http://www.theses.fr/2013BOR15261/document.
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Dans le problème inverse d’électrocardiographie, le cible est faire la reconstruction de l’activité électrophysiologique dans le cœur sans mesurer directement dans sa surface (sans interventions avec cathéter). Il est important remarque que en l’actualité la solution numérique du problème inverse est résolu avec le modèle quasi-statique. Ce modèle ne considère pas la dynamique du cœur et peut produire des erreurs dans la reconstruction de la solution sur la surface du cœur. Dans cette thèse, différents méthodologies était investigue pour résoudre le problème inverse d’électrocardiographie comme intelligence artificielle, et modèles dynamiques limites. Aussi, les effets de différents opérateurs en utilisant méthodes d’éléments de frontière , et méthodes d’élément finis était investigueIn the inverse problem of electrocardiography, the target is to make the reconstruction of electrophysiological activity in the heart without measuring directly in its surface (without interventions with catheter). It is important to note that the current numerical solution of the inverse problem is solved with the quasi-static model. This model does not consider the dynamics of the heart and can cause errors in the reconstruction of the solution on the surface of the heart. This thesis investigates different methodologies was to solve the inverse problem of electrocardiography as artificial intelligence and dynamic models limits. Also, the effects of different operators using boundary element methods, finite element methods, and was investigates
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AlAli, Amal. "Cosets in inverse semigroups and inverse subsemigroups of finite index". Thesis, Heriot-Watt University, 2016. http://hdl.handle.net/10399/3185.
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The index of a subgroup of a group counts the number of cosets of that subgroup. A subgroup of finite index often shares structural properties with the group, and the existence of a subgroup of finite index with some particular property can therefore imply useful structural information for the overgroup. Although a developed theory of cosets in inverse semigroups exists, it is defined only for closed inverse subsemigroups, and the structural correspondences between an inverse semigroup and a closed inverse subsemigroup of finte index are much weaker than in the group case. Nevertheless, many aspects of this theory remain of interest, and some of them are addressed in this thesis. We study the basic theory of cosets in inverse semigroups, including an index formula for chains of subgroups and an analogue of M. Hall’s Theorem on counting subgroups of finite index in finitely generated groups. We then look at specific examples, classifying the finite index inverse subsemigroups in polycyclic monoids and in graph inverse semigroups. Finally, we look at the connection between the properties of finite generation and having finte index: these were shown to be equivalent for free inverse monoids by Margolis and Meakin.
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Persson, Mattsson Pär. "Inverse Quantum Problem". Thesis, Uppsala universitet, Analys och tillämpad matematik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-158200.
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Fadden, Lorna Marie. "The inverse continuum". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ61427.pdf.
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Banterle, Francesco. "Inverse tone mapping". Thesis, University of Warwick, 2009. http://wrap.warwick.ac.uk/55447/.
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The introduction of High Dynamic Range Imaging in computer graphics has produced a novelty in Imaging that can be compared to the introduction of colour photography or even more. Light can now be captured, stored, processed, and finally visualised without losing information. Moreover, new applications that can exploit physical values of the light have been introduced such as re-lighting of synthetic/real objects, or enhanced visualisation of scenes. However, these new processing and visualisation techniques cannot be applied to movies and pictures that have been produced by photography and cinematography in more than one hundred years. This thesis introduces a general framework for expanding legacy content into High Dynamic Range content. The expansion is achieved avoiding artefacts, producing images suitable for visualisation and re-lighting of synthetic/real objects. Moreover, it is presented a methodology based on psychophysical experiments and computational metrics to measure performances of expansion algorithms. Finally, a compression scheme, inspired by the framework, for High Dynamic Range Textures, is proposed and evaluated.
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Varagona, Scott Smith Michel. "Inverse limit spaces". Auburn, Ala, 2008. http://hdl.handle.net/10415/1486.
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Rivero, Pindado Victor. "Monocular Visual SLAMbased on Inverse DepthParametrizationMonocular Visual SLAMbased on Inverse DepthParametrization". Thesis, Mälardalen University, School of Innovation, Design and Engineering, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-10206.
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The first objective of this research has always been carry out a study of visual techniques SLAM (Simultaneous localization and mapping), specifically the type monovisual, less studied than the stereo. These techniques have been well studied in the world of robotics. These techniques are focused on reconstruct a map of the robot enviroment while maintaining its position information in that map. We chose to investigate a method to encode the points by the inverse of its depth, from the first time that the feature was observed. This method permits efficient and accurate representation of uncertainty during undelayed initialization and beyond, all within the standard extended Kalman filter (EKF).At first, the study mentioned it should be consolidated developing an application that implements this method. After suffering various difficulties, it was decided to make use of a platform developed by the same author of Slam method mentioned in MATLAB. Until then it had developed the tasks of calibration, feature extraction and matching. From that point, that application was adapted to the characteristics of our camera and our video to work. We recorded a video with our camera following a known trajectory to check the calculated path shown in the application. Corroborating works and studying the limitations and advantages of this method.
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Lu, Linghai. "Inverse modelling and inverse simulation for system engineering and control applications". Thesis, University of Glasgow, 2007. http://theses.gla.ac.uk/2/.
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Following extensive development over the past two decades, techniques of inverse simulation have led to a range of successful applications, mainly in the fields of helicopter flight mechanics, aircraft handling qualities and associated issues in terms of model validation. However, the available methods still have some well-known limitations. The traditional methods based on the Newton-Raphson algorithm suffer from numerical problems such as high-frequency oscillations and can have limitations in their applicability due to problems of input-output redundancy. The existing approaches may also show a phenomenon which has been termed “constraint oscillations” which leads to low-frequency oscillatory behaviour in the inverse solutions. Moreover, the need for derivative information may limit their applicability for situations involving manoeuvre discontinuities, model discontinuities or input constraints. Two new methods are developed to overcome these issues. The first one, based on sensitivity-analysis theory, allows the Jacobian matrix to be calculated by solving a sensitivity equation and also overcomes problems of input-output redundancy. In addition, it can improve the accuracy of results compared with conventional methods and can deal with the problem of high-frequency oscillations to some extent. The second one, based on a constrained Nelder-Mead search-based optimisation algorithm, is completely derivative-free algorithm for inverse simulation. This approach eliminates problems which make traditional inverse simulation techniques difficult to apply in control applications involving discontinuous issues such as actuator amplitude or rate limits. This thesis also offers new insight into the relationship between mathematically based techniques of model inversion and the inverse simulation approach. The similarities and shortcomings of both these methodologies are explored. The findings point to the possibility that inverse simulation can be used successfully within the control system design process for feedforward controllers for model-based output-tracking control system structures. This avoids the more complicated and relatively tedious techniques of model inversion which have been used in the past for feedforward controller design. The methods of inverse simulation presented in this thesis have been applied to a number of problems which are concerned mainly with helicopter and ship control problems and include cases involving systems having nonminimum-phase characteristics. The analysis of results for these practical applications shows that the approaches developed and presented in this thesis are of practical importance. It is believed that these developments form a useful step in moving inverse simulation methods from the status of an academic research topic to a practical and robust set of tools for engineering system design.
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Saracco, Jérôme. "Contributions à la régression inverse par tranchage : sliced inverse regression (S.I.R.)". Toulouse 3, 1996. http://www.theses.fr/1996TOU30185.
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La regression inverse par tranchage (sliced inverse regression (s. I. R. )) est une methode de regression semiparametrique reposant sur un argument geometrique. Au contraire des autres methodes de regression semiparametrique, elle ne requiert que des temps de calcul informatique tres courts. Dans cette these, apres un panorama de l'etat actuel des travaux sur s. I. R. , nous envisageons deux aspects de cette methode, ainsi qu'une application a l'estimation simplifiee d'un modele de selection. (1) nous developpons une theorie asymptotique basee sur un decoupage non aleatoire en tranches et portant sur la loi asymptotique de la partie parametrique du modele. (2) une extension semiparametrique du modele de selection tobit peut s'interpreter geometriquement dans le cadre de s. I. R. Exploitant cette observation, nous introduisons un estimateur simplifie pour un tel modele, et nous etudions sa convergence en probabilite et en loi. Des simulations, y compris lorsque certaines hypotheses theoriques ne sont pas respectees par les donnees, confirment le bon comportement de notre estimateur. (3) pour le cas d'echantillons de petite taille, l'estimation par tranchage se revele sensible au choix des tranches. Nous proposons deux methodes alternatives a un tranchage particulier fixe par l'utilisateur, l'une est basee sur un argument nonparametrique, et l'autre est basee sur un lissage de plusieurs decoupages en tranches. Nous etablissons diverses proprietes asymptotiques de ces methodes. Nous les comparons aux methodes s. I. R. Existantes par simulations sur des echantillons de 25 et 50 observations. Les methodes que nous proposons se revelent sensiblement meilleures que les methodes anterieures. Nous avons programme l'ensemble des methodes s. I. R. En splus. Nous fournissons une illustration et un descriptif de l'implementation informatique que nous avons realisee, les differentes procedures et fonctions sont disponibles par ftp
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Kempton, Mark Condie. "The Minimum Rank, Inverse Inertia, and Inverse Eigenvalue Problems for Graphs". BYU ScholarsArchive, 2010. https://scholarsarchive.byu.edu/etd/2182.
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For a graph G we define S(G) to be the set of all real symmetric n by n matrices whose off-diagonal zero/nonzero pattern is described by G. We show how to compute the minimum rank of all matrices in S(G) for a class of graphs called outerplanar graphs. In addition, we obtain results on the possible eigenvalues and possible inertias of matrices in S(G) for certain classes of graph G. We also obtain results concerning the relationship between two graph parameters, the zero forcing number and the path cover number, related to the minimum rank problem.
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Okamoto, Kei. "Optimal numerical methods for inverse heat conduction and inverse design solidification problems". Online access for everyone, 2005. http://www.dissertations.wsu.edu/Dissertations/Fall2005/k%5Fokamoto%5F120905.pdf.
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McCrindle, Rachel Jane. "Inverse software configuration management". Thesis, Durham University, 1998. http://etheses.dur.ac.uk/5013/.
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Software systems are playing an increasingly important role in almost every aspect of today’s society such that they impact on our businesses, industry, leisure, health and safety. Many of these systems are extremely large and complex and depend upon the correct interaction of many hundreds or even thousands of heterogeneous components. Commensurate with this increased reliance on software is the need for high quality products that meet customer expectations, perform reliably and which can be cost-effectively and safely maintained. Techniques such as software configuration management have proved to be invaluable during the development process to ensure that this is the case. However, there are a very large number of legacy systems which were not developed under controlled conditions, but which still, need to be maintained due to the heavy investment incorporated within them. Such systems are characterised by extremely high program comprehension overheads and the probability that new errors will be introduced during the maintenance process often with serious consequences. To address the issues concerning maintenance of legacy systems this thesis has defined and developed a new process and associated maintenance model, Inverse Software Configuration Management (ISCM). This model centres on a layered approach to the program comprehension process through the definition of a number of software configuration abstractions. This information together with the set of rules for reclaiming the information is stored within an Extensible System Information Base (ESIB) via, die definition of a Programming-in-the- Environment (PITE) language, the Inverse Configuration Description Language (ICDL). In order to assist the application of the ISCM process across a wide range of software applications and system architectures, die PISCES (Proforma Identification Scheme for Configurations of Existing Systems) method has been developed as a series of defined procedures and guidelines. To underpin the method and to offer a user-friendly interface to the process a series of templates, the Proforma Increasing Complexity Series (PICS) has been developed. To enable the useful employment of these techniques on large-scale systems, the subject of automation has been addressed through the development of a flexible meta-CASE environment, the PISCES M4 (MultiMedia Maintenance Manager) system. Of particular interest within this environment is the provision of a multimedia user interface (MUI) to die maintenance process. As a means of evaluating the PISCES method and to provide feedback into die ISCM process a number of practical applications have been modelled. In summary, this research has considered a number of concepts some of which are innovative in themselves, others of which are used in an innovative manner. In combination these concepts may be considered to considerably advance the knowledge and understanding of die comprehension process during the maintenance of legacy software systems. A number of publications have already resulted from the research and several more are in preparation. Additionally a number of areas for further study have been identified some of which are already underway as funded research and development projects.
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Laine, A. D. "Inverse photoemission of tungsten". Thesis, University of Liverpool, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.380177.
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Allen, Peter Maurice George. "Inverse photoemission from surfaces". Thesis, Imperial College London, 1986. http://hdl.handle.net/10044/1/37921.
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Marcato, Robert W. (Robert William) 1975. "Optimizing an inverse warper". Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/47626.
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Thesis (S.B. and M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998.Includes bibliographical references (p. 50).
by Robert W. Marcato, Jr.
S.B.and M.Eng.
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Chen, Xudong 1977. "Inverse problems in electromagnetics". Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/33933.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Vita.
Includes bibliographical references (p. 155-164).
Two inverse problems in electromagnetics are investigated in this thesis. The first is the retrieval of the effective constitutive parameters of metamaterials from the measurement of the reflection and the transmission coefficients. A robust method is proposed for the retrieval of metamaterials as isotropic media, and four improvements over the existing methods make the retrieval results more stable. Next, a new scheme is presented for the retrieval of a specific bianisotropic metamaterial that consists of split-ring resonators, which signifies that the cross polarization terms of the metamaterial are quantitatively investigated for the first time. Finally, an optimization approach is designed to achieve the retrieval of general bianisotropic media with 72 unknown parameters. The hybrid algorithm combining the differential evolution (DE) algorithm and the simplex method steadily converges to the exact solution. The second inverse problem deals with the detection and the classification of buried metallic objects using electromagnetic induction (EMI). Both the exciting and the induced magnetic fields are expanded as a linear combination of basic modes in the spheroidal coordinate system. Due to the orthogonality and the completeness of the spheroidal basic modes, the scattering coefficients are uniquely determined and are characteristics of the object.
(cont.) The scattering coefficients are retrieved from the knowledge of the induced fields, where both synthetic and measurement data are used. The ill-conditioning issue is dealt with by mode truncation and Tikhonov regularization technique. Stored in a library, the scattering coefficients can produce fast forward models for use in pattern matching. In addition, they can be used to train support vector machine (SVM) to sort objects into generic classes.
by Xudong Chen.
Ph.D.
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Alaca, Ayse Carleton University Dissertation Mathematics and Statistics. "An inverse eigenvalue problem". Ottawa, 1995.
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Medin, Ashley E. "The magnetotelluric inverse problem". Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2008. http://wwwlib.umi.com/cr/ucsd/fullcit?p3336606.
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Thesis (Ph. D.)--University of California, San Diego, 2008.Title from first page of PDF file (viewed January 5, 2009). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 202-208).
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Scho¨nfelder, Apollonia Maria Oktavia. "Inverse polarity prominence equilibria". Thesis, University of St Andrews, 1995. http://hdl.handle.net/10023/14243.
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It has been supposed since the middle of this century that it is the global magnetic field surrounding a quiescent prominence that provides the force to prevent its collapse due to the sun's gravitational field. Many theoretical models, assuming that the prominence plasma is supported in a dip in the magnetic field lines associated by the magnetic tension force, have since been put forward. The aim of this thesis is to propose further models of quiescent prominences to widen our understanding and knowledge of these remarkable features. A short overview over the magnetohydrodynamic equations used to describe solar prominences, or most of the solar phenomena for that matter, are discussed in chapter 2, and a short summary of prominence observations and attempts to model them is given in chapter 3. A brief description of the numerical code used in chapters 5 and 7 is given in chapter 4. Observations of Kim (1990) and Leroy (1985) have found that most large quiescent prominences are of inverse polarity type for which the magnetic field passes through the prominence in the opposite direction to that expected from the photospheric magnetic field. Many theoretical models have been proposed, but failed. Hence, in chapter 5 we investigate first – without the inclusion of a prominence sheet – when an inverse polarity magnetic field must have the correct topology for an inverse polarity configuration before the formation of the prominence itself. Only very recently, the first basic successful model of an I-type polarity prominence was proposed by Low (1993). In chapter 6 we examine this model and investigate current sheets more complicated and realistic than the one used by Low. These analytical models deal with the force-free solution, which is matched onto an external, unsheared, potential coronal magnetic field. These solutions are mathematically interesting and allow an investigation of different profiles of the current intensity of the magnetic field vector and of the mass density in the sheet. The prominence properties predicted by these models have been examined and have been found to match the observational values. The mathematics of current sheets in general is also briefly discussed. Chapter 7 deals with numerical solutions of inverse polarity prominences embedded in a force-free magnetic flux tube, matched onto an unsheared potential coronal field. Unfortunately the solutions gained are quite sensitive to the boundary conditions imposed on them through the numerical box, showing a loss of convergence and a tendency for the solution to blow up. Finally, a short summary as well as possible future work is given in chapter 8.
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Deolmi, Giulia. "Computational Parabolic Inverse Problems". Doctoral thesis, Università degli studi di Padova, 2012. http://hdl.handle.net/11577/3423351.
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This thesis presents a general approach to solve numerically parabolic Inverse Problems, whose underlying mathematical model is discretized using the Finite Element method. The proposed solution is based upon an adaptive parametrization and it is applied specically to a geometric conduction inverse problem of corrosion estimation and to a boundary convection inverse problem of pollution rate estimation.In questa tesi viene presentato un approccio numerico volto alla risoluzione di problemi inversi parabolici, basato sull'utilizzo di una parametrizzazione adattativa. L'algoritmo risolutivo viene descritto per due specici problemi: mentre il primo consiste nella stima della corrosione di una faccia incognita del dominio, il secondo ha come scopo la quanticazione di inquinante immesso in un fiume.
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Cao, Xinlin. "Geometric structures of eigenfunctions with applications to inverse scattering theory, and nonlocal inverse problems". HKBU Institutional Repository, 2020. https://repository.hkbu.edu.hk/etd_oa/754.
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Inverse problems are problems where causes for desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development, including radar/sonar, medical imaging, geophysical exploration, invisibility cloaking and remote sensing, to name just a few. In this thesis, we focus on the theoretical study and applications of some intriguing inverse problems. Precisely speaking, we are concerned with two typical kinds of problems in the field of wave scattering and nonlocal inverse problem, respectively. The first topic is on the geometric structures of eigenfunctions and their applications in wave scattering theory, in which the conductive transmission eigenfunctions and Laplacian eigenfunctions are considered. For the study on the intrinsic geometric structures of the conductive transmission eigenfunctions, we first present the vanishing properties of the eigenfunctions at corners both in R2 and R3, based on microlocal analysis with the help of a particular type of planar complex geometrical optics (CGO) solution. This significantly extends the previous study on the interior transmission eigenfunctions. Then, as a practical application of the obtained geometric results, we establish a unique recovery result for the inverse problem associated with the transverse electromagnetic scattering by a single far-field measurement in simultaneously determining a polygonal conductive obstacle and its surface conductive parameter. For the study on the geometric structures of Laplacian eigenfunctions, we separately discuss the two-dimensional case and the three-dimensional case. In R2, we introduce a new notion of generalized singular lines of Laplacian eigenfunctions, and carefully investigate these singular lines and the nodal lines. The studies reveal that the intersecting angle between two of those lines is closely related to the vanishing order of the eigenfunction at the intersecting point. We provide an accurate and comprehensive quantitative characterization of the relationship. In R3, we study the analytic behaviors of Laplacian eigenfunctions at places where nodal or generalized singular planes intersect, which is much more complicated. These theoretical findings are original and of significant interest in spectral theory. Moreover, they are applied directly to some physical problems of great importance, including the inverse obstacle scattering problem and the inverse diffraction grating problem. It is shown in a certain polygonal (polyhedral) setup that one can recover the support of the unknown scatterer as well as the surface impedance parameter by finitely many far-field patterns. Our second topic is concerning the fractional partial differential operators and some related nonlocal inverse problems. We present some prelimilary knowledge on fractional Sobolev Spaces and fractional partial differential operators first. Then we focus on the simultaneous recovery results of two interesting nonlocal inverse problems. One is simultaneously recovering potentials and the embedded obstacles for anisotropic fractional Schrödinger operators based on the strong uniqueness property and Runge approximation property. The other one is the nonlocal inverse problem associated with a fractional Helmholtz equation that arises from the study of viscoacoustics in geophysics and thermoviscous modelling of lossy media. We establish several general uniqueness results in simultaneously recovering both the medium parameter and the internal source by the corresponding exterior measurements. The main method utilized here is the low-frequency asymptotics combining with the variational argument. In sharp contrast, these unique determination results are unknown in the local case, which would be of significant importance in thermo- and photo-acoustic tomography.
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Debarnot, Valentin. "Microscopie computationnelle". Thesis, Toulouse 3, 2020. http://www.theses.fr/2020TOU30156.
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Les travaux présentés de cette thèse visent à proposer des outils numériques et théoriques pour la résolution de problèmes inverses en imagerie. Nous nous intéressons particulièrement au cas où l'opérateur d'observation (e.g. flou) n'est pas connu. Les résultats principaux de cette thèse s'articulent autour de l'estimation et l'identification de cet opérateur d'observation. Une approche plébiscitée pour estimer un opérateur de dégradation consiste à observer un échantillon contenant des sources ponctuelles (microbilles en microscopie, étoiles en astronomie). Une telle acquisition fournit une mesure de la réponse impulsionnelle de l'opérateur en plusieurs points du champ de vue. Le traitement de cette observation requiert des outils robustes pouvant utiliser rapidement les données rencontrées en pratique. Nous proposons une boîte à outils qui estime un opérateur de dégradation à partir d'une image contenant des sources ponctuelles. L'opérateur estimé à la propriété qu'en tout point du champ de vue, sa réponse impulsionnelle s'exprime comme une combinaison linéaire de fonctions élémentaires. Cela permet d'estimer des opérateurs invariants (convolutions) et variants (développement en convolution-produit) spatialement. Une spécificité importante de cette boîte à outils est son caractère automatique : seul un nombre réduit de paramètres facilement accessibles permettent de couvrir une grande majorité des cas pratiques. La taille de la source ponctuelle (e.g. bille), le fond et le bruit sont également pris en compte dans l'estimation. Cet outil se présente sous la forme d'un module appelé PSF-Estimator pour le logiciel Fiji, et repose sur une implémentation parallélisée en C++. En réalité, les opérateurs modélisant un système optique varient d'une expérience à une autre, ce qui, dans l'idéal, nécessite une calibration du système avant chaque acquisition. Pour pallier à cela, nous proposons de représenter un système optique non pas par un unique opérateur de dégradation, mais par un sous-espace d'opérateurs. Cet ensemble doit permettre de représenter chaque opérateur généré par un microscope. Nous introduisons une méthode d'estimation d'un tel sous-espace à partir d'une collection d'opérateurs de faible rang (comme ceux estimés par la boîte à outils PSF-Estimator). Nous montrons que sous des hypothèses raisonnables, ce sous-espace est de faible dimension et est constitué d'éléments de faible rang. Dans un second temps, nous appliquons ce procédé en microscopie sur de grands champs de vue et avec des opérateurs variant spatialement. Cette mise en œuvre est possible grâce à l'utilisation de méthodes complémentaires pour traiter des images réelles (e.g. le fond, le bruit, la discrétisation de l'observation). La construction d'un sous-espace d'opérateurs n'est qu'une étape dans l'étalonnage de systèmes optiques et la résolution de problèmes inverses. [...]The contributions of this thesis are numerical and theoretical tools for the resolution of blind inverse problems in imaging. We first focus in the case where the observation operator is unknown (e.g. microscopy, astronomy, photography). A very popular approach consists in estimating this operator from an image containing point sources (microbeads or fluorescent proteins in microscopy, stars in astronomy). Such an observation provides a measure of the impulse response of the degradation operator at several points in the field of view. Processing this observation requires robust tools that can rapidly use the data. We propose a toolbox that estimates a degradation operator from an image containing point sources. The estimated operator has the property that at any location in the field of view, its impulse response is expressed as a linear combination of elementary estimated functions. This makes it possible to estimate spatially invariant (convolution) and variant (product-convolution expansion) operators. An important specificity of this toolbox is its high level of automation: only a small number of easily accessible parameters allows to cover a large majority of practical cases. The size of the point source (e.g. bead), the background and the noise are also taken in consideration in the estimation. This tool, coined PSF-estimator, comes in the form of a module for the Fiji software, and is based on a parallelized implementation in C++. The operators generated by an optical system are usually changing for each experiment, which ideally requires a calibration of the system before each acquisition. To overcome this, we propose to represent an optical system not by a single operator (e.g. convolution blur with a fixed kernel for different experiments), but by subspace of operators. This set allows to represent all the possible states of a microscope. We introduce a method for estimating such a subspace from a collection of low rank operators (such as those estimated by the toolbox PSF-Estimator). We show that under reasonable assumptions, this subspace is low-dimensional and consists of low rank elements. In a second step, we apply this process in microscopy on large fields of view and with spatially varying operators. This implementation is possible thanks to the use of additional methods to process real images (e.g. background, noise, discretization of the observation).The construction of an operator subspace is only one step in the resolution of blind inverse problems. It is then necessary to identify the degradation operator in this set from a single observed image. In this thesis, we provide a mathematical framework to this operator identification problem in the case where the original image is constituted of point sources. Theoretical conditions arise from this work, allowing a better understanding of the conditions under which this problem can be solved. We illustrate how this formal study allows the resolution of a blind deblurring problem on a microscopy example.[...]
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Rabaiotti, Carlo. "Inverse analysis in road geotechnics /". Zürich : ETH, 2008. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=18135.
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Mas, Baixeras Albert. "Optimization of inverse reflector design". Doctoral thesis, Universitat de Girona, 2011. http://hdl.handle.net/10803/22705.
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Aquesta tesi presenta un nou mètode pel disseny invers de reflectors. Ens hem centrat en tres temes principals: l’ús de fonts de llum reals i complexes, la definició d’un algoritme ràpid pel càlcul de la il•luminació del reflector, i la definició d’un algoritme d’optimització per trobar més eficientment el reflector desitjat.
Les fonts de llum estan representades per models near-field, que es comprimeixen amb un error molt petit, fins i tot per fonts de llum amb milions de raigs i objectes a il•luminar molt propers. Llavors proposem un mètode ràpid per obtenir la distribució de la il•luminació d’un reflector i la seva comparació amb la il•luminació desitjada, i que treballa completament en la GPU. Finalment, proposem un nou mètode d’optimització global que permet trobar la solució en menys passos que molts altres mètodes d’optimització clàssics, i alhora evitant mínims locals.This thesis presents new methods for the inverse reflector design problem. We have focused on three main topics: the use of real and complex light sources, the definition of a fast lighting simulation algorithm to compute the reflector lighting, and the definition of an optimization algorithm to more efficiently find the desired reflector. The light sources are represented by near-field datasets, that are compressed with a low error, even with millions of rays and for very close objects. Then, we propose a fast method to obtain the outgoing light distribution of a reflector and the comparison with the desired one, working completely in the GPU. Finally, a new global optimization method is proposed to search the solution in less steps than most other classic optimization methods, also avoiding local minima.
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Baysal, Arzu. "Inverse Problems For Parabolic Equations". Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12605623/index.pdf.
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In this thesis, we study inverse problems of restoration of the unknown function in a boundary condition, where on the boundary of the domain there is a convective heat exchange with the environment. Besides the temperature of the domain, we seek either the temperature of the environment in Problem I and II, or the coefficient of external boundary heat emission in Problem III and IV. An additional information is given, which is the overdetermination condition, either on the boundary of the domain (in Problem III and IV) or on a time interval (in
Problem I and II). If solution of inverse problem exists, then the temperature can be defined everywhere on the domain at all instants.
The thesis consists of six chapters. In the first chapter, there is the introduction where the definition and applications of inverse problems are given and definition of the four inverse problems, that we will analyze in this thesis, are stated. In the second chapter, some definitions and theorems which we will use to obtain some conclusions about the corresponding direct problem of our four inverse problems are stated, and the conclusions about direct problem are obtained.
In the third, fourth, fifth and sixth chapters we have the analysis of inverse problems I, II, III and IV, respectively.
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Roland, Julien. "Inverse multi-objective combinatorial optimization". Doctoral thesis, Universite Libre de Bruxelles, 2013. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209383.
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The initial question addressed in this thesis is how to take into account the multi-objective aspect of decision problems in inverse optimization. The most straightforward extension consists of finding a minimal adjustment of the objective functions coefficients such that a given feasible solution becomes efficient. However, there is not only a single question raised by inverse multi-objective optimization, because there is usually not a single efficient solution. The way we define inverse multi-objectiveoptimization takes into account this important aspect. This gives rise to many questions which are identified by a precise notation that highlights a large collection of inverse problems that could be investigated. In this thesis, a selection of inverse problems are presented and solved. This selection is motivated by their possible applications and the interesting theoretical questions they can rise in practice.
Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished
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Medd, Adam Jon. "Inverse design of turbomachinery blades". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape17/PQDD_0010/MQ34391.pdf.
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Beane, Robbie Allen. "Inverse limits of permutation maps". Diss., Rolla, Mo. : Missouri University of Science and Technology, 2008. http://scholarsmine.mst.edu/thesis/pdf/Beane_09007dcc804f93c9.pdf.
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Thesis (Ph. D.)--Missouri University of Science and Technology, 2008.Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed May 9, 2008) Includes bibliographical references (p. 71-73).
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Li, Xi. "Focused inverse method for LF". Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=18796.
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Logical frameworks allow us to specify formal systems and prove properties about them. One interesting logical framework is Twelf, a language that uses higher order abstract syntax to encode object languages into the meta language. Currently, uniform proofs have been used for describing proof search in backwards logic programming style. However, there are certain limitations to a backward system, for example, loop-detection mechanisms are required for some of the simplest problems to yield a solution. As a consequence, the search for a more effective proof search algorithm prevails and a forward system is proposed. This thesis will discuss the theoretical foundations for a forward uniform sequent calculus and the implementation of an inverse method prover for Twelf.Les cadres logiques nous permettent de spécifier des systèmes formels et de prouver des propriétés à leur sujet. Un cadre logique intéressant est Twelf, un langage qui emploie la syntaxe abstraite d'ordre supérieur pour encoder des langages objet dans le méta-langage. Actuellement, nous employons des preuves uniformes pour décrire la recherche dans le style de programmation logique arrière. Cependant, il y a certaines limitations à un système arrière: des mécanismes de détection de boucle sont nécessaires pour trouver une solution à certains des problèmes les plus simples. Par conséquent, la recherche d'un algorithme plus efficace de recherche de preuve règne et un système vers l'avant est proposé. Cette thèse discutera les bases théoriques d'un calcul séquent uniforme vers l'avant et l'implantation d'un prouveur à méthode inverse pour Twelf.
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Murch, Ross David. "Inverse scattering and shape reconstruction". Thesis, University of Canterbury. Electrical and Electronic Engineering, 1990. http://hdl.handle.net/10092/5600.
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Investigations of new and improved solutions to inverse problems are considered. Three of the solutions are concerned with inverse scattering. The other two solutions deal with reconstructing binary images from few projections and determining the shape and orientation of a three-dimensional object from silhouettes. In addition, a review of solutions to direct and inverse scattering problems is presented.
An inverse scattering algorithm for reconstructing variable refractive index distributions is examined. The inversion algorithm is based on an expression for the wave function which explicitly incorporates the inverse scattering data. It is claimed that this considerably increases the efficiency of the algorithm. The algorithm is implemented in two-dimensional space and examples of reconstructions of objects from computer-generated scattering data are presented.
The problem of determining the shape of a two-dimensional impenetrable obstacle from a set of measurements of its far-field scattering amplitude is considered. The problem is formulated as a non-linear operator equation which is solved by an iterative method. The use of the null-field method to solve the direct problem leads to efficient evaluation of the Fréchet derivative of the non-linear operator. Computational implementations confirm the numerical accuracy of the algorithm.
An extension to the Rayleigh-Gans (Born) approximation is examined. The extension involves incorporating a high frequency approximation to the wave field into the conventional Rayleigh-Gans (Born) approximation. Numerical implementation of an algorithm based on this extension to the Rayleigh-Gans (Born) approximation indicates that its reconstruction accuracy is generally superior to that of the conventional Rayleigh-Gans (Born) approximation.
Efficient algorithms for reconstructing a binary cross-section (each of whose pixel amplitudes is either zero or unity) from few one-dimensional projections are introduced and illustrated by example. It is shown that only two projections are needed to reconstruct a convex cross-section. Non-convex cross-sections need more projections but far fewer than are necessary to reconstruct grey-scale images. When presented with noisy one-dimensional projections, the algorithms remain useful, although their performance improves with the number of given projections.
Determination of a three-dimensional object's shape and orientation from its silhouettes is studied, on the understanding that the relative orientations of the given silhouettes are unknown a priori. The result of this study is an algorithm which could be suitable for incorporation into a robot's vision system. The algorithm is based on a method for determining the orientation of an object from its two-dimensional projections. To overcome the reduced information content of silhouettes as compared with two-dimensional projections, a self consistency check is introduced. Numerical implementations of the algorithm confirm that it can generate usefully accurate estimates of the orientations and shapes of technologically non-trivial objects.
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Connolly, T. John. "Nonlinear methods for inverse problems". Thesis, University of Canterbury. Mathematics, 1989. http://hdl.handle.net/10092/8563.
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The general inverse problem is formulated as a nonlinear operator equation. The solution of this via the Newton-Kantorovich method is outlined. Fréchet differentiability of the operator is given by the implicit function theorem. We also consider questions such as uniqueness, stability and regularization of the inverse problem.
This general theory is then applied to a number of different inverse problems. The Newton-Kantorovich method is derived for each example and Fréchet differentiability examined. In some cases numerical results are provided, for others our work provides a theoretical basis for results obtained by different authors.
The problems considered include an interior measurement inverse problem from steady-state diffusion, and a boundary measurement problem for electrical conductivity imaging. We also examine the determination of refractive indices and scattering boundaries for the Helmholtz equation from measurements of the farfield. In addition an inverse problem from geometric optics is investigated.
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Stewart, K. A. "Inverse problems in signal processing". Thesis, University of Strathclyde, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382448.
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Neocleous, Pelagia. "Inverse methods for wire antennae". Thesis, King's College London (University of London), 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427821.
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Aljohani, Hassan Musallam S. "Wavelet methods and inverse problems". Thesis, University of Leeds, 2017. http://etheses.whiterose.ac.uk/18830/.
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Archaeological investigations are designed to acquire information without damaging the archaeological site. Magnetometry is one of the important techniques for producing a surface grid of readings, which can be used to infer underground features. The inversion of this data, to give a fitted model, is an inverse problem. This type of problem can be ill-posed or ill-conditioned, making the estimation of model parameters less stable or even impossible. More precisely, the relationship between archaeological data and parameters is expressed by a likelihood. It is not possible to use the standard regression estimate obtained through the likelihood, which means that no maximum likelihood estimate exists. Instead, various constraints can be added through a prior distribution with an estimate produced using the posterior distribution. Current approaches incorporate prior information describing smoothness, which is not always appropriate. The biggest challenge is that the reconstruction of an archaeological site as a single layer requires various physical features such as depth and extent to be assumed. By applying a smoothing prior in the analysis of stratigraphy data, however, these features are not easily estimated. Wavelet analysis has proved to be highly efficient at eliciting information from noisy data. Additionally, complicated signals can be explained by interpreting only a small number of wavelet coefficients. It is possible that a modelling approach, which attempts to describe an underlying function in terms of a multi-level wavelet representation will be an improvement on standard techniques. Further, a new method proposed uses an elastic-net based distribution as the prior. Two methods are used to solve the problem, one is based on one-stage estimation and the other is based on two stages. The one-stage considers two approaches a single prior for all wavelet resolution levels and a level-dependent prior, with separate priors at each resolution level. In a simulation study and a real data analysis, all these techniques are compared to several existing methods. It is shown that the methodology using a single prior provides good reconstruction, comparable even to several established wavelet methods that use mixture priors.
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Cavanaugh, Andrew F. "Inverse Synthetic Array Reconciliation Tomography". Digital WPI, 2013. https://digitalcommons.wpi.edu/etd-dissertations/278.
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This dissertation introduces Inverse Synthetic Array Reconciliation Tomography (ISART), an algorithm that exploits the short-time accuracy of inertial navigation systems (INS) and the time-stability of radio frequency (RF) positioning algorithms to achieve a high level of positioning accuracy. Novel array processing and data fusion techniques are employed to acheive performance far greater than RF and INS algorithms previously developed. This research is directed toward addressing the need for a viable tracking solution for firefighters and other first responders in urban and indoor environments. The approaches in this work are fundamentally different from other RF-INS fusion approaches, in the way we combine INS data with RF data. Rather than simply fusing the measurements from two systems that are estimating position (or states directly related to position) we use the inertial navigation data to improve the accuracy of our RF estimates at the signal level, before integrating them into an overall fusion system through the use of an extended Kalman filter (EKF). This work outlines the theoretical basis for ISART, and shows the results of simulations that support the claimed accuracy improvement of the ISART algorithm over existing methods. The viability of ISART in real world settings is then examined through the results of three field tests what were conducted in support of this research.
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Parker, Michael J. (Michael Joseph). "An inverse problem for networks". Thesis, Massachusetts Institute of Technology, 1990. http://hdl.handle.net/1721.1/85704.
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Marroquin, J. L. (Jose Luis). "Probabilistic solution of inverse problems". Thesis, Massachusetts Institute of Technology, 1985. http://hdl.handle.net/1721.1/15286.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1985.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING.
Bibliography: p. 195-200.
by Jose Luis Marroquin.
Ph.D.
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Agapiou, Sergios. "Aspects of Bayesian inverse problems". Thesis, University of Warwick, 2013. http://wrap.warwick.ac.uk/60138/.
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The goal of this thesis is to contribute to the formulation and understanding of the Bayesian approach to inverse problems in function space. To this end we examine two important aspects of this approach: the frequentist asymptotic properties of the posterior, and the extraction of information from the posterior via sampling. We work in a separable Hilbert space setting and consider Gaussian priors on the unknown in conjugate Gaussian models. In the first part of this work we consider linear inverse problems with Gaussian additive noise and study the contraction in the small noise limit of the Gaussian posterior distribution to a Dirac measure centered on the true parameter underlying the data. In a wide range of situations, which include both mildly and severely ill-posed problems, we show how carefully calibrating the scaling of the prior as a function of the size of the noise, based on a priori known information on the regularity of the truth, yields optimal rates of contraction. In the second part we study the implementation in RN of hierarchical Bayesian linear inverse problems with Gaussian noise and priors, and with hyper-parameters introduced through the scalings of the prior and noise covariance operators. We use function space intuition to understand the large N behaviour of algorithms designed to sample the posterior and show that the two scaling hyper-parameters evolve under these algorithms in contrasting ways: as N grows the prior scaling slows down while the noise scaling speeds up. We propose a reparametrization of the prior scaling which is robust with respect to the increase in dimension. Our theory on the slowing down of the evolution of the prior scaling extends to hierarchical approaches in more general conjugate Gaussian settings, while our intuition covers other parameters of the prior covariance operator as well. Throughout the thesis we use a blend of results from measure theory and probability theory with tools from the theory of linear partial differential equations and numerical analysis.
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Budhraja, Karan Kumar. "Neuroevolution Based Inverse Reinforcement Learning". Thesis, University of Maryland, Baltimore County, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10140581.
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Motivated by such learning in nature, the problem of Learning from Demonstration is targeted at learning to perform tasks based on observed examples. One of the approaches to Learning from Demonstration is Inverse Reinforcement Learning, in which actions are observed to infer rewards. This work combines a feature based state evaluation approach to Inverse Reinforcement Learning with neuroevolution, a paradigm for modifying neural networks based on their performance on a given task. Neural networks are used to learn from a demonstrated expert policy and are evolved to generate a policy similar to the demonstration. The algorithm is discussed and evaluated against competitive feature-based Inverse Reinforcement Learning approaches. At the cost of execution time, neural networks allow for non-linear combinations of features in state evaluations. These valuations may correspond to state value or state reward. This results in better correspondence to observed examples as opposed to using linear combinations. This work also extends existing work on Bayesian Non-Parametric Feature construction for Inverse Reinforcement Learning by using non-linear combinations of intermediate data to improve performance. The algorithm is observed to be specifically suitable for a linearly solvable non-deterministic Markov Decision Processes in which multiple rewards are sparsely scattered in state space. Performance of the algorithm is shown to be limited by parameters used, implying adjustable capability. A conclusive performance hierarchy between evaluated algorithms is constructed.
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Lian, Duan. "Bayesian methods for inverse problems". Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:b4000e98-7d56-4274-8210-a22b04be436c.
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This thesis describes two novel Bayesian methods: the Iterative Ensemble Square Filter (IEnSRF) and the Warp Ensemble Square Root Filter (WEnSRF) for solving the barcode detection problem, the deconvolution problem in well testing and the history matching problem of facies patterns. For the barcode detection problem, at the expanse of overestimating the posterior uncertainty, the IEnSRF efficiently achieves successful detections with very challenging real barcode images which the other considered methods and commercial software fail to detect. It also performs reliable detection on low-resolution images under poor ambient light conditions. For the deconvolution problem in well testing, the IEnSRF is capable of quantifying estimation uncertainty, incorporating the cumulative production data and estimating the initial pressure, which were thought to be unachievable in the existing well testing literature. The estimation results for the considered real benchmark data using the IEnSRF significantly outperform the existing methods in the commercial software. The WEnSRF is utilised for solving the history matching problem of facies patterns. Through the warping transformation, the WEnSRF performs adjustment on the reservoir features directly and is thus superior in estimating the large-scale complicated facies patterns. It is able to provide accurate estimates of the reservoir properties robustly and efficiently with reasonably reliable prior reservoir structural information.
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Sun, Luyang. "Inverse methods in cochlear mechanics". Thesis, University of Southampton, 2016. https://eprints.soton.ac.uk/413460/.
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Cochlear modelling is used to provide insight into the physical mechanics of the cochlea. The complicated, three dimensional geometry of the fluid chambers in the cochlea is often represented in models of its mechanics by a box with a uniform area along its length. The first part of this thesis is concerned with the development of a tapered box model of the cochlea, in which the geometry of the cochlea is assumed to vary in a linear way along its length. Previous measurements of the variation in area of the two fluid chambers along the length of the cochlea in various mammals has been used to calculate a linear fit to the variation in the "effective area" that determines the 1D fluid coupling. The width of the basilar membrane is also assumed to vary linearly along the length of the model. The analytic form of the 1D fluid pressure distribution due to elemental BM motion is derived for this tapered box model, together with the added mass due to near field acoustic coupling. The coupled response in the 1D and 3D, uniform and tapered box model of passive cochlea can then be readily calculated. Although the form of the fluid coupling are very different in the uniform and tapered box models, the distribution of the basilar membrane vibration in the coupled models are very similar. The second part of the thesis is concerned with deriving the parameters of cochlear models from measured data using inverse methods. Previous inverse methods are first reviewed before a novel direct method is introduced, based on modelling the poles and zeros of the micromechanical response. This is compared with other inverse methods, using previously measured data on basilar membrane vibration in the cochlea, and relatively simple models are shown to provide a good fit to the data.
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Finn-Sell, Martin. "Inverse semigroups in coarse geometry". Thesis, University of Southampton, 2013. https://eprints.soton.ac.uk/361324/.
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Inverse semigroups provide a natural way to encode combinatorial data from geometric settings. Examples of this occur in both geometry and topology, where the data comes in the form of partial bijections that preserve the topology, and operator algebras, where the partial bijections encode *-subsemigroups of partial isometries of Hilbert space. In this thesis we explore the connections between these two pictures within the backdrop of coarse geometry. The first collection of results is concerned primarily with inverse semigroups and their C*-algebras. We give a construction of a six term sequence of C*-algebras connecting the semigroup C*-algebra to that of a naturally associated group C*-algebra. This result is a generalisation of the ideas of Pimsner and Voiculescu, who were concerned with computing K-theory groups associated to actions of groups. We outline how to connect this picture, via groupoids, to that of a partial translation algebra of Brodzki, Niblo andWright, and further consider applications of these sequences to computations of certain K-groups associated with group and semigroup C*-algebras. Secondly, we give an account of the coarse Baum-Connes conjecture associated to a uniformly discrete bounded geometry metric space and rephrase the conjecture in terms of groupoids and their C*-algebras that can naturally be associated to a metric space. We then consider the well known counterexamples to this conjecture, giving a unifying framework for their study in terms of groupoids and a new conjecture for metric spaces that we call the boundary coarse Baum-Connes conjecture. Generalising a result of Willett and Yu we prove this conjecture for certain classes of expanders including those of large girth by constructing a partial action of a discrete group on such spaces.
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Li, Jing. "Inverse Problems in Structural Mechanics". Diss., Virginia Tech, 2005. http://hdl.handle.net/10919/30075.
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This dissertation deals with the solution of three inverse problems in structural mechanics. The first one is load updating for finite element models (FEMs). A least squares fitting is used to identify the load parameters. The basic studies are made for geometrically linear and nonlinear FEMs of beams or frames by using a four-noded curved beam element, which, for a given precision, may significantly solve the ill-posed problem by reducing the overall number of degrees of freedom (DOF) of the system, especially the number of the unknown variables to obtain an overdetermined system. For the basic studies, the unknown applied load within an element is represented by a linear combination of integrated Legendre polynomials, the coefficients of which are the parameters to be extracted using measured displacements or strains. The optimizer L-BFGS-B is used to solve the least squares problem.
The second problem is the placement optimization of a distributed sensing fiber optic sensor for a smart bed using Genetic Algorithms (GA), where the sensor performance is maximized. The sensing fiber optic cable is represented by a Non-uniform Rational B-Splines (NURBS) curve, which changes the placement of a set of infinite number of the infinitesimal sensors to the placement of a set of finite number of the control points. The sensor performance is simplified as the integration of the absolute curvature change of the fiber optic cable with respect to a perturbation due to the body movement of a patient. The smart bed is modeled as an elastic mattress core, which supports a fiber optic sensor cable. The initial and deformed geometries of the bed due to the body weight of the patient are calculated using MSC/NASTRAN for a given body pressure. The deformation of the fiber optic cable can be extracted from the deformation of the mattress. The performance of the fiber optic sensor for any given placement is further calculated for any given perturbation.
The third application is stiffened panel optimization, including the size and placement optimization for the blade stiffeners, subject to buckling and stress constraints. The present work uses NURBS for the panel and stiffener representation. The mesh for the panel is generated using DistMesh, a triangulation algorithm in MATLAB. A NASTRAN/MATLAB interface is developed to automatically transfer the data between the analysis and optimization processes respectively. The optimization consists of minimizing the weight of the stiffened panel with design variables being the thickness of the plate and height and width of the stiffener as well as the placement of the stiffeners subjected to buckling and stress constraints under in-plane normal/shear and out-plane pressure loading conditions.Ph. D.
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Wills, Andrew Johan. "Topics in Inverse Galois Theory". Thesis, Virginia Tech, 2011. http://hdl.handle.net/10919/32160.
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Galois theory, the study of the structure and symmetry of a polynomial or associated field extension, is a standard tool for showing the insolvability of a quintic equation by radicals. On the other hand, the Inverse Galois Problem, given a finite group G, find a finite extension of the rational field Q whose Galois group is G, is still an open problem. We give an introduction to the Inverse Galois Problem and compare some radically different approaches to finding an extension of Q that gives a desired Galois group. In particular, a proof of the Kronecker-Weber theorem, that any finite extension of Q with an abelian Galois group is contained in a cyclotomic extension, will be discussed using an approach relying on the study of ramified prime ideals. In contrast, a different method will be explored that defines rigid groups to be groups where a selection of conjugacy classes satisfies a series of specific properties. Under the right conditions, such a group is also guaranteed to be the Galois group of an extension of Q.Master of Science
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Bledsoe, Keith C. "Inverse Methods for Radiation Transport". The Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1259206496.
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Contensin, Magali. "Problème inverse d'éclairement en radiosité". Aix-Marseille 2, 2000. http://www.theses.fr/2000AIX22013.
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Rachele, Lizabeth. "An inverse problem in elastodynamics /". Thesis, Connect to this title online; UW restricted, 1996. http://hdl.handle.net/1773/5735.
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Flenner, Arjuna. "Lévy processes in inverse problems /". free to MU campus, to others for purchase, 2004. http://wwwlib.umi.com/cr/mo/fullcit?p3144416.
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Wokiyi, Dennis. "Non-linear inverse geothermal problems". Licentiate thesis, Linköpings universitet, Matematik och tillämpad matematik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-143031.
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The inverse geothermal problem consist of estimating the temperature distribution below the earth’s surface using temperature and heat-flux measurements on the earth’s surface. The problem is important since temperature governs a variety of the geological processes including formation of magmas, minerals, fosil fuels and also deformation of rocks. Mathematical this problem is formulated as a Cauchy problem for an non-linear elliptic equation and since the thermal properties of the rocks depend strongly on the temperature, the problem is non-linear. This problem is ill-posed in the sense that it does not satisfy atleast one of Hadamard’s definition of well-posedness. We formulated the problem as an ill-posed non-linear operator equation which is defined in terms of solving a well-posed boundary problem. We demonstrate existence of a unique solution to this well-posed problem and give stability estimates in appropriate function spaces. We show that the operator equation is well-defined in appropriate function spaces. Since the problem is ill-posed, regularization is needed to stabilize computations. We demostrate that Tikhonov regularization can be implemented efficiently for solving the operator equation. The algorithm is based on having a code for solving a well- posed problem related to the operator equation. In this study we demostrate that the algorithm works efficiently for 2D calculations but can also be modified to work for 3D calculations.