The aim of this thesis is to implement flexible interpolators and decimators onField Programmable Gate Array (FPGA). Interpolators and decimators of differentwordlengths (WL) are implemented in VHDL. The Farrow structure is usedfor the realization of the polyphase components of the interpolation/decimationfilters. A fixed set of subfilters and adjustable fractional-delay multiplier valuesof the Farrow structure give different linear-phase finite-length impulse response(FIR) lowpass filters. An FIR filter is designed in such a way that it can be implementedfor different wordlengths (8-bit, 12-bit, 16-bit). Fixed-point representationis used for representing the fractional-delay multiplier values in the Farrow structure. To perform the fixed-point operations in VHDL, a package called fixed pointpackage [1] is used. A 8-bit, 12-bit, and 16-bit interpolator are implemented and their performancesare verified. The designs are compiled in Quartus-II CAD tool for timing analysisand for logical registers usage. The designs are synthesised by selecting Cyclone IVGX family and EP4X30CF23C6 device. The wordlength issues while implementingthe interpolators and decimators are discussed. Truncation of bits is required inorder to reduce the output wordlength of the interpolator and decimator.

L'arrivée massive d'écrans LCD dits de haute-définition sur le marché, entraîne un besoin acru d'algorithmes d'augmentation de résolution pour l'affichage d'images ou de vidéos dont la résolution est inférieure à celle de l'écran. Nous proposons un schéma novateur d'interpolation d'images, basée sur une analyse multirésolution de la direction des contours. Le but de cette approche est de corriger les artefacts classiques d'interpolation qui apparaissent lorsque des méthodes habituelles sont utilisées (bilinéaire, bicubique), tout en évitant l'apparition des artefacts engendrés par la plupart des méthodes d'interpolation directionnelle. Notre estimation d'orientation de contours, basée sur une division de l'image originale en quadtree et une étude fréquentielle des contours est comparée à deux méthodes faisant référence dans l'état de l'art (transformée de Radon et algorithme de projection utilisé pour la création des bandelettes). Cette comparaison permet d'étudier les comportements de chaque méthode en vue d'une application à des images naturelles. Par la suite, l'interpolation en elle-même est introduite. Elle est basée sur l'utilisation d'un noyau d'interpolation isotrope (cubic-spline), qui est corrigée grâce à un filtrage Gaussien localement orienté dans la direction des contours. Les régions ne contenant pas de contour sont préservées grâce à la création d'un masque construit à partir de filtres de Gabor. Enfin, les résultats de notre interpolation sont comparés à des méthodes d'interpolation directionnelle récentes, afin d'illustrer les bonnes performances de notre algorithme sur des images naturelles de natures variées. / The recent success of high definition screens has increased the need of interpolation algorithms, to display images or videos which resolution is smaller than the screen resolution. We propose a new image interpolation process, based on a multiresolution edge orientation analysis. The goal of this technique is to correct usual artifacts that appear on edges when classical interpolation methods are used (bilinear, bicubic), without introducing new artifacts that are often produced by directional interpolations. Our orientation estimation, based on a quadtree division and a multiresolution approach is evaluated and compared to two other state-of-the-art methods (Radon transform, and the projection method used in the Bandlet transform algorithm), to study its advantages in the context of an application to natural images. Then, we introduce our interpolation technique, based on an isotropic reference interpolation (cubic-spline) that is corrected by a two-dimension Gaussian filter, locally oriented in the direction of the edge. Edge-free regions are preserved with a Gabor mask that is built to protect pixels which do not need any correction. Finally, our results are compared to recent state-of-the-art directional interpolations to illustrate the good performance of our algorithm on various contents of natural images.

published_or_final_version / Mathematics / Master / Master of Philosophy

Small cells are low-powered radio access nodes that operate in licensed and unlicensed spectrum that have a range of 10 meters to 200 meters, compared to a mobile macrocell which might have a range of a few kilometres. This dissertation proposes algorithms for the enhancement of small cells installed in high speed rails. The thesis addresses two main points: the link between the small cell and the base station, and the link between the end-users and the small cell. The channel between the small cell and the base station is a fast fading channel due to the mobility of the high speed rail. The first part of the thesis proposes methods to enhance the link between the small cell and the base station using Low-Density Parity-Check codes (LDPC) for fast fading channels. The proposed uses nonuniform reconstruction methods based on the soft output log-likelihood ratio (LLR) provided by the LDPC decoder. The LLRs provide information about the location of the symbols with high probability of being correct. The grid formed under the assumption of a correlated Rayleigh channel affecting the transmitted data is highly nonuniform. Reconstruction of the channel under such assumptions is highly unstable. A signal-to-noise- ratio dependent regularization method is implemented to enhance the performance under imperfect Doppler spread estimation. The second part of the thesis proposes algorithms for the link between the end-user and the small cell. Since power efficiency is a major factor for end-users employing battery powered devices, we propose a Linear Programming (LP) algorithm for signal shaping to minimize the average transmitted power. The other problem the thesis addresses is the minimization of Peak-to-Average Power-Ratio (PAPR) of Orthogonal Frequency Division Multiplexing (OFDM) signals. The PAPR is minimized using a set of phase shifts for the constituting subcarriers of the OFDM signal. The set of phase shifts is determined using a LP approach that minimizes the complexity when the block length is high. A real-time implementation of some of the algorithms is carried out using the TMS320C6713 Texas Instruments board. The results for fixed-point versus floating-point implementation is shown for a different number of precision bits. / Thesis (Ph.D, Electrical & Computer Engineering) -- Queen's University, 2013-04-27 16:54:32.464

Wong Man-Lung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 99-103). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgments --- p.iii / List of Figures --- p.viii / List of Tables --- p.ix / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.2 --- Objectives --- p.5 / Chapter 2 --- Cartesian Representation of Membership Function --- p.7 / Chapter 2.1 --- The Cartesian Representation --- p.8 / Chapter 2.2 --- Region of Well-defined Membership Functions --- p.10 / Chapter 2.3 --- Similarity Triangle Interpolation Method --- p.12 / Chapter 2.4 --- The Interpolation Example --- p.18 / Chapter 2.5 --- Further Issues --- p.23 / Chapter 2.6 --- Conclusions --- p.24 / Chapter 3 --- Membership Function as Elements in Function Space --- p.26 / Chapter 3.1 --- L2[0，2] Representation --- p.27 / Chapter 3.2 --- "The Inner Product Space of L2[0,2]" --- p.31 / Chapter 3.3 --- The Similarity Triangle Interpolation Method --- p.32 / Chapter 3.4 --- The Interpolation Example --- p.36 / Chapter 3.5 --- Conclusions --- p.48 / Chapter 4 --- Radius of Influence of Membership Functions --- p.50 / Chapter 4.1 --- Previous Works on Mountain Method --- p.51 / Chapter 4.2 --- Combining Mountain Method and Cartesian Representation --- p.56 / Chapter 4.3 --- Extensibility Function and Weighted-Sum-Averaging Equation --- p.61 / Chapter 4.4 --- Radius of Influence --- p.62 / Chapter 4.5 --- Combining Radius of Influence and Fuzzy Interpolation Technique --- p.64 / Chapter 4.6 --- Model Identification Example --- p.66 / Chapter 4.7 --- Eliminative Extraction --- p.67 / Chapter 4.8 --- Eliminative Extraction Example --- p.70 / Chapter 4.9 --- Conclusions --- p.71 / Chapter 5 --- Fuzzy Inferencing --- p.73 / Chapter 5.1 --- Fuzzy Inferencing and Interpolation in Cartesian Representation --- p.74 / Chapter 5.2 --- Sparse Rule Extraction via Radius of Influence and Elimination --- p.77 / Chapter 5.3 --- Single Input and Single Output Case --- p.78 / Chapter 5.4 --- Multiple Input and Single Output Case --- p.81 / Chapter 5.5 --- Application --- p.89 / Chapter 5.6 --- Conclusions --- p.94 / Chapter 6 --- Conclusions --- p.96 / Appendix --- p.99 / Bibliography --- p.99

Chan, Chi Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 123-125). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

EBI and iEBI mechanism have all the desirable properties of a good interpolation: all given input-output examples are satisfied exactly, and the interpolation is smooth with minimum oscillations between the examples. / Example-Based Interpolation (EBI) is a powerful method to interpolate function from a set of input-output examples. The first part of the dissertation exams the EBI in detail and proposes a new enhanced EBI, indexed function Example-Based Interpolation (iEBI). The second part demonstrates the application of both EBI and iEBI to solve three well-defined problems of computer vision. / First, the dissertation has analyzed EBI solution in detail. It argues and demonstrates that there are three desired properties for any EBI solution. To satisfy all three desirable properties, the EBI solution must have adequate degrees of freedom. This dissertation shows in details that, for the EBI solution to have enough degrees of freedom, it needs only be in a simple format: the sum of a basis function plus a linear function. This dissertation also presents that a particular EBI solution, in a certain least-squares-error sense, could satisfy exactly all the three desirable properties. / Moreover, this dissertation also points out EBI's restriction and describes a new interpolation mechanism that could overcome EBI's restriction by constructing general indexed function from examples. The new mechanism, referred to as the general indexed function Example-Based Interpolation (iEBI) mechanism, first applies EBI to establish the initial correspondences over all input examples, and then interpolates the general indexed function from those initial correspondences. / Novel View Synthesis (NVS) is an important problem in image rendering. It tries to synthesize an image of a scene at any specified (novel) viewpoint using only a few images of that scene at some sample viewpoints. To avoid explicit 3-D reconstruction of the scene, this dissertation formulates the problem of NVS as an indexed function interpolation problem by treating viewpoint and image as the input and output of a function. The interpolation formulation has at least two advantages. First, it allows certain imaging details like camera intrinsic parameters to be unknown. Second, the viewpoint specification need not be physical. For example, the specification could consist of any set of values that adequately describe the viewpoint space and need not be measured in metric units. This dissertation solves the NVS problem using the iEBI formulation and presents how the iEBI mechanism could be used to synthesize images at novel viewpoints and acquire quality novel views even from only a few example views. / Stereo matching, or the determination of corresponding image points projected by the same 3-D feature, is one of the fundamental and long-studied problems in computer vision. Yet, few have tried to solve it using interpolation. This dissertation presents an interpolation approach, Interpolation-based Iterative Stereo Matching (IISM), that could construct dense correspondences in stereo image from sparse initial correspondences. IISM improves the existing EBI to ensure that the established correspondences satisfy exactly the epipolar constraint of the image pair, and to a certain extent, preserve discontinuities in the stereo disparity space of the imaged scene. IISM utilizes the refinement technique of coarse-to-fine to iteratively apply the improved EBI algorithm, and eventually, produces the dense disparity map for stereo image pair. / The second part of the dissertation focuses on applying the EBI and iEBI methods to solve three correspondence-based problems in computer vision: (1) stereo matching, (2) novel view synthesis, and (3) viewpoint determination. / This dissertation also illustrates, for all the three problems, experimental results on a number of real and benchmarking image datasets, and shows that interpolation-based methods could be effective in arriving at good solution even with sparse input examples. / Viewpoint determination of image is the problem of, given an image, determining the viewpoint from which the image was taken. This dissertation demonstrates to solve this problem without referencing to or estimating any explicit 3-D structure of the imaged scene. Used for reference are a small number of sample snapshots of the scene, each of which has the associated viewpoint. By treating image and its associated viewpoint as the input and output of a function, and the given snapshot-viewpoint pairs as examples of that function, the problem has a natural formulation of interpolation. Same as that in NVS, the interpolation formulation allows the given images to be uncalibrated and the viewpoint specification to be not necessarily measured. This dissertation presents an interpolation-based solution using iEBI mechanism that guarantees all given sample data are satisfied exactly with the least complexity in the interpolated function. / Liang Bodong. / "February 2006." / Adviser: Ronald Chi-kit Chung. / Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6516. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (p. 127-145). / 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. / Abstracts in English and Chinese. / School code: 1307.

Logistic and economic constraints often dictate the spatial sampling of a seismic survey. The process of acquisition records a finite number of spatial samples of the continuous wave field. The latter leads to a regular or irregular distribution of seismograms. Seismic reconstruction methods are used to recover non-acquired data and to synthesize a dense distribution of sources and receivers that mimics a properly sampled survey. This dissertation examines the seismic sampling problem and proposes algorithms for efficient multidimensional seismic data reconstruction. In particular, I address the problem of reconstructing irregularly sampled data using multidimensional linear prediction filters. The methodology entails a strategy that consists of two steps. First, the unaliased part of the wave field is reconstructed via Fourier reconstruction (Minimum Weighted Norm Interpolation). Then, prediction filters for all the frequencies are extracted from the reconstructed low frequencies. The latter permits the the recovery of aliased data with Multi-Step Auto-Regressive (MSAR) algorithm. The recovered prediction filters are used to reconstruct the complete data in either the f-x domain (MSAR-X) or the f-k domain (MSAR-K). The thesis also presents the use of Exponentially Weighted Recursive Least Squares (EWRLS) to estimate adaptive prediction filters for f-x seismic interpolation. Adaptive prediction filters are able to model signals where the dominant wavenumbers are varying in space. This concept leads to a f-x interpolation method that does not require windowing strategies for optimal results. In other words, adaptive prediction filters can be used to interpolate waveforms with spatially variant dips. / Geophysics

The classical interpolation theorem for the open complex unit disk, due to Nevanlinna and Pick in the early 20th century, gives an elegant criterion for the solvability of the problem as an eigenvalue problem. In the 1960s, Sarason reformulated problems of this type firmly in the language of operator theoretic function theory. This thesis will explore connections between interpolation problems on various domains (both single and several complex variables) with the viewpoint that Sarason’s work suggests. In Chapter 1, some essential preliminaries on bounded operators on Hilbert space and the functionals that act on them will be presented, with an eye on the various ways distances can be computed between operators and a certain type of ideal. The various topologies one may define on B(H) will play a prominent role in this development. Chapter 2 will introduce the concept of a reproducing kernel Hilbert space, and a distinguished operator algebra that we associate to such spaces know as the multiplier algebra. The various operator theoretic properties that multiplier algebras enjoy will be presented, with a particular emphasis on their invariant subspace lattices and the connection to distance formulae. In Chapter 3, the Nevanlinna-Pick problem will be invested in general for any repro- ducing kernel Hilbert space, with the basic heuristic for distance formulae being presented. Chapter 4 will treat a large class of reproducing kernel Hilbert spaces associated to measure spaces, where a Pick-like theorem will be established for many members of this class. This approach will closely follow similar results in the literature, including recent treatments by McCullough and Cole-Lewis-Wermer. Reproducing kernel Hilbert spaces where the analogue of the Nevanlinna-Pick theorem holds are particularly nice. In Chapter 5, the operator theory of these so-called complete Pick spaces will be developed, and used to tackle certain interpolation problems where additional constraints are imposed on the solution. A non-commutative view of interpola- tion will be presented, with the non-commutative analytic Toeplitz algebra of Popescu and Davidson-Pitts playing a prominent role. It is often useful to consider reproducing kernel Hilbert spaces which arise as natural products of other spaces. The Hardy space of the polydisk is the prime example of this. A general commutative and non-commutative view of such spaces will be presented in Chapter 6, using the left regular representation of higher-rank graphs, first introduced by Kribs-Power. A recent factorization theorem of Bercovici will be applied to these algebras, from which a Pick-type theorem may be deduced. The operator-valued Pick problem for these spaces will also be discussed. In Chapter 7, the various tools developed in this thesis will be applied to two related problems, known as the Douglas problem and the Toeplitz corona problem.

Thesis Ph. D.--Applied mathematics--Åbo akademi, 2005. / Bibliogr. p. 95-99.