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## ‣ Codebook based broadband audio coder using wavelet transforms

Fonte: Universidade da Flórida
Publicador: Universidade da Flórida

Tipo: Artigo de Revista Científica
Formato: viii, 174 leaves : ill. ; 29 cm.

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#Signal processing -- Digital techniques ( lcsh )#Coding theory ( lcsh )#Wavelets (Mathematics) ( lcsh )#Electrical and Computer Engineering thesis, Ph. D#Dissertations, Academic -- Electrical And Computer Engineering

(Thesis) Thesis (Ph. D.)--University of Florida, 1996.; (Bibliography) Includes bibliographical references (leaves 168-173).; (Statement of Responsibility) by Kwang Rip Hyun.; Typescript.; Vita.

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## ‣ Listless zerotree image and video coding / Wen-Kuo Lin.

Fonte: Universidade de Adelaide
Publicador: Universidade de Adelaide

Tipo: Tese de Doutorado
Formato: 80470 bytes; application/pdf

Publicado em //2001
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Thesis (Ph.D.)--University of Adelaide, Dept. of Electrical and Electronic Engineering, 2002; Includes bibliographical references (leaves 199-214); xxx, 214 leaves : ill. (some col.), plates (col.) ; 30 cm.; Title page, contents and abstract only. The complete thesis in print form is available from the University Library.

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## ‣ Wavelet based image texture segementation using a modified K-means algorithm / by Brian W. Ng.

Fonte: Universidade de Adelaide
Publicador: Universidade de Adelaide

Tipo: Tese de Doutorado
Formato: 122395 bytes; application/pdf

Publicado em //2003
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In this thesis, wavelet transforms are chosen as the primary analytical tool for texture analysis. Specifically, Dual-Tree Complex Wavelet Transform is applied to the texture segmentation problem. Several possibilities for feature extraction and clustering steps are examined, new schemes being introduced and compared to known techniques.; Thesis (Ph.D.)--University of Adelaide, Dept. of Electrical and Electronic Engineering, 2003; "August, 2003"; Bibliography: p. 261-268.; xxvi, 268 p. : ill. (some col.) ; 30 cm.; Title page, contents and abstract only. The complete thesis in print form is available from the University Library.

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## ‣ Essays on the arbitrage pricing theory and wavelet analysis

Fonte: Instituto Universitário Europeu
Publicador: Instituto Universitário Europeu

Tipo: Tese de Doutorado
Formato: Paper

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Defence date: 13 July 1998; Examining board: Prof. Anindya Banerjee, Oxford University ; Prof. Søren Johansen, EUI ; Prof. Grayham Mizon, EUI, Supervisor ; Prof. Klaus Sandmann, University of Mainz

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## ‣ Theory and applications of the shift-invariant, time-varying and undecimated wavelet transforms

Fonte: Universidade Rice
Publicador: Universidade Rice

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In this thesis, we generalize the classical discrete wavelet transform, and construct wavelet transforms that are shift-invariant, time-varying, undecimated, and signal dependent. The result is a set of powerful and efficient algorithms suitable for a wide variety of signal processing tasks, e.g., data compression, signal analysis, noise reduction, statistical estimation, and detection. These algorithms are comparable and often superior to traditional methods. In this sense, we put wavelets in action.

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## ‣ Introduction to real orthogonal polynomials

Fonte: Monterey, California. Naval Postgraduate School
Publicador: Monterey, California. Naval Postgraduate School

Tipo: Tese de Doutorado

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The fundamental concept of orthogonality of mathematical objects occurs in a wide variety of physical and engineering disciplines. The theory of orthogonal functions, for example, is central to the development of Fourier series and wavelets, essential for signal processing. In particular, various families of classical orthogonal polynomials have traditionally been applied to fields such as electrostatics, numerical analysis, and many others. This thesis develops the main ideas necessary for understanding the classical theory of orthogonal polynomials. Special emphasis is given to the Jacobi polynomials and to certain important subclasses and generalizations, some recently discovered. Using the theory of hypergeometric power series and their q -extensions, various structural properties and relations between these classes are systematically investigated. Recently, these classes have found significant applications in coding theory and the study of angular momentum, and hold much promise for future applications. orthogonal polynomials, hypergeometric series

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## ‣ Inverse problems in image processing

Fonte: Universidade Rice
Publicador: Universidade Rice

Tipo: Thesis; Text
Formato: 135 p.; application/pdf

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Inverse problems involve estimating parameters or data from inadequate observations; the observations are often noisy and contain incomplete information about the target parameter or data due to physical limitations of the measurement devices. Consequently, solutions to inverse problems are non-unique. To pin down a solution, we must exploit the underlying structure of the desired solution set. In this thesis, we formulate novel solutions to three image processing inverse problems: deconvolution, inverse halftoning, and JPEG compression history estimation for color images.
Deconvolution aims to extract crisp images from blurry observations. We propose an efficient, hybrid Fourier-Wavelet Regularized Deconvolution (ForWaRD) algorithm that comprises blurring operator inversion followed by noise attenuation via scalar shrinkage in both the Fourier and wavelet domains. The Fourier shrinkage exploits the structure of the colored noise inherent in deconvolution, while the wavelet shrinkage exploits the piecewise smooth structure of real-world signals and images. ForWaRD yields state-of-the-art mean-squared-error (MSE) performance in practice. Further, for certain problems, ForWaRD guarantees an optimal rate of MSE decay with increasing resolution.
Halftoning is a technique used to render gray-scale images using only black or white dots. Inverse halftoning aims to recover the shades of gray from the binary image and is vital to process scanned images. Using a linear approximation model for halftoning...

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## ‣ Caracterización dinámica de señales electromiográficas usando filtros adaptativos

Fonte: Universidad Tecnológica de Pereira; Facultad de Ciencias Básicas
Publicador: Universidad Tecnológica de Pereira; Facultad de Ciencias Básicas

Tipo: Artigo de Revista Científica
Formato: PDF

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Se presentan esquemas de caracterización dinámica aplicados sobre señales electromiográficas utilizando una estructura de bancos de filtros con variación de parámetros adaptativos. Los bancos de filtros son calculados a partir de
esquemas de actualización. Los criterios de adaptabilidad utilizados para la caracterización dinámica son momentos estadísticos y vector gradiente. Para la selección de características se utiliza el módulo máximo. Los resultados de
clasificación con los métodos adaptativos son superiores en un 9 % a los resultados obtenidos con bancos de filtros de parámetros fijos. Se utiliza para la clasificación un clasificador bayesiano con la distancia de Mahalanobis.

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## ‣ Intrinsic Localization of Anisotropic Frames II: $\alpha$-Molecules

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 06/03/2014
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This article is a continuation of the recent paper [Grohs, Intrinsic
localization of anisotropic frames, ACHA, 2013], where off-diagonal-decay
properties (often referred to as 'localization' in the literature) of
Moore-Penrose pseudoinverses of (bi-infinite) matrices are established,
whenever the latter possess similar off-diagonal-decay properties. This problem
is especially interesting if the matrix arises as a discretization of an
operator with respect to a frame or basis. Previous work on this problem has
been restricted to wavelet- or Gabor frames. In the previous work we extended
these results to frames of parabolic molecules, including curvelets or
shearlets as special cases. The present paper extends and unifies these results
by establishing analogous properties for frames of $\alpha$-molecules as
introduced in recent work [Grohs, Keiper, Kutyniok, Sch\"afer, Alpha molecules:
curvelets, shearlets, ridgelets, and beyond, Proc. SPIE. 8858, 2013]. Since
wavelets, curvelets, shearlets, ridgelets and hybrid shearlets all constitute
instances of $\alpha$-molecules, our results establish localization properties
for all these systems simultaneously.; Comment: 16 pages

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## ‣ Uniform convergence of compactly supported wavelet expansions of Gaussian random processes

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/08/2013
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New results on uniform convergence in probability for expansions of Gaussian
random processes using compactly supported wavelets are given. The main result
is valid for general classes of nonstationary processes. An application of the
obtained results to stationary processes is also presented. It is shown that
the convergence rate of the expansions is exponential.; Comment: This is an Author's Accepted Manuscript of an article published in
the Communications in Statistics - Theory and Methods. 15 pages

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## ‣ Quantization of the sphere with coherent states

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 24/02/2003
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Quantization with coherent states allows to " quantize " any space X of
parameters. In the case where X is a phase space, this leads to the usual
quantum mechanics. But the procedure is much more general, and does not require
a symplectic, or any kind of structure in X, other than a measure. It is simply
considered as a different way to look at the system, the choice of a
resolution, in analogy with data handling, where coherent states (e.g., under
the form of wavelets) are very efficient.
Here, we present the complex coherent states quantization of the 2-sphere,
with emphasis on the links with group representation. We show how this
procedure leads naturally to the fuzzy sphere and to non commutative geometry.; Comment: 9 pages, no figure. Int. J. Theor. Phys. 2003, in press

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## ‣ Regularity of Non-Stationary Multivariate Subdivision

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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In this paper, we study scalar multivariate non-stationary subdivision
schemes with integer dilation matrix M=mI, m >=2, and present a general
approach for checking their convergence and for determining their H\"older
regularity. The combination of the concepts of asymptotic similarity and
approximate sum rules allows us to link stationary and non-stationary settings
and to employ recent advances in methods for exact computation of the joint
spectral radius. As an application, we prove a recent conjecture on the
H\"older regularity of the generalized Daubechies wavelets. We illustrate our
results with several examples.

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## ‣ Quantum Channels, Wavelets, Dilations and Representations of $O_n$

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/09/2003
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We show that the representations of the Cuntz C$^\ast$-algebras $O_n$ which
arise in wavelet analysis and dilation theory can be classified through a
simple analysis of completely positive maps on finite-dimensional space. Based
on this analysis, an application in quantum information theory is obtained;
namely, a structure theorem for the fixed point set of a unital quantum
channel. We also include some open problems motivated by this work.; Comment: 15 pages, preprint version

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## ‣ Shannon-Like Wavelet Frames on a Class of Nilpotent Lie Groups

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We prove and construct Shannon-like Parseval wavelet frames for a class of
two step connected, and simply connected nilpotent Lie groups, using a mixture
of representation theory, group Fourier theory, and Gabor theory. Moreover, we
are able to compute an upperbound for the norm of these Parseval frame
wavelets.

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## ‣ Vessel Segmentation in Medical Imaging Using a Tight-Frame Based Algorithm

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/08/2011
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Tight-frame, a generalization of orthogonal wavelets, has been used
successfully in various problems in image processing, including inpainting,
impulse noise removal, super-resolution image restoration, etc. Segmentation is
the process of identifying object outlines within images. There are quite a few
efficient algorithms for segmentation that depend on the variational approach
and the partial differential equation (PDE) modeling.
In this paper, we propose to apply the tight-frame approach to automatically
identify tube-like structures such as blood vessels in Magnetic Resonance
Angiography (MRA) images. Our method iteratively refines a region that encloses
the possible boundary or surface of the vessels. In each iteration, we apply
the tight-frame algorithm to denoise and smooth the possible boundary and
sharpen the region. We prove the convergence of our algorithm. Numerical
experiments on real 2D/3D MRA images demonstrate that our method is very
efficient with convergence usually within a few iterations, and it outperforms
existing PDE and variational methods as it can extract more tubular objects and
fine details in the images.

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## ‣ Fractional Brownian fields, duality, and martingales

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/12/2006
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In this paper the whole family of fractional Brownian motions is constructed
as a single Gaussian field indexed by time and the Hurst index simultaneously.
The field has a simple covariance structure and it is related to two
generalizations of fractional Brownian motion known as multifractional Brownian
motions. A mistake common to the existing literature regarding multifractional
Brownian motions is pointed out and corrected. The Gaussian field, due to
inherited ``duality'', reveals a new way of constructing martingales associated
with the odd and even part of a fractional Brownian motion and therefore of the
fractional Brownian motion. The existence of those martingales and their
stochastic representations is the first step to the study of natural wavelet
expansions associated to those processes in the spirit of our earlier work on a
construction of natural wavelets associated to Gaussian-Markov processes.; Comment: Published at http://dx.doi.org/10.1214/074921706000000770 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org)

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## ‣ A Note on Spherical Needlets

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/08/2015
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Compared with the traditional spherical harmonics, the spherical needlets are
a new generation of spherical wavelets that possess several attractive
properties. Their double localization in both spatial and frequency domains
empowers them to easily and sparsely represent functions with small spatial
scale features. This paper is divided into two parts. First, it reviews the
spherical harmonics and discusses their limitations in representing functions
with small spatial scale features. To overcome the limitations, it introduces
the spherical needlets and their attractive properties. In the second part of
the paper, a Matlab package for the spherical needlets is presented. The
properties of the spherical needlets are demonstrated by several examples using
the package.; Comment: 12 pages, 7 figures, technical report

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## ‣ Compressed Sensing and Reconstruction of Unstructured Mesh Datasets

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/08/2015
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#Computer Science - Information Theory#Computer Science - Distributed, Parallel, and Cluster Computing#Computer Science - Systems and Control#Mathematics - Optimization and Control

Exascale computing promises quantities of data too large to efficiently store
and transfer across networks in order to be able to analyze and visualize the
results. We investigate Compressive Sensing (CS) as a way to reduce the size of
the data as it is being stored. CS works by sampling the data on the
computational cluster within an alternative function space such as wavelet
bases, and then reconstructing back to the original space on visualization
platforms. While much work has gone into exploring CS on structured data sets,
such as image data, we investigate its usefulness for point clouds such as
unstructured mesh datasets found in many finite element simulations. We sample
using second generation wavelets (SGW) and reconstruct using the Stagewise
Orthogonal Matching Pursuit (StOMP) algorithm. We analyze the compression
ratios achievable and quality of reconstructed results at each compression
rate. We are able to achieve compression ratios between 10 and 30 on moderate
size datasets with minimal visual deterioration as a result of the lossy
compression.; Comment: 18 pages, 7 figures

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## ‣ Coorbit spaces with voice in a Fr\'echet space

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 17/02/2014
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We set up a new general coorbit space theory for reproducing representations
of a locally compact second countable group $G$ that are not necessarily
irreducible nor integrable. Our basic assumption is that the kernel associated
with the voice transform belongs to a Fr\'echet space $\mathcal T$ of functions
on $G$, which generalizes the classical choice $\mathcal T=L_w^1(G)$. Our basic
example is $ \mathcal T=\bigcap_{p\in(1,+\infty)} L^p(G)$, or a weighted
versions of it. By means of this choice it is possible to treat, for instance,
Paley-Wiener spaces and coorbit spaces related to Shannon wavelets and
Schr\"odingerlets.; Comment: 52 pages, 1 figures

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## ‣ Differentiation by integration using orthogonal polynomials, a survey

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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This survey paper discusses the history of approximation formulas for n-th
order derivatives by integrals involving orthogonal polynomials. There is a
large but rather disconnected corpus of literature on such formulas. We give
some results in greater generality than in the literature. Notably we unify the
continuous and discrete case. We make many side remarks, for instance on
wavelets, Mantica's Fourier-Bessel functions and Greville's minimum R_alpha
formulas in connection with discrete smoothing.; Comment: 35 pages, 3 figures; minor corrections, subsection 3.11 added;
accepted by J. Approx. Theory

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