This paper presents a study on wavelets and their characteristics for the specific purpose of serving as a feature extraction tool for speaker verification (SV), considering a Radial Basis Function (RBF) classifier, which is a particular type of Artificial Neural Network (ANN). Examining characteristics such as support-size, frequency and phase responses, amongst others, we show how Discrete Wavelet Transforms (DWTs), particularly the ones which derive from Finite Impulse Response (FIR) filters, can be used to extract important features from a speech signal which are useful for SV. Lastly, an SV algorithm based on the concepts presented is described.; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); FAPESP Sao Paulo Research Foundation[2005/00015-1]

A área que trata de compressão de imagem com perdas é, atualmente, de grande importância. Isso se deve ao fato de que as técnicas de compressão permitem representar de uma forma eficiente uma imagem reduzindo assim, o espaço necessário para armazenamento ou um posterior envio da imagem através de um canal de comunicações. Em particular, o algoritmo SPIHT (Set Partitioning of Hierarchical Trees) muito usado em compressão de imagens é de implementação simples e pode ser aproveitado em aplicações onde se requer uma baixa complexidade. Este trabalho propõe um esquema de compressão de imagens utilizando uma forma personalizada de armazenamento da transformada DWT (Discrete Wavelet Transform), codificação flexível da ROI (Region Of Interest) e a compressão de imagens usando o algoritmo SPIHT. A aplicação consiste na transmissão dos dados correspondentes usando-se codificação turbo. A forma personalizada de armazenamento da DWT visa um melhor aproveitamento da memória por meio do uso de algoritmo SPIHT. A codificação ROI genérica é aplicada em um nível alto da decomposição DWT. Nesse ponto, o algoritmo SPIHT serve para ressaltar e transmitir com prioridade as regiões de interesse. Os dados a serem transmitidos...

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2006.; O Deinterleaving de seqüências de pulsos de sinais radar é uma tarefa essencial para a identificação de radares em guerra eletrônica. Algumas formas de se realizar o deinterleaving baseiam-se em técnicas temporais, que utilizam histogramações e recursividade, e em técnicas baseadas em transformadas ortogonais, que utilizam as assinaturas espectrais para detecção das seqüências. Qualquer uma das abordagens onera grande esforço computacional. Entretanto, as técnicas que utilizam transformadas ortogonais são mais robustas devido às propriedades de minimização da correlação entre as diversas fontes de sinais. As assinaturas espectrais no espaço transformado apresentam um comportamento típico mais evidente. Este trabalho propõe uma técnica composta de três etapas distintas. Primeiramente, tem-se um pré-processamento pelo qual toda a faixa de valores de interesse é segmentada em sub-faixas por meio de subamostragens e filtragem digital. Em seguida, utiliza-se a análise tempo-freqüência por meio da transformada de wavelet contínua de forma a separar os padrões espectrais de interesse. Na última etapa...

The construction of needlet-type wavelets on sections of the spin line bundles over the sphere has been recently addressed in Geller and Marinucci (2008), and Geller et al. (2008,2009). Here we focus on an alternative proposal for needlets on this spin line bundle, in which needlet coefficients arise from the usual, rather than the spin, spherical harmonics, as in the previous constructions. We label this system mixed needlets and investigate in full their properties, including localization, the exact tight frame characterization, reconstruction formula, decomposition of functional spaces, and asymptotic uncorrelation in the stochastic case. We outline astrophysical applications.; Comment: 26 pages

Image data are often composed of two or more geometrically distinct constituents; in galaxy catalogs, for instance, one sees a mixture of pointlike structures (galaxy superclusters) and curvelike structures (filaments). It would be ideal to process a single image and extract two geometrically `pure' images, each one containing features from only one of the two geometric constituents. This seems to be a seriously underdetermined problem, but recent empirical work achieved highly persuasive separations. We present a theoretical analysis showing that accurate geometric separation of point and curve singularities can be achieved by minimizing the $\ell_1$ norm of the representing coefficients in two geometrically complementary frames: wavelets and curvelets. Driving our analysis is a specific property of the ideal (but unachievable) representation where each content type is expanded in the frame best adapted to it. This ideal representation has the property that important coefficients are clustered geometrically in phase space, and that at fine scales, there is very little coherence between a cluster of elements in one frame expansion and individual elements in the complementary frame. We formally introduce notions of cluster coherence and clustered sparsity and use this machinery to show that the underdetermined systems of linear equations can be stably solved by $\ell_1$ minimization; microlocal phase space helps organize the calculations that cluster coherence requires.; Comment: 59 pages...

We analyze the structure of co-invariant subspaces for representations of the Cuntz algebras O_N for N = 2,3,..., N < infinity, with special attention to the representations which are associated to orthonormal and tight-frame wavelets in L^2(R) corresponding to scale number N.; Comment: 32 pages, LaTeX2e "birkart" document class; accepted for publication in the Proceedings of the 2002 IWOTA conference at Virginia Tech in Blacksburg, VA. v4 revision: changes and corrections to Theorem 4.4 and Corollary 7.1. Also Theorem 4.4 is relabeled "Proposition 4.4", and clarifying remarks are added

We consider the problem of characterizing the wavefront set of a tempered distribution $u\in\mathcal{S}'(\mathbb{R}^{d})$ in terms of its continuous wavelet transform, where the latter is defined with respect to a suitably chosen dilation group $H\subset{\rm GL}(\mathbb{R}^{d})$. In this paper we develop a comprehensive and unified approach that allows to establish characterizations of the wavefront set in terms of rapid coefficient decay, for a large variety of dilation groups. For this purpose, we introduce two technical conditions on the dual action of the group $H$, called microlocal admissibilty and (weak) cone approximation property. Essentially, microlocal admissibilty sets up a systematical relationship between the scales in a wavelet dilated by $h\in H$ on one side, and the matrix norm of $h$ on the other side. The (weak) cone approximation property describes the ability of the wavelet system to adapt its frequency-side localization to arbitrary frequency cones. Together, microlocal admissibility and the weak cone approximation property allow the characterization of points in the wavefront set using multiple wavelets. Replacing the weak cone approximation by its stronger counterpart gives access to single wavelet characterizations. We illustrate the scope of our results by discussing -- in any dimension $d\ge2$ -- the similitude...

We give a comprehensive introduction to a general modular frame construction in Hilbert C*-modules and to related modular operators on them. The Hilbert space situation appears as a special case. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modulesover unital C*-algebras that admit an orthonormal Riesz basis. Interrelations and applications to classical linear frame theory are indicated. As an application we describe the nature of families of operators {S_i} such that SUM_i S*_iS_i=id_H, where H is a Hilbert space. Resorting to frames in Hilbert spaces we discuss some measures for pairs of frames to be close to one another. Most of the measures are expressed in terms of norm-distances of different kinds of frame operators. In particular, the existence and uniqueness of the closest (normalized) tight frame to a given frame is investigated. For Riesz bases with certain restrictions the set of closetst tight frames often contains a multiple of its symmetric orthogonalization (i.e. L\"owdin orthogonalization).; Comment: SPIE's Annual Meeting, Session 4119: Wavelets in Signal and Image Processing; San Diego, CA, U.S.A., July 30 - August 4, 2000. to appear in: Proceedings of SPIE v. 4119(2000)...

The goal of the present paper is a short introduction to a general module frame theory in C*-algebras and Hilbert C*-modules. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal bases, and of reconstruction of the frames by projections and other bounded module operators with suitable ranges. We obtain frame representation and decomposition theorems, as well as similarity and equivalence results. The relative position of two and more frames in terms of being complementary or disjoint is investigated in detail. In the last section some recent results by P. G. Casazza are generalized to our setting. The Hilbert space situation appears as a special case. For detailled proofs we refer to another paper also contained in the ArXiv.; Comment: Latex2e, amsproc.cls required, 21 pages, presented at: Functional and Harmonic Analysis of Wavelets (Joint Math. Meeting, San Antonio, TX, Jan. 1999)

We construct representations of a q-oscillator algebra by operators on Fock space on positive matrices. They emerge from a multiresolution scaling construction used in wavelet analysis. The representations of the Cuntz Algebra arising from this multiresolution analysis are contained as a special case in the Fock Space construction.; Comment: (03/11/03):18 pages; LaTeX2e, "article" document class with "letterpaper" option An outline was added under the abstract (p.1), paragraphs added to Introduction (p.2), mat'l added to Proofs in Theorems 1 and 6 (pgs.5&17), material added to text for the conclusion (p.17), one add'l reference added [12]. (04/22/03):"number 1" replace with "term C" (p.9), single sentences reformed into a one paragraph (p.13), QED symbol moved up one paragraph and last paragraph labeled as "Concluding Remarks."

The Fourier transforms of Laguerre functions play the same canonical role in wavelet analysis as do the Hermite functions in Gabor analysis. We will use them as analyzing wavelets in a similar way the Hermite functions were recently by K. Groechenig and Y. Lyubarskii in "Gabor frames with Hermite functions, C. R. Acad. Sci. Paris, Ser. I 344 157-162 (2007)". Building on the work of K. Seip, "Beurling type density theorems in the unit disc, Invent. Math., 113, 21-39 (1993)", concerning sampling sequences on weighted Bergman spaces, we find a sufficient density condition for constructing frames by translations and dilations of the Fourier transform of the nth Laguerre function. As in Groechenig-Lyubarskii theorem, the density increases with n, and in the special case of the hyperbolic lattice in the upper half plane it is given by b\log a<\frac{4\pi}{2n+\alpha}, where alpha is the parameter of the Laguerre function.; Comment: 15 pages

In this paper we are discussing various aspects of wavelet filters. While there are earlier studies of these filters as matrix valued functions in wavelets, in signal processing, and in systems, we here expand the framework. Motivated by applications, and by bringing to bear tools from reproducing kernel theory, we point out the role of non-positive definite Hermitian inner products (negative squares), for example Krein spaces, in the study of stability questions. We focus on the non-rational case, and establish new connections with the theory of generalized Schur functions and their associated reproducing kernel Pontryagin spaces, and the Cuntz relations.

Although much research has been devoted to the problem of restoring Poissonian images, namely in the fields of medical and astronomical imaging, applying the state of the art regularizers (such as those based on wavelets or total variation) to this class of images is still an open research front. This paper proposes a new image deconvolution approach for images with Poisson statistical models, with the following building blocks: (a) a standard regularization/MAP criterion, combining the Poisson log-likelihood with a regularizer (log-prior) is adopted; (b) the resulting optimization problem (which is difficult, since it involves a non-quadratic and non-separable term plus a non-smooth term) is transformed into an equivalent constrained problem, via a variable splitting procedure; (c) this constrained problem is addressed using an augmented Lagrangian framework. The effectiveness of the resulting algorithm is illustrated in comparison with current state-of-the-art methods.; Comment: Submitted to the 2009 IEEE Workshop on Statistical Signal Processing

We give a brief account of a construction called tokens here, which is significant in algebra, analysis, combinatorics, and physics. Tokens allow to express a semigroup on one set via a semigroup convolution on another set. Therefore tokens are similar to intertwining operators but are more flexible. Keywords: semigroups, hypergroups, tokens, poset, multiplicative functions, polynomial sequence of binomial type, integral kernel, wavelets, refinement equation, special functions, quantum propagator, path integral, quantum computing.; Comment: LaTeX, 10 pages, 3 PS figures

We show that every biorthogonal wavelet determines a representation by operators on Hilbert space satisfying simple identities, which captures the established relationship between orthogonal wavelets and Cuntz-algebra representations in that special case. Each of these representations is shown to have tractable finite-dimensional co-invariant doubly-cyclic subspaces. Further, motivated by these representations, we introduce a general Fock-space Hilbert space construction which yields creation operators containing the Cuntz--Toeplitz isometries as a special case.; Comment: 32 pages, LaTeX ("amsart" document class), one EPS graphic file used for shading, accepted March 2002 for J. Funct. Anal

An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally represented as a modulated oscillation, demodulated by its own instantaneous frequency, and then Taylor-expanded at each point in time. The terms in this expansion, called the instantaneous modulation functions, are time-varying functions which quantify, at increasingly higher orders, the local departures of the signal from a uniform sinusoidal oscillation. Closed-form expressions for these functions are found in terms of Bell polynomials and derivatives of the signal's instantaneous frequency and bandwidth. The analytic wavelet transform is shown to depend upon the interaction between the signal's instantaneous modulation functions and frequency-domain derivatives of the wavelet, inducing a hierarchy of departures of the transform away from a perfect representation of the signal. The form of these deviation terms suggests a set of conditions for matching the wavelet properties to suit the variability of the signal, in which case our expressions simplify considerably. One may then quantify the time-varying bias associated with signal estimation via wavelet ridge analysis...

Given a modular form which is not a cusp form $M_k(z)=\sum_{n=0}^{\infty}r_ne^{2\pi inz}$ of weight $k \geq 4$, we define the series $M_{k,s}(x)=\sum_{n=1}^{\infty}\frac{r_n}{n^s}\sin(2\pi nx),$ which converges for all $x\in\mathbb{R}$ when $s>k$. In this paper, we compute the H\"{o}lder regularity exponent of $M_{k,s}$ at irrational points. In our analysis we apply wavelets methods proposed by Jaffard in 1996 in the study of the Riemann series. We find that the H\"{o}lder regularity exponent at a point $x$ is related to the fine diophantine properties of $x$, in a very precise way.; Comment: 19 pages, added references, improved results

Let G be a stratified Lie group and L be the sub-Laplacian on G. Let 0 \neq f\in S(R^+). We show that Lf(L)\delta, the distribution kernel of the operator Lf(L), is an admissible function on G. We also show that, if \xi f(\xi) satisfies Daubechies' criterion, then L f(L)\delta generates a frame for any sufficiently fine lattice subgroup of G.; Comment: 30 pages

Assuming that $(X_t)_{t\in\Z}$ is a vector valued time series with a common marginal distribution admitting a density $f$, our aim is to provide a wide range of consistent estimators of $f$. We consider different methods of estimation of the density as kernel, projection or wavelets ones. Various cases of weakly dependent series are investigated including the Doukhan & Louhichi (1999)'s $\eta$-weak dependence condition, and the $\tilde \phi$-dependence of Dedecker & Prieur (2005). We thus obtain results for Markov chains, dynamical systems, bilinear models, non causal Moving Average... From a moment inequality of Doukhan & Louhichi (1999), we provide convergence rates of the term of error for the estimation with the $\L^q$ loss or almost surely, uniformly on compact subsets.

This dissertation presents novel models for purely discrete-time self-similar processes and scale- invariant systems. The results developed are based on the definition of a discrete-time scaling (dilation) operation through a mapping between discrete and continuous frequencies. It is shown that it is possible to have continuous scaling factors through this operation even though the signal itself is discrete-time. Both deterministic and stochastic discrete-time self-similar signals are studied. Conditions of existence for self-similar signals are provided. Construction of discrete-time linear scale-invariant (LSI) systems and white noise driven models of self-similar stochastic processes are discussed. It is shown that unlike continuous-time self-similar signals, a wide class of non-trivial discrete-time self-similar signals can be constructed through these models. The results obtained in the one-dimensional case are extended to multi-dimensional case. Constructions of discrete-space self-similar ran dom fields are shown to be potentially useful for the generation, modeling and analysis of multi-dimensional self-similar signals such as textures. Constructions of discrete-time and discrete-space self-similar signals presented in the dissertation provide potential tools for applications such as image segmentation and classification...