Why Restrict Ourselves to Compactly Supported Basis Functions?

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The paper presents a procedure for fault location in distribution networks, based on the use of the integrated time-frequency wavelet decompositions of the voltage transients associated with the fault-originated travelling waves. The proposed analysis of time-frequency wavelet decompositions has been found to improve the identification accuracy of the frequencies associated to the characteristic patterns of a fault location with respect to a sole frequency-domain wavelet analysis. Several laboratory fault t

This master thesis deals with the problematic of the integration of Global Positioning System (GPS) measurements with inertial data acquired by a Micro-Electro-Mechanical System (MEMS) Inertial Measurement Units (IMU). This technology is employed for the purposes of sport performances assessment, as it enables reconstructing accurately athletes trajectories. Based on a recent development at the TOPO laboratory at the Swiss Federal Institute of Technology of Lausanne (EPFL), a new software's architecture is

Wavelet-based statistical analysis methods for fMRI are able to detect brain activity without smoothing the data. Typically, the statistical inference is performed in the wavelet domain by testing the t-values of each wavelet coefficient; subsequently, an activity map is reconstructed from the significant coefficients. The limitation of this approach is that there is no direct statistical interpretation of the reconstructed map. In this paper, we propose a new methodology that takes advantage of wavelet pro

Building good sparse approximations of functions is one of the major themes in approximation theory. When applied to signals, images or any kind of data, it allows to deal with basic building blocks that essentially synthesize all the information at hand. It is known since the early successes of wavelet analysis that sparse expansions very often result in efficient algorithms for characterizing signals in noise or even for analyzing and compressing signals. The very strong links between approximation theory

I. Introduction Wavelets are the result of collective efforts that recognized common threads between ideas and concepts that had been independently developed and investigated by distinct research communities. They provide a unifying framework for decomposing images, volumes, and time-series data into their elementary constituents across scale. Although a relatively recent construct, wavelets have become a tool of choice for engineers, physicists, and mathematicians, leading to efficient solutions in time a

Risk assessment is in urgent need of more accurate toxic effect endpoints than those currently in use, especially for low concentrations. Often such endpoints are estimated by analysis of variance, linear interpolation, or smoothing. As these statistical methods are not always satisfactory, some authors have proposed to describe the entire dose-response curves by fully formalized parametric regression models whose parameters have toxicological meaning. These models allow a better evaluation of pollutant eff

We investigate stabilized Galerkin approximations of linear and nonlinear convection-diffusion-reaction equations. We derive nonlinear streamline and cross-wind diffusion methods that guarantee a discrete maximum principle for strictly acute meshes and first order polynomial interpolation. For pure convection-diffusion problems, the discrete maximum principle is achieved using a nonlinear cross-wind diffusion factor that depends on the angle between the discrete solution and the flow velocity. For convectio

The ridgelet transform (Candes and Donoho, 1999) was introduced as a new multiscale representation for functions on continuous spaces that are smooth away from discontinuities along lines. In this paper, we present several discrete versions of the ridgelet transform that lead to algorithmic implementations. The resulting transforms are invertible, non-redundant and computed via fast algorithms. Furthermore, this construction leads to a family of directional orthonormal bases for digital images. Numerical re

Introduction: A reliable measurement of the physical activity in everyday life should allow a better assessment of the utility and the relevance of a number of medical treatments. Continuous 24-h recordings of posture and motion can be generally useful in behaviour assessment. Categorising body postures (sitting, standing and lying) and locomotion (walking) based on only one miniature kinematic sensor has been studied [1]. The purpose of this study is to improve the accuracy of that system and to provide ot

Over the last decade or so, wavelets have had a growing impact on signal processing theory and practice, both because of the unifying role and their successes in applications. Filter banks, which lie at the heart of wavelet-based algorithms, have become standard signal processing operators, used routinely in applications ranging from compression to modems. The contributions of wavelets have often been in the subtle interplay between discrete-time and continuous-time signal processing. The purpose of this ar

This chapter presents a survey of interpolation and resampling techniques in the context of exact, separable interpolation of regularly sampled data. In this context, the traditional view of interpolation is to represent an arbitrary continuous function as a discrete sum of weighted and shifted synthesis functions—in other words, a mixed convolution equation. An important issue is the choice of adequate synthesis functions that satisfy interpolation properties. Examples of finite-support ones are the square

We develop a spline calculus for dealing with fractional derivatives. After a brief review of fractional splines, we present the main formulas for computing the fractional derivatives of the underlying basis functions. In particular, we show that the

γ ^{ th }

fractional derivative of a B-spline of degree α (not necessarily integer) is given by the

γ ^{ th }

fractional difference of a B-spline of degree α-γ. We use these results to derive an improved version the filtered backprojection algorithm for

We present two digital image processing methods for image quality enhancement in Digital Holographic Microscopy (DHM). With the first method, the Fourier transform of an off-axis hologram is spatially filtered in order to eliminate the zero order of diffraction and the twin image. We show that this operation enhances the image contrast and the signal to background ratio. The second method describes an original technique to perform the apodization of the hologram with a transmission profile which follows a c

A method is proposed for designing apodized apertures with a transmission profile which follows a curve defined using a cubic spline interpolation. The method is applied in digital holographic microscopy to perform digitally the apodization of the aperture of holograms recorded by a CCD camera. The transmission of the apodized aperture is entirely defined by four parameters which are adjusted iteratively to minimize intensity and phase fluctuations appearing in the images obtained by numerical reconstructio

We extend the classical interpolation method to generalized interpolation. This extension is done by replacing the interpolating function by a non-interpolating function that is applied to prefiltered data, in order to preserve the interpolation condition. We show, both theoretically and practically, that this approach performs much better than classical methods, for the same computational cost.

We consider the construction of least squares pyramids using shifted polynomial spline basis functions. We derive the pre- and post-filters as a function of the degree n and the shift parameter Δ. We show that the underlying projection operator is entirely specified by two transfer functions acting on the even and odd signal samples, respectively. We introduce a measure of shift-invariance and show that the most favorable configuration is obtained when the knots of the splines are centered with respect to t

Why Restrict Ourselves to Compactly Supported Basis Functions?

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Integrated Use of Time-Frequency Wavelet Decompositions for Fault Location in Distribution Networks: Theory and Experimental Validation

Automated Processing of GPS/MEMS-IMU Data for Position, Velocity and Attitude Determination

Wavelet-Based fMRI Statistical Analysis and Spatial Interpretation: A Unifying Approach

Tree-Based Pursuit

Guest Editorial: Wavelets in Medical Imaging

Effects of dinoseb on the life cycle of Daphnia magna : modeling survival time and a proposal for an alternative to the no-observed-effect concentration

Nonlinear diffusion and discrete maximum principle for stabilized Galerkin approximations of the convection-diffusion-reaction equation

Discrete Ridgelet Transforms for Image Representation

ESMAC-SIAMOC 2001 Joint Congress: Body Postures and Walking Period Estimation Using a Kinematic Sensor: Application for Long Term Monitoring of Physical Activity in Elderly Subjects

Wavelets, approximation, and compression

Image Interpolation and Resampling

Fractional derivatives, splines and tomography

Spatial filtering and aperture apodization in digital holographic microscopy

Aperture apodization using cubic spline interpolation: application in digital holographic microscopy

Generalized Interpolation: Higher Quality at no Additional Cost

Multiresolution Approximation Using Shifted Splines