Wavelets, Their Friends, and What They Can Do for You

  title={Wavelets, Their Friends, and What They Can Do for You},
  author={Martin J. Mohlenkamp and Mar{\'i}a Cristina Pereyra},
These notes were created by Maŕia Cristina Pereyra for the short course Wavelets: Theory and Applications, at the I Panamerican Advanced Studies Institute in Computational Science and Engineering (PASI), Universidad Nacional de Cordoba, Cordoba, Argentina, June 24–July 5, 2002. They were modified and extended by Martin J. Mohlenkamp for the short course Wavelets and Partial Differential Equations, at the II Panamerican Advanced Studies Institute in Computational Science and Engineering… 

Adaptive Waveletmethoden zur Approximation von Bildern

This thesis is concerned with adaptive wavelet methods for the approximation of images. First, the Easy-Path-Wavelet-Transform (EPWT) is introduced. The EPWT works as follows. We determine a path

Harmonic Analysis : from Fourier to Haar Maŕıa Cristina Pereyra

Contents Introduction xv Chapter 1. Fourier series: some motivation 1 1.1. Some examples and key definitions 1 1.2. Main questions 5 1.3. Fourier series and Fourier coefficients 7 1.4. A little

Different Perspectives and Formulas for Capturing Deviation from Ergodicity

  • S. E. Scott
  • Computer Science
    SIAM J. Appl. Dyn. Syst.
  • 2013
This paper describes the development of the Haar ergodicity defect, a technique for assessing the extent to which a given dynamical system falls short of being ergodic, and alternate and recursive formulas for this Haar are given.

Harmonic Shape Analysis : From Fourier to Wavelets

The theoretical background of the manifold Fourier analysis is explained, focusing on its connection with signal processing and heat diffusion, and a survey of various types of manifold wavelet transform, particularly the spectral manifoldWavelet transform is provided.

The continuous wavelet transform and window functions

. We define a window function ψ as an element of L 2 ( R n ) satisfying certain boundedness properties with respect to the L 2 ( R n ) norm and prove that it satisfies the admissibility condition if

Superfast Wavelet Transform Using QTT Approximation. I: Haar Wavelets

A superfast discrete Haar wavelet transform (SFHWT) as well as its inverse, using the QTT representation for the Haar transform matrices and input-output vectors is proposed, and it outperforms the traditional FHWT for grid size larger than a certain value depending on the spacial dimension.

Smoothlets—Multiscale Functions for Adaptive Representation of Images

  • A. Lisowska
  • Mathematics, Computer Science
    IEEE Transactions on Image Processing
  • 2011
From the theoretical considerations and experiments, it follows that smoothlets can assure better image compression than the other known adaptive geometrical methods, namely, wedgelets and second-order wedgelets.

Evidence for Past Knot Mergers in the HH34 Jet

alineados. Las posiciones y los movimientos propios de estos nudos pueden ser usados para determinar tiempos dinamicos, y para estimar el per´oodo de eyeccion (tomando diferencias entre los tiempos

Comparing field data using Alpert multi-wavelets

A method to compare sets of full-field data using Alpert tree-wavelet transforms for comparison of field data sets coming from two different sources such as when comparing simulation field data to experimental field data is introduced.

Texture features for the reproduction of the perceptual organization of sound

It is concluded that harmonic, impact and continuous process sounds can be largely separated with energy based tonality, pulsality and noisiness.



Wavelets and Fast Numerical Algorithms

The so-called non-standard form (which achieves decoupling among the scales) and the associated fast numerical algorithms are considered and examples of non- standard forms of several basic operators (e.g. derivatives) will be computed explicitly.

Diffusion Wavelets

An algorithm for the machine calculation of complex Fourier series

Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.

A fast transform for spherical harmonics

A fast transform analogous to the Fast Fourier Transform (FFT) is provided for spherical harmonic series and it is shown that although these matrices are dense and oscillatory, locally they can be represented efficiently in trigonometric series.

Ridgelets: estimating with ridge functions

In a nonparametric regression setting, this article suggests expanding noisy data into a ridgelet series and applying a scalar nonlinearity to the coefficients (damping); this is unlike existing approaches based on stepwise additions of elements.

Fast wavelet transforms and numerical algorithms I

The algorithms presented here are based on the recently developed theory of wavelets and are applicable to all Calderon-Zygmund and pseudo-differential operators, and indicate that many previously intractable problems become manageable with the techniques presented here.

Factoring wavelet transforms into lifting steps

This article is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple

The contourlet transform: an efficient directional multiresolution image representation

A "true" two-dimensional transform that can capture the intrinsic geometrical structure that is key in visual information is pursued and it is shown that with parabolic scaling and sufficient directional vanishing moments, contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves.

Numerical operator calculus in higher dimensions

It is proved that the multiparticle Schrödinger operator, as well as the inverse Laplacian, can be represented very efficiently in this form and conjecture and provide numerical evidence that functions of operators inherit this property, in which case numerical operator calculus in higher dimensions becomes feasible.