Wavelets and Multiscale Signal Processing

  title={Wavelets and Multiscale Signal Processing},
  author={Albert Cohen and Robert D. Ryan},
Multi-resolution analysis: The continuous point of view The discrete point of view The multivariate case. Wavelets and conjugate quadrature filters: The general case The finite case Wavelets with compact support action of the FWT on oscillating signals. The regularity of scaling functions and wavelets: Regularity and oscillation The sub-division algorithms Spectral estimates of the regularity Estimates of the Lp-Sobolev exponent Applications. Biorthogonal wavelet bases: General principles of… Expand
Introduction to Wavelets and Wavelet Transforms: A Primer
1. Introduction to Wavelets. 2. A Multiresolution Formulation of Wavelet Systems. 3. Filter Banks and the Discrete Wavelet Transform. 4. Bases, Orthogonal Bases, Biorthogonal Bases, Frames, TightExpand
Characterizing wavelet coefficient decay of discrete-time signals
Abstract We present an intrinsically discrete-time characterization of wavelet coefficient decay. To be more precise, let f = ( f ( n ) ) n ∈ Z be a sequence and denote by ( d j , l ) j ⩾ 1 , l ∈ ZExpand
A Nonparametric Regression Spectrum : Estimation, Asymptotic Properties and Data Analysis
Classical spectral analysis in statistics considers decomposition of stationary time series into sinusoidal components. The autocovariance and the spectrum are fundamental elements for analyzing aExpand
Directional and Time-Scale Wavelet Analysis
  • R. Zuidwijk
  • Computer Science, Mathematics
  • SIAM J. Math. Anal.
  • 2000
Discrete wavelet X-ray transforms are described which make use of wavelet orthonormal bases and, more generally, of biorthogonal systems ofwavelet Riesz bases. Expand
Data adaptive wavelet methods for Gaussian long-memory processes
In this thesis, we investigate some adaptive wavelet approaches for a so-called nonparametric regression model with strongly dependent Gaussian residuals. At first, we discuss data adaptive waveletExpand
The Mathematics of Signal Processing
1. Introduction 2. Normed vector spaces 3. Analytic tools 4. Fourier series 5. Fourier transforms 6. Compressive sensing 7. Discrete transforms 8. Linear filters 9. Windowed Fourier transforms,Expand
An Introduction to Wavelet Theory and Analysis
This report reviews the history, theory and mathematics of wavelet analysis, and the most common algorithms for performing efficient, discrete wavelet transforms for signal analysis and inverse discrete wavelets for signal reconstruction are presented. Expand
Discrete Framelet Transforms
This chapter introduces a standard (both one-level and multilevel) discrete framelet transform and filter banks, and investigates three fundamental properties of a standard discreteframelet transform: perfect reconstruction, sparsity, and stability. Expand
Regularity of refinable functions with exponentially decaying masks
The regularity of refinable functions is an important issue in all multiresolution analysis and has a strong impact on applications of wavelets to image processing, geometric and numerical solutionsExpand
Quasi wavelets and quasi interpolating wavelets
Abstract This Letter introduces two families of new wavelets, quasi wavelets and quasi interpolating wavelets. It is found that the mathematical regularization of Shannon's orthonormal interpolatingExpand