# Wavelets and Multiscale Signal Processing

@inproceedings{Cohen1995WaveletsAM, title={Wavelets and Multiscale Signal Processing}, author={Albert Cohen and Robert D. Ryan}, year={1995} }

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

#### 224 Citations

Introduction to Wavelets and Wavelet Transforms: A Primer

- Mathematics
- 1997

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, Tight… Expand

Characterizing wavelet coefficient decay of discrete-time signals

- Mathematics
- 2006

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 ∈ Z… Expand

A Nonparametric Regression Spectrum : Estimation, Asymptotic Properties and Data Analysis

- Mathematics
- 2007

Classical spectral analysis in statistics considers decomposition of stationary time series into sinusoidal components. The autocovariance and the spectrum are fundamental elements for analyzing a… Expand

Directional and Time-Scale Wavelet Analysis

- 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

- Mathematics
- 2012

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 wavelet… Expand

The Mathematics of Signal Processing

- Mathematics
- 2012

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

- Computer Science
- 1998

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

- Computer Science
- 2017

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

- Mathematics
- 2010

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 solutions… Expand

Quasi wavelets and quasi interpolating wavelets

- Mathematics
- 1998

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 interpolating… Expand