Orthonormal bases of compactly supported wavelets
1988/10/01 by Ingrid Daubechies · 8,202 citations
Computer Science · Engineering · Mathematics · #Advanced Image Fusion Techniques #Algebra over a field #Applied mathematics #Artificial intelligence #Computer science #Construct (python library) #Decomposition #Discrete wavelet transform #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Mathematics #Multiresolution analysis #Order (exchange) #Orthonormal basis #Pure mathematics #Wavelet #Wavelet transform
paper · doi:10.1002/cpa.3160410705
published in Communications on Pure and Applied Mathematics 41(7), 909-996 (Wiley)
openalex publication_date 1988/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract
Abstract We construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity. The order of regularity increases linearly with the support width. We start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction. The construction then follows from a synthesis of these different approaches.
Citations
Cited by
- Automatic microseismic denoising and onset detection using the synchrosqueezed continuous wavelet transform
- De-noising by soft-thresholding
- The wavelet transform, time-frequency localization and signal analysis
- Color Compressive Sensing Imaging of Arbitrary-Shaped Scatterers
- Bayesian decomposition using Besov priors
- Fully adaptive multiresolution finite volume schemes for conservation laws
- Extraction of spots in biological images using multiscale products
- Continuous and Discrete Wavelet Transforms
- Multiresolution Representation of Data: A General Framework
- Computer-based model for the transient dynamics of a tall building during digitally simulated Andrews AFB thunderstorm
- WAVELET TRANSFORMS AND THEIR APPLICATIONS TO TURBULENCE
- Endpoint Criteria for One-Dimensional Bilinear Rough Singular Integrals
- Fast non parametric entropy estimation for spatial-temporal saliency method
- Multivariate methods in metabolomics – from pre-processing to dimension reduction and statistical analysis
- Analysis of the electroencephalographic activity during the Necker cube reversals by means of the wavelet transform
- Compressed Sensing with Deep Image Prior and Learned Regularization
- A Note on the Daubechies Approach in the Construction of Spline Type Orthogonal Scaling Functions
- Rate of convergence of wavelet series by cesaro means
- Paraunitary Matrices
- A Wavelet-Based Approach To Monitoring Parkinson's Disease Symptoms
- HDW-SR: High-Frequency Guided Diffusion Model based on Wavelet Decomposition for Image Super-Resolution
- Dynamical Sampling: A Survey
- A Wavelet Based Pile-Up Mitigation Method for the LHC Upgrade
- One model to solve them all: 2BSDE families via neural operators
- On the absence of the RIP in real-world applications of compressed sensing and the RIP in levels
- Fractional and Complex Pseudo-Splines and the Construction of Parseval Frames
- Multivariate Variational Mode Decomposition
- The dual-tree complex wavelet transform
- On Bilinear Maximal Bochner-Riesz Operators
- Gibbs Phenomenon for Wavelets
- Extracting the Spectrum by Spatial Filtering
- NETT: Solving Inverse Problems with Deep Neural Networks
- Approximation by crystal-refinable function
- Poly-locality in quantum computing
- Time-domain and Frequency-domain Signals and their Analysis
- Provable test-time adaptivity and distributional robustness of in-context learning
- Improved estimates for bilinear rough singular integrals
- Hölder Regularity of Distributional Volume Forms
- A Novel Application of Lifting Scheme for Multiresolution Correlation of Complex Radar Signals
- On Parametrization of Compact Wavelet Matrices
- An Iterative Method for Parallel MRI SENSE-based Reconstruction in the Wavelet Domain
- Confidence intervals for the Hurst parameter of a fractional Brownian motion based on finite sample size
- The Hörmander multiplier theorem, II: The bilinear local L2 case
- Image Processing Tools for Financial Time Series Classification
- On the Design of Multi-Dimensional Compactly Supported Parseval Framelets with Directional Characteristics
- Semi-parametric estimation of the variogram of a Gaussian process with stationary increments
- Multiresolution in the Bergman space
- An approximation of Daubechies wavelet matrices by perfect\n reconstruction filter banks with rational coefficients
- A theory for multiresolution signal decomposition: the wavelet representation
- Higher order perturbation estimates in quasi-Banach Schatten spaces through wavelets
- Multiwavelet-based Operator Learning for Differential Equations
- Using normal to find abnormal: AI-based anomaly detection in gravitational wave data
- The Discrete Wavelet Transform in S
- On Wavelet Decomposition over Finite Fields
- Wavelet Mixture of Experts for Time Series Forecasting
- Sparse and redundant signal representations for x-ray computed tomography
- Physics-informed Multiresolution Wavelet Neural Network Method for Solving Partial Differential Equations
- CVC: The Contourlet Video Compression algorithm for real-time applications
- Practical error estimates for sparse recovery in linear inverse problems
- PRISM: Lightweight Multivariate Time-Series Classification through Symmetric Multi-Resolution Convolutional Layers
- Koopman Theory and Linear Approximation Spaces
- TIR-Diffusion: Diffusion-based Thermal Infrared Image Denoising via Latent and Wavelet Domain Optimization
- Advances in pre-processing and model generation for mass spectrometric data analysis
- Generalized spaces of pointwise regularity: To a general framework for the WLM
- Wavelet Based Dictionaries for Piecewise Dimensionality Reduction of ECG Signals
- Construction of Compactly Supported Shearlet Frames
- Density of the Set of Generators of Wavelet Systems
- A New Multilevel Method for Electrostatic Problems through Hierarchical Loop Basis
- Image Fusion Techniques in Remote Sensing
- Where the Buffalo Roam: Infinite Processes and Infinite Complexity
- Neural Mode Decomposition based on Fourier neural network and frequency clustering
- Wavelet transforms versus Fourier transforms
- Some Results about Frames
- Approximation of integral operators using convolution-product expansions
- Efficient Quantum Transforms
- On construction of multivariate symmetric MRA-based wavelets
- Scale-dependent functions in statistical hydrodynamics: a functional analysis point of view
- Functional principal component analysis for global sensitivity analysis of model with spatial output
- Breaking the coherence barrier: A new theory for compressed sensing
- Two weight Commutators in the Dirichlet and Neumann Laplacian settings
- Simultaneous Translational and Multiplicative Tiling and Wavelet Sets in R2
- Generative model for optimal density estimation on unknown manifold
- Accelerating Discrete Wavelet Transforms on GPUs
- Linear Phase Perfect Reconstruction Filters and Wavelets with Even Symmetry
- Uncertainty Quantification for Linear Inverse Problems with Besov Prior: A Randomize-Then-Optimize Method
- Analysis on Non-negative Factorizations and Applications
- Improved invariant polytope algorithm and applications
- Scaling limit of a directed polymer among a Poisson field of independent walks
- Representation of Reinforcement Learning Policies in Reproducing Kernel Hilbert Spaces
- PhysioWave: A Multi-Scale Wavelet-Transformer for Physiological Signal Representation
- Invariant polytopes of linear operators with applications to regularity of wavelets and of subdivisions
- A Douglas-Rachford construction of non-separable continuous compactly supported multidimensional wavelets
- Best approximation with wavelets in weighted Orlicz spaces
- Spread Spectrum based Robust Image Watermark Authentication
- Nonlinear Approximation and Image Representation using Wavelets
- Compressed Learning for Tactile Object Classification
- Fast simulation of two-phase flow in three-dimensional digital images of heterogeneous porous media using multiresolution curvelet transformation
- Wavelets centered on a knot sequence: theory, construction, and\n applications
- Orthonormal Compactly Supported Wavelets with Optimal Sobolev Regularity
- On wavelet-based sampling Kantorovich operators and their study in multi-resolution analysis
- Orthonormal Bases of Compactly Supported Wavelets II. Variations on a Theme
- Mallows-type model averaging: Non-asymptotic analysis and all-subset combination
- Efficient function approximation on general bounded domains using wavelets on a cartesian grid
- Wavelet decomposition and bandwidth of functions defined on vector spaces over finite fields
- Probabilistic multiscale image segmentation
- Approximative Atomic Systems for operators in Banach spaces
- Wavelets and spectral triples for higher-rank graphs
- Deep Representation with ReLU Neural Networks
- Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives
- Learning Wavelet-Sparse FDK for 3D Cone-Beam CT Reconstruction
- Weak and Strong type Ap Estimates for Calderón-Zygmund Operators
- WaLRUS: Wavelets for Long-range Representation Using SSMs
- Multi-Order Wavelet Derivative Transform for Deep Time Series Forecasting
- Beyond Edge Maps: Wavelet-Domain Conditioning for Multi-Adapter Map-to-Satellite Diffusion
- Fre-GAN: Adversarial Frequency-consistent Audio Synthesis
- Wavelet Analysis of the Besov Regularity of Lévy White Noises
- Noiselets
- Fast wavelet transforms and numerical algorithms I
- Extraction of the electron self-energy from angle-resolved photoemission data: Application toBi2Sr2CaCu2O8+x
- Quantum tomography with wavelet transform in Banach space on homogeneous space
- First results on characterization of Cherenkov images through combined use of Hillas, fractal and wavelet parameters
- PARAMETER ESTIMATION FROM TIME-SERIES DATA WITH CORRELATED ERRORS: A WAVELET-BASED METHOD AND ITS APPLICATION TO TRANSIT LIGHT CURVES
- Bilinear Decompositions of Products of Hardy and Lipschitz Spaces Through Wavelets
- Learning and adaptive estimation for marker-dependent counting processes
- Quantum Complexities of Ordered Searching, Sorting, and Element Distinctness
- QUANTUM HIERARCHIC MODELS FOR INFORMATION PROCESSING
- Short-term traffic speed forecasting hybrid model based on Chaos–Wavelet Analysis-Support Vector Machine theory
- A wavelet characterization for the upper global Holder index
- Mathematical properties of the jpeg2000 wavelet filters
- Matrix-Weighted Besov--Triebel--Lizorkin Spaces of Optimal Scale: Boundedness of Pseudo-Differential, Trace, and Calderón--Zygmund Operators
- M-channel compactly supported biorthogonal cosine-modulated wavelet bases
- Temperature fluctuations in the intergalactic medium
- A generalized parametric PR-QMF design technique based on Bernstein polynomial approximation
- An Ideal Mass Assignment Scheme for Measuring the Power Spectrum with Fast Fourier Transforms
- Entanglement Renormalization and Wavelets
- Compression of correlation matrices and an efficient method for forming matrix product states of fermionic Gaussian states
- Wavelets applied to cosmic microwave background maps: a multiresolution analysis for denoising
- Wavelet Design with Optimally Localized Ambiguity Function: a Variational Approach
- DETECTION OF POTENTIAL TRANSIT SIGNALS IN 17 QUARTERS OF KEPLER MISSION DATA
- A pseudo-probabilistic approach to the dilation equation for wavelets
- A Structurally Regularized Convolutional Neural Network for Image Classification Using Wavelet-Based Subband Decomposition
- Spontaneous emission rates of dipoles in photonic crystal membranes
- Robust Image Watermarking Under Pixel Wise Masking Framework
- Substructure recovery by three-dimensional discrete wavelet transforms
- Application of wavelets to singular integral scattering equations
- Weighted estimates for Multilinear Singular Integrals with Rough Kernels
- Ingrid Daubechies [wikipedia]
- Data-driven haemodynamic response function extraction using Fourier-wavelet regularised deconvolution. [europepmc]
- Altered oscillatory cerebral blood flow velocity and autoregulation in postural tachycardia syndrome. [europepmc]
- Using compressive sensing to recover images from PET scanners with partial detector rings. [europepmc]
- Exploring possible DNA structures in real-time polymerase kinetics using Pacific Biosciences sequencer data. [europepmc]
- Effect of Subliminal Lexical Priming on the Subjective Perception of Images: A Machine Learning Approach. [europepmc]
- Choosing Wavelet Methods, Filters, and Lengths for Functional Brain Network Construction. [europepmc]
- Fetal Heart Sounds Detection Using Wavelet Transform and Fractal Dimension. [europepmc]
- Automatic Detection of Atrial Fibrillation Based on Continuous Wavelet Transform and 2D Convolutional Neural Networks. [europepmc]
- Disentangling Multispectral Functional Connectivity With Wavelets. [europepmc]
- Adaptive particle representation of fluorescence microscopy images. [europepmc]
- Dynamic Imaging of Glucose and Lactate Metabolism by 13 C-MRS without Hyperpolarization. [europepmc]
- Measurement Noise Recommendation for Efficient Kalman Filtering over a Large Amount of Sensor Data. [europepmc]
- Design and Implementation of an Ultra-Low Resource Electrodermal Activity Sensor for Wearable Applications ‡ . [europepmc]
- Methodological Considerations on the Use of Different Spectral Decomposition Algorithms to Study Hippocampal Rhythms. [europepmc]
- Comparison of Bagging and Boosting Ensemble Machine Learning Methods for Automated EMG Signal Classification. [europepmc]
- Learning to synthesize: robust phase retrieval at low photon counts. [europepmc]
- Automatic recognition of breast invasive ductal carcinoma based on terahertz spectroscopy with wavelet packet transform and machine learning. [europepmc]
- Learning the properties of adaptive regions with functional data analysis. [europepmc]
- Reduction of Influence of the High-Frequency Noise on the Results of Surface Topography Measurements. [europepmc]
- Machine Learning Techniques for THz Imaging and Time-Domain Spectroscopy. [europepmc]
- Data Processing in Functional Near-Infrared Spectroscopy (fNIRS) Motor Control Research. [europepmc]
- A large collection of real-world pediatric sleep studies. [europepmc]
- Artificial Intelligence-Based Robust Hybrid Algorithm Design and Implementation for Real-Time Detection of Plant Diseases in Agricultural Environments. [europepmc]
- Get a New Perspective on EEG: Convolutional Neural Network Encoders for Parametric t-SNE. [europepmc]
- Digital Image Processing to Detect Adaptive Evolution. [europepmc]
Related