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Everything about Fast wavelet transform
Mathematical algorithm
The fast wavelet transform is a mathematical algorithm designed to turn a waveform or signal in the time domain into a sequence of coefficients based on an orthogonal basis of small finite waves, or wavelets. The transform can be easily extended to multidimensional signals, such as images, where the time domain is replaced with the space domain. This algorithm was introduced in 1989 by Stéphane Mallat. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Fast wavelet transformA 5-minute orientation
- Skim a recent paper: A Deep Learning and Fast Wavelet Transform-Based Hybrid Approach for Denoising of PPG SignalsInfluential work since 2022
- Pick up a classic book: Computer Engineering and TechnologyThe most-reprinted book on the subject
- Read the landmark paper: Multiscale contrast enhancement for radiographies: Laplacian pyramid versus fast wavelet transformCited 165 times
- Go sideways: Discrete wavelet transformA closely related topic
- Go sideways: Orthogonal waveletA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Multiscale contrast enhancement for radiographies: Laplacian pyramid versus fast wavelet transform
Fast implementation of the continuous wavelet transform with integer scales
FAST LEARNING ALGORITHM OF WAVELET NETWORK BASED ON FAST WAVELET TRANSFORM
Fast Directional Continuous Spherical Wavelet Transform Algorithms
Fast solution of electromagnetic integral equations using adaptive wavelet packet transform
Rational multiresolution analysis and fast wavelet transform: application to wavelet shrinkage denoising
Fast surface interpolation using multiresolution wavelet transform
VLSI architecture for fast 2D discrete orthonormal wavelet transform
🆕 Influential since 2022
A Deep Learning and Fast Wavelet Transform-Based Hybrid Approach for Denoising of PPG Signals
Comparisons between fast algorithms for the continuous wavelet transform and applications in cosmology: the 1D case
Fast image encryption algorithm based on 2D-FCSM and pseudo-wavelet transform
Fast hologram calculation method using wavelet transform: WASABI-2
Fast High‐Fidelity Fourier Ptychographic Microscopy via Wavelet Transform and Linear Attention
📚 Books worth reading
Computer Engineering and TechnologyWeixia Xu · 2013
Wavelets Made EasyYves Nievergelt · 2012- 📕Applied data miningGuandong Xu · 2013
Emerging Technologies for Information Systems, Computing, and ManagementW. Eric Wong · 2013
Fourier and Wavelet AnalysisGeorge Bachman · 2000
Scale Space and Variational Methods in Computer VisionArjan Kuijper · 2013
Coding the MatrixPhilip N. Klein · 2013- 📕Fast wavelet transforms for matrices arising from boundary element methodsDave M. Bond · 1994
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Discrete wavelet transform In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled…
- Orthogonal wavelet An orthogonal wavelet is a wavelet whose associated wavelet transform is orthogonal. That is, the inverse wavelet transform is the adjoint of the wavelet…
- Frame (linear algebra) In linear algebra, a frame of an inner product space is a generalization of a basis of a vector space to sets that may be linearly dependent. In the terminology…
- Daubechies wavelet The Daubechies wavelets, based on the work of Ingrid Daubechies, are a family of orthogonal wavelets defining a discrete wavelet transform and characterized…
- Wavelet transform In mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated…
- Generating function transformation In mathematics a transformation of a sequence's generating function provides a method of converting the generating function for one sequence into a generating…
- Cauchy wavelet In mathematics, Cauchy wavelets are a family of continuous wavelets, used in the continuous wavelet transform. The Cauchy wavelet of order p {\displaystyle…
- Multiresolution analysis A multiresolution analysis (MRA) or multiscale approximation (MSA) is the design method of most of the practically relevant discrete wavelet transforms…