# Category: Wavelets

Multiresolution analysis
A multiresolution analysis (MRA) or multiscale approximation (MSA) is the design method of most of the practically relevant discrete wavelet transforms (DWT) and the justification for the algorithm of
Symlet
In applied mathematics, symlet wavelets are a family of wavelets. They are a modified version of Daubechies wavelets with increased symmetry.
Set partitioning in hierarchical trees
Set partitioning in hierarchical trees (SPIHT) is an image compression algorithm that exploits the inherent similarities across the subbands in a wavelet decomposition of an image. The algorithm was d
Modified Morlet wavelet
Modified Mexican hat, Modified Morlet and Dark soliton or Darklet wavelets are derived from hyperbolic (sech) (bright soliton) and hyperbolic tangent (tanh) (dark soliton) pulses. These functions are
Filter bank
In signal processing, a filter bank (or filterbank) is an array of bandpass filters that separates the input signal into multiple components, each one carrying a single frequency sub-band of the origi
Multigrid method
In numerical analysis, a multigrid method (MG method) is an algorithm for solving differential equations using a hierarchy of discretizations. They are an example of a class of techniques called multi
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 by a wavelet. This article provides a formal, m
Gabor wavelet
Gabor wavelets are wavelets invented by Dennis Gabor using complex functions constructed to serve as a basis for Fourier transforms in information theory applications. They are very similar to Morlet
Polyphase matrix
In signal processing, a polyphase matrix is a matrix whose elements are filter masks. It represents a filter bank as it is used in sub-band coders alias discrete wavelet transforms. If are two filters
Non-separable wavelet
Non-separable wavelets are multi-dimensional wavelets that are not directly implemented as tensor products of wavelets on some lower-dimensional space.They have been studied since 1992.They offer a fe
Transfer matrix
In applied mathematics, the transfer matrix is a formulation in terms of a block-Toeplitz matrix of the two-scale equation, which characterizes refinable functions. Refinable functions play an importa
Curvelet
Curvelets are a non-adaptive technique for multi-scale object representation. Being an extension of the wavelet concept, they are becoming popular in similar fields, namely in image processing and sci
ICER
ICER is a wavelet-based image compression file format used by the NASA Mars Rovers. ICER has both lossy and lossless compression modes. The Mars Exploration Rovers Spirit and Opportunity both used ICE
Mathieu wavelet
The Mathieu equation is a linear second-order differential equation with periodic coefficients. The French mathematician, E. Léonard Mathieu, first introduced this family of differential equations, no
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. As with other wavelet transforms, a key advant
Wavelet transform modulus maxima method
The wavelet transform modulus maxima (WTMM) is a method for detecting the fractal dimension of a signal. More than this, the WTMM is capable of partitioning the time and scale domain of a signal into
Diffusion wavelets
Diffusion wavelets are a fast multiscale framework for the analysis of functions on discrete (or discretized continuous) structures like graphs, manifolds, and point clouds in Euclidean space. Diffusi
Bandelet (computer science)
Bandelets are an orthonormal basis that is adapted to geometric boundaries. Bandelets can be interpreted as a warped wavelet basis. The motivation behind bandelets is to perform a transform on functio
Dirac (video compression format)
Dirac is an open and royalty-free video compression format, specification and system developed by BBC Research & Development. Schrödinger and dirac-research (formerly just called "Dirac") are open and
Prolate spheroidal wave function
The prolate spheroidal wave functions are eigenfunctions of the Laplacian in prolate spheroidal coordinates, adapted to boundary conditions on certain ellipsoids of revolution (an ellipse rotated arou
In digital signal processing, a quadrature mirror filter is a filter whose magnitude response is the mirror image around of that of another filter. Together these filters, first introduced by Croisier
Lifting scheme
The lifting scheme is a technique for both designing wavelets and performing the discrete wavelet transform (DWT). In an implementation, it is often worthwhile to merge these steps and design the wave
Shearlet
In applied mathematical analysis, shearlets are a multiscale framework which allows efficient encoding of anisotropic features in multivariate problem classes. Originally, shearlets were introduced in
In the mathematical topic of wavelet theory, the cascade algorithm is a numerical method for calculating function values of the basic scaling and wavelet functions of a discrete wavelet transform usin
List of wavelet-related transforms
A list of wavelet related transforms: * Continuous wavelet transform (CWT) * Discrete wavelet transform (DWT) * Multiresolution analysis (MRA) * Lifting scheme * Binomial QMF (BQMF) * Fast wavel
Scale co-occurrence matrix
Scale co-occurrence matrix (SCM) is a method for image feature extraction within scale space after wavelet transformation, proposed by Wu Jun and Zhao Zhongming (Institute of Remote Sensing Applicatio
Second-generation wavelet transform
In signal processing, the second-generation wavelet transform (SGWT) is a wavelet transform where the filters (or even the represented wavelets) are not designed explicitly, but the transform consists
Strömberg wavelet
In mathematics, the Strömberg wavelet is a certain orthonormal wavelet discovered by Jan-Olov Strömberg and presented in a paper published in 1983. Even though the Haar wavelet was earlier known to be
Spline wavelet
In the mathematical theory of wavelets, a spline wavelet is a wavelet constructed using a spline function. There are different types of spline wavelets. The interpolatory spline wavelets introduced by
Non-linear multi-dimensional signal processing
In signal processing, nonlinear multidimensional signal processing (NMSP) covers all signal processing using nonlinear multidimensional signals and systems. Nonlinear multidimensional signal processin
Fast wavelet transform
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 w
Dual wavelet
In mathematics, a dual wavelet is the dual to a wavelet. In general, the wavelet series generated by a square-integrable function will have a dual series, in the sense of the Riesz representation theo
Legendre wavelet
In functional analysis, compactly supported wavelets derived from Legendre polynomials are termed Legendre wavelets or spherical harmonic wavelets. Legendre functions have widespread applications in w
Fractional wavelet transform
Fractional wavelet transform (FRWT) is a generalization of the classical wavelet transform (WT). This transform is proposed in order to rectify the limitations of the WT and the fractional Fourier tra
Wavelet for multidimensional signals analysis
Wavelets are often used to analyse piece-wise smooth signals. Wavelet coefficients can efficiently represent a signal which has led to data compression algorithms using wavelets. Wavelet analysis is e
Meyer wavelet
The Meyer wavelet is an orthogonal wavelet proposed by Yves Meyer. As a type of a continuous wavelet, it has been applied in a number of cases, such as in adaptive filters, fractal random fields, and
Progressive Graphics File
PGF (Progressive Graphics File) is a wavelet-based bitmapped image format that employs lossless and lossy data compression. PGF was created to improve upon and replace the JPEG format. It was develope
Refinable function
In mathematics, in the area of wavelet analysis, a refinable function is a function which fulfils some kind of self-similarity. A function is called refinable with respect to the mask if This conditio
Stationary wavelet transform
The Stationary wavelet transform (SWT) is a wavelet transform algorithm designed to overcome the lack of translation-invariance of the discrete wavelet transform (DWT). Translation-invariance is achie
Generalized lifting
No description available.
Harmonic wavelet transform
In the mathematics of signal processing, the harmonic wavelet transform, introduced by in 1993, is a wavelet-based linear transformation of a given function into a time-frequency representation. It co
Pixlet
Pixlet is a video codec created by Apple and based on wavelets, designed to enable viewing of full-resolution, HD movies in real time at low DV data rates. According to Apple's claims, it allows for a
Gabor atom
In applied mathematics, Gabor atoms, or Gabor functions, are functions used in the analysis proposed by Dennis Gabor in 1946 in which a family of functions is built from translations and modulations o
Poisson wavelet
In mathematics, in functional analysis, several different wavelets are known by the name Poisson wavelet. In one context, the term "Poisson wavelet" is used to denote a family of wavelets labeled by t
Complex wavelet transform
The complex wavelet transform (CWT) is a complex-valued extension to the standard discrete wavelet transform (DWT). It is a two-dimensional wavelet transform which provides multiresolution, sparse rep
Coiflet
Coiflets are discrete wavelets designed by Ingrid Daubechies, at the request of Ronald Coifman, to have scaling functions with vanishing moments. The wavelet is near symmetric, their wavelet functions
Dynamic link matching is a graph-based system for image recognition. It uses wavelet transformations to encode incoming image data.
Contourlet
Contourlets form a multiresolution directional tight frame designed to efficiently approximate images made of smooth regions separated by smooth boundaries. The contourlet transform has a fast impleme
Embedded Zerotrees of Wavelet transforms
Embedded Zerotrees of Wavelet transforms (EZW) is a lossy image compression algorithm. At low bit rates, i.e. high compression ratios, most of the coefficients produced by a subband transform (such as
Wavelet modulation
Wavelet modulation, also known as fractal modulation, is a modulation technique that makes use of wavelet transformations to represent the data being transmitted. One of the objectives of this type of
Wavelet packet decomposition
Originally known as optimal subband tree structuring (SB-TS), also called wavelet packet decomposition (WPD)(sometimes known as just wavelet packets or subband tree), is a wavelet transform where the
Wavelet
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of
WaveLab (mathematics software)
WaveLab is a collection of MATLAB functions for wavelet analysis. Following the success of WaveLab package, there is now the availability of CurveLab and ShearLab. * v * t * e * v * t * e
JPEG 2000
JPEG 2000 (JP2) is an image compression standard and coding system. It was developed from 1997 to 2000 by a Joint Photographic Experts Group committee chaired by Touradj Ebrahimi (later the JPEG presi