Animation showing the compactly supported cardinal B-spline wavelets of orders 1, 2, 3, 4 and 5.
In the mathematical theory of wavelets, a spline wavelet is a wavelet constructed using a spline function.[1] There are different types of spline wavelets. The interpolatory spline wavelets introduced by C.K. Chui and J.Z. Wang are based on a certain spline interpolation formula.[2] Though these wavelets are orthogonal, they do not have compact supports. There is a certain class of wavelets, unique in some sense, constructed using B-splines and having compact supports. Even though these wavelets are not orthogonal they have some special properties that have made them quite popular.[3] The terminology spline wavelet is sometimes used to refer to the wavelets in this class of spline wavelets. These special wavelets are also called B-spline wavelets and cardinal B-spline wavelets.[4] The Battle-Lemarie wavelets are also wavelets constructed using spline functions.[5]
^Michael Unser (1997). Aldroubi, Akram; Laine, Andrew F.; Unser, Michael A. (eds.). "Ten good reasons for using spline wavelets" (PDF). Proc. SPIE Vol. 3169, Wavelets Applications in Signal and Image Processing V. Wavelet Applications in Signal and Image Processing V. 3169: 422–431. Bibcode:1997SPIE.3169..422U. doi:10.1117/12.292801. S2CID 12705597. Retrieved 21 December 2014.
^Chui, Charles K, and Jian-zhong Wang (1991). "A cardinal spline approach to wavelets" (PDF). Proceedings of the American Mathematical Society. 113 (3): 785–793. doi:10.2307/2048616. JSTOR 2048616. Retrieved 22 January 2015.{{cite journal}}: CS1 maint: multiple names: authors list (link)
^Charles K. Chui and Jian-Zhong Wang (April 1992). "On Compactly Supported Spline Wavelets and a Duality Principle" (PDF). Transactions of the American Mathematical Society. 330 (2): 903–915. doi:10.1090/s0002-9947-1992-1076613-3. Retrieved 21 December 2014.
^Charles K Chui (1992). An Introduction to Wavelets. Academic Press. p. 177.
^Ingrid Daubechies (1992). Ten Lectures on Wavelets. Philadelphia: Society for Industrial and Applied Mathematics. pp. 146–153. ISBN 9780898712742.
wavelets, a splinewavelet is a wavelet constructed using a spline function. There are different types of splinewavelets. The interpolatory spline wavelets...
Lindeberg (2015). The Mexican hat wavelet can also be approximated by derivatives of cardinal B-splines. Morlet wavelet "Archived copy" (PDF). Archived...
histograms, other types of density estimators include parametric, spline, wavelet and Fourier series. Kernel density estimators were first introduced...
box splines are piecewise polynomial functions of several variables. Box splines are considered as a multivariate generalization of basis splines (B-splines)...
Discrete interpolatory splines have been used to construct biorthogonal wavelets. Tom Lyche (1979). "Discrete Cubic Spline Interpolation". BIT. 16 (3):...
surfaces together M-spline — a non-negative spline I-spline — a monotone spline, defined in terms of M-splines Smoothing spline — a spline fitted smoothly...
The error in some other methods, including polynomial interpolation and spline interpolation (described below), is proportional to higher powers of the...
function, either by windowing or by giving a spline approximation, either by cubics or higher order splines. In the case of windowed sinc filters, the frequency...
mathematician Charles Hermite (1822–1901): Cubic Hermite spline, a type of third-degree spline Gauss–Hermite quadrature, an extension of Gaussian quadrature...
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...
orthogonal wavelet is a wavelet whose associated wavelet transform is orthogonal. That is, the inverse wavelet transform is the adjoint of the wavelet transform...
filter: Spline filters ISO 16610-68: Linear areal filter: End-effects (planned for the future) ISO 16610-69: Linear areal filter: Splinewavelets ISO 16610-70:...
algorithms for step detection are therefore best understood as either 0-degree spline fitting, or level set recovery, methods. When there are only a few unique...
recent work on model-free analyses, wavelet transform based methods (for example locally stationary wavelets and wavelet decomposed neural networks) have...
were dedicated to wavelets and splines, specifically to hex-splines, isotropic polyharmonic B-splinewavelets, and operator wavelets. This research also...
(Engle, Granger, Rice and Weiss, 1986). They also applied the smoothing spline technique for their research. There was a case of application of partially...
basis-functions are used along with new basis functions, such as splines, radial basis functions, and wavelets. These families of basis functions offer a more parsimonious...
)=\left(\|\mathbf {v} -\mathbf {c} \|^{2}+a^{2}\right)^{-{\frac {1}{2}}}} Polyharmonic splines where c {\displaystyle \mathbf {c} } is the vector representing the function...
Global Information