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A frequency-spatial dual perception network for efficient and accurate medical image segmentation. [PDF]
Sci RepChen D, Wu J, Zhang XY, Wang DH.
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Haar Wavelets in Data Analysis
Advanced Materials Research, 2010One century ago (1910), the Hungarian mathematician Alfred Haar introduced the simplest wavelets in approximation theory, which are now known as the Haar wavelets. This type of wavelets can effectively be used to fit data in statistical applications.
Yu Qin Sun +2 more
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Crystallographic Haar Wavelets
Journal of Fourier Analysis and Applications, 2011Let \(\Gamma\) be a \(d\)-dimensional crystallographic group and let \(a:\,{\mathbb R}^d \to {\mathbb R}^d\) be an expanding affine map. By definition, \((\Gamma,a)\)-crystallographic multiwavelets form a finite set of functions \(\{\psi^1,\ldots, \psi^L\}\), which generate an orthonormal basis, a Riesz basis or a Parseval frame for \(L^1({\mathbb R}^d)
González, Alfredo L. +1 more
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Journal of Interdisciplinary Mathematics, 2001
Abstract In this paper is discussed the numerical approximation of differential operators using Haar wavelet bases and their spline-derivatives. It is shown how to smooth the Haar family of wavelets using splines, and to compute the derivatives of the Haar function using the splines.
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Abstract In this paper is discussed the numerical approximation of differential operators using Haar wavelet bases and their spline-derivatives. It is shown how to smooth the Haar family of wavelets using splines, and to compute the derivatives of the Haar function using the splines.
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Applied Mathematics and Computation, 2004
The authors give a detailed description of the Haar wavelet transform associated with non-uniform partitions of the real line. Algorithms for decomposition and reconstruction are studied.
François Dubeau +2 more
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The authors give a detailed description of the Haar wavelet transform associated with non-uniform partitions of the real line. Algorithms for decomposition and reconstruction are studied.
François Dubeau +2 more
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WEIGHTED HAAR WAVELETS ON THE SPHERE
International Journal of Wavelets, Multiresolution and Information Processing, 2007Starting from the one-dimensional Haar wavelets on the interval [0,1], we construct spherical Haar wavelets which are orthogonal with respect to a given scalar product. This scalar product induces a norm which is equivalent to the usual ‖ · ‖2norm of L2(𝕊2).
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Wavelets in Generalized Haar Spaces
Journal of Mathematical Sciences, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Journal of Physics A: Mathematical and General, 1996
Summary: We construct a new type of Haar wavelets, called \(\tau\)-wavelets of Haar, using the arithmetics of the solutions \(\tau=\frac 12 (1+\sqrt{5})\) and \(\sigma=\frac 12 (1-\sqrt{5})\) of the algebraic equation \(x^2=x+1\).
Gazeau, J.-P., Patera, J.
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Summary: We construct a new type of Haar wavelets, called \(\tau\)-wavelets of Haar, using the arithmetics of the solutions \(\tau=\frac 12 (1+\sqrt{5})\) and \(\sigma=\frac 12 (1-\sqrt{5})\) of the algebraic equation \(x^2=x+1\).
Gazeau, J.-P., Patera, J.
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The Haar wavelets operational matrix of integration
International Journal of Systems Science, 1996The Haar wavelets operational matrix of integration P is derived, which is similar to those previously derived for other types of orthogonal functions such as Walsh, block-pulse, Laguerre, Legendre and Chebyshev. A general procedure of forming this matrix P is summarized.
Jin-Sheng Guf, Wei-Sun Jiang
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Int-Haar: Improving Precision of the Haar Interval Wavelet Extension
2013 2nd Workshop-School on Theoretical Computer Science, 2013This work describes the interval extension of the Haar Wavelet Transform (HWT), implemented with C-XSC, being the first step on the development of the Int-DWTs library, which will provide interval results for several Discrete Wavelet Transforms (DWTs).
Vinicius R. dos Santos +3 more
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