The first type of pseudo-splines were introduced by [Daubechies, Han, Ron and Shen, 2003] (DHRS) to construct tight framelets with desired approximation orders via the unitary extension principle of [Ron and Shen, 1997]. In the spirit of the first type of pseudo-splines, we introduce here a new type (the second type) of pseudo-splines to construct symmetric or antisymmetric tight framelets with...

A novel construction of compactly supported orthogonal scaling functions and wavelets with spline functions is presented in this paper. Let [Formula: see text] be the center B-spline of order n, except for the case of order one, we know [Formula: see text] is not orthogonal. But by the formula of orthonormalization procedure, we can construct an orthogonal scaling function corresponding to [For...

This paper is concerned with the construction of biorthogonal multiresolution analyses on [0; 1] such that the corresponding wavelets realize any desired order of moment conditions throughout the interval. Our starting point is the family of biorthogonal pairs consisting of cardinal B-splines and compactly supported dual generators on IR developed by Cohen, Daubechies and Feauveau. In contrast ...

In this article, a novel and efficient collocation method based on Fibonacci wavelets is proposed for the numerical solution of non-linear Hunter–Saxton equation. Firstly, operational matrices integration associated with are constructed by following strategy Chen Hsiao. The merged used to convert given problem into system algebraic equations that can be solved any classical method, such as Newt...

In this paper we construct certain continuous piecewise rational wavelets on arbitrary spherical triangulations, giving explicit expressions of these wavelets. Our wavelets have small support, a fact which is very important in working with large amounts of data, since the algorithms for decomposition, compression and reconstruction deal with sparse matrices. We also give a quasi-interpolant ass...

This paper introduces a novel framework for single-pixel imaging via compressive sensing (CS) in shift-invariant (SI) spaces by exploiting the sparsity property of wavelet representation. We reinterpret acquisition procedure camera as filtering observed signal with continuous-domain functions that lie an SI subspace spanned integer shifts box function. The is modeled arbitrary generator whose s...

A texture classification system is described, based on isotropic polyharmonic B–spline wavelets that identify lung tissue patterns from high–resolution computed tomography (HRCT) images of patients affected with interstitial lung diseases (ILD). Along with several desirable properties for isotropic texture analysis, the nonseparable transform with a quincunx subsambling scheme allows a mean of ...

2 Fast Wavelet Transform The 2D fast wavelet transform can be represented as a convolution of the image with one-dimensional low-pass h(n) and high-pass g(n) filters (see Figure 1). This procedure results in subband images which provide the global context as well as image details at horizontal, vertical and diagonal directions. Therefore, this tool is suitable for representing numerical charact...

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We consider Boolean sums of univariate interpolation operators which define multivariate jth order blending interpolation operators on sparse grids. Sample spaces are defined as range of the blending operators. Sample and wavelet spaces have significantly lower dimension and good approximation order for certain function spaces. Fast decomposition and reconstruction algorithms for bivariate spli...