THE CONSTRUCTION OF A CLASS OF TRIVARIATE NONSEPARABLE COMPACTLY SUPPORTED WAVELETS

2009 ◽  
Vol 07 (03) ◽  
pp. 255-267 ◽  
Author(s):  
YONGDONG HUANG ◽  
SHOUZHI YANG ◽  
ZHENGXING CHENG
Keyword(s):  
General Theory ◽  
Mild Condition ◽  
Scaling Function ◽  
Moment Condition ◽  
Compactly Supported ◽  
Vanishing Moment ◽  
The Scaling Function

In this paper, under a mild condition, the construction of compactly supported [Formula: see text]-wavelets is obtained. Wavelets inherit the symmetry of the corresponding scaling function and satisfy the vanishing moment condition originating in the symbols of the scaling function. An example is also given to demonstrate the general theory.

Design of High Dimensional Nonseparable Compactly Supported Wavelets with Special Dilation Matrix

2012 ◽  
Vol 542-543 ◽  
pp. 547-550
Author(s):  
Lan Li
Keyword(s):  
Mild Condition ◽  
Scaling Function ◽  
New Method ◽  
High Dimensional ◽  
Moment Condition ◽  
Compactly Supported ◽  
Vanishing Moment ◽  
Dilation Matrix ◽  
The Scaling Function

In this paper, a new method to construct the compactly supported M- wavelet under a mild condition are given. The constructed wavelet satisfies the vanishing moment condition which is originated from the symbols of the scaling function.

Construction of a Class of Nonseparable Compactly Supported Wavelets with Special Dilation Matrix in L2(R4)

2011 ◽  
Vol 393-395 ◽  
pp. 659-662
Author(s):  
Na Li
Keyword(s):  
Mild Condition ◽  
Scaling Function ◽  
Moment Condition ◽  
Compactly Supported ◽  
Vanishing Moment ◽  
Dilation Matrix ◽  
Novel Method ◽  
The Scaling Function

In this paper, a novel method to construct the compactly supported wavelet under a mild condition. The constructed wavelet satisfies the vanishing moment condition which is originated from the symbols of the scaling function.

scholarly journals Maximum Vanishing Moment of Compactly Supported B-spline Wavelets

2019 ◽  
pp. 1-8
Author(s):  
Kanchan Lata Gupta ◽  
B. Kunwar ◽  
V. K. Singh
Keyword(s):  
Scaling Function ◽  
Simple Procedure ◽  
Smoothness Property ◽  
Vanishing Moments ◽  
B Spline ◽  
B Splines ◽  
Compactly Supported ◽  
Spline Wavelets ◽  
Vanishing Moment ◽  
Rule Order

Spline function is of very great interest in field of wavelets due to its compactness and smoothness property. As splines have specific formulae in both time and frequency domain, it greatly facilitates their manipulation. We have given a simple procedure to generate compactly supported orthogonal scaling function for higher order B-splines in our previous work. Here we determine the maximum vanishing moments of the formed spline wavelet as established by the new refinable function using sum rule order method.

scholarly journals Multiresolution and wavelets

1994 ◽  
Vol 37 (2) ◽  
pp. 271-300 ◽  
Author(s):  
Rong-Qing Jia ◽  
Zuowei Shen
Keyword(s):  
General Theory ◽  
Vector Fields ◽  
Scaling Function ◽  
Necessary And Sufficient Condition ◽  
Intrinsic Properties ◽  
Orthogonal Wavelets ◽  
Shift Invariant Spaces ◽  
Necessary And Sufficient ◽  
Invariant Spaces ◽  
The Scaling Function

Multiresolution is investigated on the basis of shift-invariant spaces. Given a finitely generated shift-invariant subspace S of L2(ℝd), let Sk be the 2k-dilate of S (k∈ℤ). A necessary and sufficient condition is given for the sequence {Sk}k∈ℤ to fom a multiresolution of L2(ℝd). A general construction of orthogonal wavelets is given, but such wavelets might not have certain desirable properties. With the aid of the general theory of vector fields on spheres, it is demonstrated that the intrinsic properties of the scaling function must be used in constructing orthogonal wavelets with a certain decay rate. When the scaling function is skew-symmetric about some point, orthogonal wavelets and prewavelets are constructed in such a way that they possess certain attractive properties. Several examples are provided to illustrate the general theory.

Riesz basis of wavelets constructed from trigonometric B-splines

2015 ◽  
Vol 13 (04) ◽  
pp. 419-436
Author(s):  
Mahendra Kumar Jena
Keyword(s):  
Differential Operator ◽  
Sobolev Space ◽  
Sobolev Spaces ◽  
Riesz Basis ◽  
Scaling Function ◽  
Wavelet Bases ◽  
B Splines ◽  
Compactly Supported ◽  
The Scaling Function

In this paper, we construct a class of compactly supported wavelets by taking trigonometric B-splines as the scaling function. The duals of these wavelets are also constructed. With the help of these duals, we show that the collection of dilations and translations of such a wavelet forms a Riesz basis of 𝕃2(ℝ). Moreover, when a particular differential operator is applied to the wavelet, it also generates a Riesz basis for a particular generalized Sobolev space. Most of the proofs are based on three assumptions which are mild generalizations of three important lemmas of Jia et al. [Compactly supported wavelet bases for Sobolev spaces, Appl. Comput. Harmon. Anal. 15 (2003) 224–241].

CONSTRUCTION OF COMPACTLY SUPPORTED WAVELETS FROM TRIGONOMETRIC B-SPLINES

2011 ◽  
Vol 09 (05) ◽  
pp. 843-865 ◽  
Author(s):  
M. K. JENA
Keyword(s):  
Convex Hull ◽  
Autocorrelation Function ◽  
Scaling Function ◽  
Partition Of Unity ◽  
B Spline ◽  
B Splines ◽  
Compactly Supported ◽  
Odd Order ◽  
Subdivision Algorithm ◽  
The Scaling Function

We construct a class of semiorthogonal wavelets by taking a normalized trigonometric B-spline of any order as the scaling function. The construction is based on generalized Euler–Frobenius polynomial and generalized autocorrelation function. We also show that the odd order normalized trigonometric B-spline satisfies convex hull property as well as partition of unity property. Moreover, we also present a subdivision algorithm for the convolution of normalized trigonometric B-splines. Several examples of wavelet are also provided.

scholarly journals Adjust of energy with compactly supported orthogonal wavelet for steganographic algorithms using the scaling function

2013 ◽  
Vol 8 (4) ◽  
pp. 157-166 ◽  
Author(s):  
E Carvajal Gaacute mez Blanca ◽  
J Gallegos Funes Francisco ◽  
J Rosales Silva Alberto ◽  
L Loacute pez Bonilla Joseacute
Keyword(s):  
Scaling Function ◽  
Orthogonal Wavelet ◽  
Compactly Supported ◽  
The Scaling Function

Assessing Model Uncertainty for the Scaling Function Inversion of Potential Fields

Geophysics ◽  
2021 ◽  
pp. 1-39
Author(s):  
Mahak Singh Chauhan ◽  
Ivano Pierri ◽  
Mrinal K. Sen ◽  
Maurizio FEDI
Keyword(s):  
Simulated Annealing Algorithm ◽  
Scaling Function ◽  
Vertical Section ◽  
Gravity Data ◽  
Geometric Model ◽  
Salt Dome ◽  
The Body ◽  
Gravity Inversion ◽  
Geometrical Parameters ◽  
The Scaling Function

We use the very fast simulated annealing algorithm to invert the scaling function along selected ridges, lying in a vertical section formed by upward continuing gravity data to a set of altitudes. The scaling function is formed by the ratio of the field derivative by the field itself and it is evaluated along the lines formed by the zeroes of the horizontal field derivative at a set of altitudes. We also use the same algorithm to invert gravity anomalies only at the measurement altitude. Our goal is analyzing the different models obtained through the two different inversions and evaluating the relative uncertainties. One main difference is that the scaling function inversion is independent on density and the unknowns are the geometrical parameters of the source. The gravity data are instead inverted for the source geometry and the density simultaneously. A priori information used for both the inversions is that the source has a known depth to the top. We examine the results over the synthetic examples of a salt dome structure generated by Talwani’s approach and real gravity datasets over the Mors salt dome and the Decorah (USA) basin. For all these cases, the scaling function inversion yielded models with a better sensitivity to specific features of the sources, such as the tilt of the body, and reduced uncertainty. We finally analyzed the density, which is one of the unknowns for the gravity inversion and it is estimated from the geometric model for the scaling function inversion. The histograms over the density estimated at many iterations show a very concentrated distribution for the scaling function, while the density contrast retrieved by the gravity inversion, according to the fundamental ambiguity density/volume, is widely dispersed, this making difficult to assess its best estimate.

NEW AMY AND DELPHI MULTIPLICITY DATA AND THE LOGNORMAL DISTRIBUTION

1991 ◽  
Vol 06 (03) ◽  
pp. 245-257 ◽  
Author(s):  
R. SZWED ◽  
G. WROCHNA ◽  
A.K. WRÓBLEWSKI
Keyword(s):  
Energy Dependence ◽  
Lognormal Distribution ◽  
Scaling Function ◽  
Average Multiplicity ◽  
Linear Functions ◽  
The Mean ◽  
Multiplicity Distributions ◽  
The Scaling Function ◽  
Skewness And Kurtosis

Multiplicity distributions for e+e−→ hadrons recently reported by the AMY and DELPHI collaborations are compared with the data obtained at lower energies. It is proven that the new data obey the KNO-G scaling and the scaling function can be described by the lognormal distribution. The dispersions are linear functions of the mean as for the data measured at lower energies and the standardized moments (such as skewness and kurtosis) are independent of the energy. The energy dependence of the average multiplicity is described by <nch>=β sα−1.

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