scholarly journals Non-equispaced B-spline wavelets

2016 ◽  
Vol 14 (06) ◽  
pp. 1650056 ◽  
Author(s):  
Maarten Jansen
Keyword(s):  
Wavelet Transforms ◽  
Orthogonal Wavelet ◽  
B Spline ◽  
Wavelet Representation ◽  
Spline Wavelets ◽  
New Construction ◽  
Irregular Point ◽  
Interpolating Wavelets ◽  
New Framework ◽  
Orthogonal Wavelet Transform

This paper has three main contributions. The first is the construction of wavelet transforms from B-spline scaling functions defined on a grid of non-equispaced knots. The new construction extends the equispaced, biorthogonal, compactly supported Cohen–Daubechies–Feauveau wavelets. The new construction is based on the factorization of wavelet transforms into lifting steps. The second and third contributions are new insights on how to use these and other wavelets in statistical applications. The second contribution is related to the bias of a wavelet representation. It is investigated how the fine scaling coefficients should be derived from the observations. In the context of equispaced data, it is common practice to simply take the observations as fine scale coefficients. It is argued in this paper that this is not acceptable for non-interpolating wavelets on non-equidistant data. Finally, the third contribution is the study of the variance in a non-orthogonal wavelet transform in a new framework, replacing the numerical condition as a measure for non-orthogonality. By controlling the variances of the reconstruction from the wavelet coefficients, the new framework allows us to design wavelet transforms on irregular point sets with a focus on their use for smoothing or other applications in statistics.

REFINEMENT INDEPENDENT WAVELETS FOR USE IN ADAPTIVE MULTIRESOLUTION SCHEMES

2008 ◽  
Vol 06 (04) ◽  
pp. 521-539 ◽  
Author(s):  
MAARTEN JANSEN
Keyword(s):  
Wavelet Transforms ◽  
Point Sets ◽  
Orthogonal Wavelet ◽  
Multiscale Decomposition ◽  
Irregular Point ◽  
Multiresolution Schemes ◽  
Linear Interpolating

This paper constructs a class of semi-orthogonal and bi-orthogonal wavelet transforms on possibly irregular point sets with the property that the scaling coefficients are independent from the order of refinement. That means that scaling coefficients at a given scale can be constructed with the configuration at that scale only. This property is of particular interest when the refinement operation is data dependent, leading to adaptive multiresolution analyses. Moreover, the proposed class of wavelet transforms are constructed using a sequence of just two lifting steps, one of which contains a linear interpolating prediction operator. This operator easily allows extensions towards directional offsets from predictions, leading to an edge-adaptive nonlinear multiscale decomposition.

ORTHOGONAL WAVELET TRANSFORM OF SIGNAL BASED ON COMPLEX B-SPLINE BASES

2012 ◽  
Vol 10 (06) ◽  
pp. 1250054 ◽  
Author(s):  
XIU-GE ZHU ◽  
BAO-BIN LI ◽  
DENG-FENG LI
Keyword(s):  
Wavelet Transform ◽  
Haar Wavelet ◽  
Orthogonal Wavelet ◽  
Explicit Formulas ◽  
Daubechies Wavelets ◽  
B Spline ◽  
Continuous Signal ◽  
Accurate Computation ◽  
Base Functions ◽  
Orthogonal Wavelet Transform

In this paper, an orthogonal wavelet transform of signal based on complex B-spline bases is given. The new wavelet transform realizes accurate computation of coefficients of complex B-spline base functions. It integrates good properties of orthogonality, symmetry and continuity, and offers better approximations to continuous signal than do the Haar wavelet and Daubechies wavelets. All algorithms of the new orthogonal wavelet transform are based on explicit formulas and easy to be implemented.

scholarly journals Wavelet tools to study intermittency: application to vortex bursting

2009 ◽  
Vol 636 ◽  
pp. 427-453 ◽  
Author(s):  
JORI RUPPERT-FELSOT ◽  
MARIE FARGE ◽  
PHILIPPE PETITJEANS
Keyword(s):  
Wavelet Transform ◽  
Particle Image ◽  
Three Dimensional ◽  
Local Spectrum ◽  
Orthogonal Wavelet ◽  
Wavelet Representation ◽  
Image Velocimetry ◽  
Laminar Channel Flow ◽  
Steady Laminar ◽  
Orthogonal Wavelet Transform

This paper proposes statistical tools adapted to study highly unsteady and inhomogeneous flows, such as vortex bursting. For this, we use the wavelet representation in which each coefficient keeps track of both location and scale, in contrast to Fourier representation which requires keeping the phase of all coefficients to preserve the spatial structure of the flow. Based on the continuous wavelet transform, we propose several diagnostics, such as the local spectrum and the local intermittency measure. We also use the orthogonal wavelet transform to split each flow realization into coherent and incoherent contributions, which are then analysed independently and from which we define the coherency measure. We apply these wavelet tools to analyse the bursting of a three-dimensional stretched vortex immersed in a steady laminar channel flow. The time evolution of the velocity field is measured by particle image velocimetry during several successive bursts.

scholarly journals Performance Comparison of Wavelets Generated from Four Different Orthogonal Transforms for Watermarking With Various Attacks

2013 ◽  
Vol 9 (3) ◽  
pp. 1139-1152 ◽  
Author(s):  
H. B. Kekre ◽  
Tanuja Sarode ◽  
Shachi Natu
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Image Watermarking ◽  
Histogram Equalization ◽  
Performance Comparison ◽  
Orthogonal Wavelet ◽  
Good Comparison ◽  
Orthogonal Transform ◽  
Contrast Stretching ◽  
Orthogonal Wavelet Transform

This paper proposes a watermarking technique using different orthogonal wavelet transforms like Hartley wavelet, Kekrewavelet, Slant wavelet and Real Fourier wavelet transform generated from corresponding orthogonal transform. Theseorthogonal wavelet transforms have been generated using different sizes of component orthogonal transform matrices.For example 256*256 size orthogonal wavelet transform can be generated using 128*128 and 2*2 size componentorthogonal transform. It can also be generated using 64*64 and 4*4, 32*32 and 8*8, 16*16 and 16*16 size componentorthogonal transform matrices. In this paper the focus is to compare the performance of above mentioned transformsgenerated using 128*128 and 2*2 size component orthogonal transform and 64*64 and 4*4 size component orthogonaltransform in digital image watermarking. The other two combinations are not considered as their performance iscomparatively not as good. Comparison shows that wavelet transforms generated using (128,2) combination of orthogonal transform give better performances than wavelet transforms generated using (64,4) combination of orthogonaltransformfor contrast stretching, cropping, Gaussian noise, histogram equalization and resizing attacks. Real Fourierwavelet and Slant wavelet prove to be better for histogram equalization and resizing attack respectively than DCT waveletand Walsh wavelet based watermarking presented in previous work.

scholarly journals Wavelet transforms and their applications to MHD and plasma turbulence: a review

2015 ◽  
Vol 81 (6) ◽  
Author(s):  
Marie Farge ◽  
Kai Schneider
Keyword(s):  
Numerical Simulation ◽  
Wavelet Transform ◽  
Wavelet Analysis ◽  
Turbulent Flows ◽  
Coherent Structures ◽  
Wavelet Transforms ◽  
Three Dimensional ◽  
Plasma Turbulence ◽  
Orthogonal Wavelet ◽  
Orthogonal Wavelet Transform

Wavelet analysis and compression tools are reviewed and different applications for the study of MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics based on the wavelet coefficients. We then show how to extract coherent structures out of fully developed turbulent flows using wavelet-based denoising. Finally some multiscale numerical simulation schemes using wavelets are described. Several examples for analysing, compressing and computing one-, two- and three-dimensional turbulent MHD or plasma flows are presented.

Wavelet Transforms with a Compact Carrier on the Basis of Spline Wavelets

2007 ◽  
Vol 66 (6) ◽  
pp. 505-512
Author(s):  
A. D. Kukharev ◽  
Yu. S. Evstifeev ◽  
V. G. Yakovlev
Keyword(s):  
Wavelet Transforms ◽  
Spline Wavelets

scholarly journals Solution of nonlinear Fredholm-Hammerstein integral equations by using semiorthogonal spline wavelets

2005 ◽  
Vol 2005 (1) ◽  
pp. 113-121 ◽  
Author(s):  
M. Lakestani ◽  
M. Razzaghi ◽  
M. Dehghan
Keyword(s):  
Integral Equations ◽  
Algebraic Equations ◽  
B Spline ◽  
Compactly Supported ◽  
Hammerstein Integral Equations ◽  
Spline Wavelets

Compactly supported linear semiorthogonal B-spline wavelets together with their dual wavelets are developed to approximate the solutions of nonlinear Fredholm-Hammerstein integral equations. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of integral equations to some algebraic equations. The method is computationally attractive, and applications are demonstrated through an illustrative example.

scholarly journals SNR Improvement for Evoked Potential Estimation using Bi – Orthogonal Wavelet Transform

IJARCCE ◽  
2015 ◽  
Vol 4 (8) ◽  
pp. 408-413
Author(s):  
Shailesh M L ◽  
Dr. Anand Jatti ◽  
Madhushree K S ◽  
Siddesh M B
Keyword(s):  
Wavelet Transform ◽  
Evoked Potential ◽  
Orthogonal Wavelet ◽  
Snr Improvement ◽  
Evoked Potential Estimation ◽  
Orthogonal Wavelet Transform
Sign in / Sign up

Export Citation Format

Share Document