Questions tagged [wavelet]
Referring to the study of brief oscillations whose amplitude grows and decays in a finite time.
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Dimensionality reduction between discrete wavelet families
I have what it may be a ridiculous question (since I don't know much about wavelets), but here I go.
I am using different Discrete Wavelet families to extract texture features from images. I plan to ...
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Numerical evaluation of Fourier transform of a scaling function
Given a set of filter taps $\{h_n\}_{n=0}^{m-1}$, define a scaling function $\phi$ by $$\phi(x) = \sqrt{2}\sum_{n} h_n \phi(2x-n).$$
In keeping with the notation from Daubechies "Ten Lectures on ...
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Wrong Boundary Conditions Result Using Wavelet Collocation
I have a functional $S$,
$$S = \int_{x_0}^{x_b} dx \frac{1}{z(x)^d} \sqrt{1 + \frac{z'(x)^2}{f(z)}}, \qquad f(z) = 1-\left(\frac{z(x)}{z_h}\right)^{d+1}
$$
where $d=3$ is the dimension and $z_h$ is ...
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Questions on Daubechies wavelets
Is the refinement equation for the orthonormal Daubechies scaling function
$$\phi(x) = \sqrt{2} \sum_n h_n \phi(2x-n) \;?$$
The filter coefficients for Daubechies wavelets have been given e.g. in
this ...
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Advantage of fractional Fourier transform over multiscale wavelet?
What could be the arguments of using fractional Fourier transform instead of multiscale wavelet for data analysis ?
Optimization of the good time-frequency domain parameter? good in the sens of best ...
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Open Source Packages Implementing Continuous Wavelet and Scaling Functions
I'm looking for an open source software package that provides a fast evaluation of continuous Daubechies/Symmlet wavelet/scaling functions.
GSL only has the discrete wavelets, and PyWavelets comes ...
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How to construct Diffusion Wavelet Packets?
I understand the idea of constructing Low-pass and High-pass filters as a projection on the Numerical Range and Numerical Kernel of dyadic powers of a diffusion operator in the work Diffusion Wavelet ...
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Can Mallat's pyramidal algorithm be extended to non-power of 2 input sizes?
Mallat's pyramidal algorithm for the discrete wavelet transform operates on power-of-2 vector lengths. Can it be extended to work on inputs of any size without resorting to zero padding?
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What is the difference between the curl component, and the divergence-free component, of a vector field?
The term divergence-free sounds more general and appears particularly in wavelet-related approaches to the Navier-Stokes equations. However I have yet to find a discussion focusing on the distinction, ...
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Reduction of linear system with decaying unknown
I have a linear system of equations $Ax = b$ where the number of unknowns $N$ is intractably large but the right-hand side has only small support and the unknown $x$ is known to decay exponentially. I ...
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Adjoint of the MATLAB $\tt dwt3$ (3D wavelet transform) operator
How do I compute the adjoint of MATLAB's dwt3 operator?
In other words, how do I compute the adjoint of the linear operator that takes a 3D complex array ...
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Computing 3-term Connection Coefficients for Wavelets
I am trying to calculate the three-term connection coefficients
$$
Λ_{l,m}^{d_1,d_2,d_3} = ∫_{-∞}^∞ φ^{(d_1)}(x) φ^{(d_2)}_l(x) φ^{(d_3)}_m(x) dx
$$
for Daubechies wavelets numerically using Python. ...
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How to add a Ricker Wavelet (Mexican Hat) to a 2D/ 3D fem mesh?
I have a 2D square mesh and a 3D beam shaped mesh and I want to propagate a seismic wave in them. I am trying to simulate them using Open source FEM codes (fenics). I have left the top surface to be ...
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3D Stationary Wavelet Transform implementations
I'm interested in using a SWT to perform Multi Resolution Analysis over 3D data arrays. However I could not find any software package that implements it. The Matlab Toolbox of wavelets (the most ...
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What are the most popular wavelet or tight frame regularizers for image reconstruction problems?
A common approach to image reconstruction is to solve the convex optimization problem
\begin{equation}
\text{minimize} \quad \frac12 \| Ax - b \|^2 + \gamma \| Dx \|_1
\end{equation}
where $b$ is a ...
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wavelet for numerical partial differential equations
Is there a good introduction into wavelet Galerkin schemes for numerical partial (and ordinary) differential equations?
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Spatio-temopral wavelet analysis
Am quite new to wavelet analysis and would like some help. I am performing a spatio-temporal analysis of monthly gridded rainfall data. With PCA, I can reduce the dimension of the rainfall data into a ...
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How to compute the wavelet approximation of a function?
For the function $f(x)=x$, how to compute the wavelet approximation using Haar basis?
I'm new to wavelet, I'm looking for a package which will do something like this
...
user729
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Wavelets frame for $L^2[0,\infty)$
I need a wavelet frame for $L^2[0,\infty)$. Moreover, the wavelet should be twice differentiable and with continuous second order derivatives. Hopefully, the wavelet should have compact support (...
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How can wavelets be applied to PDE?
I would like to learn how wavelet methods can be applied to PDE, but unfortunately I do not know a good resource to learn about this topic.
It seems that many introductions to wavelets focus on ...
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