Questions tagged [wavelet]

Referring to the study of brief oscillations whose amplitude grows and decays in a finite time.

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18
votes
1answer
2k views

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 ...
7
votes
2answers
3k views

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 ...
5
votes
0answers
118 views

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 (...
3
votes
1answer
76 views

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 ...
3
votes
0answers
52 views

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?
3
votes
0answers
120 views

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 ...
2
votes
3answers
90 views

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 ...
2
votes
2answers
331 views

wavelet for numerical partial differential equations

Is there a good introduction into wavelet Galerkin schemes for numerical partial (and ordinary) differential equations?
1
vote
3answers
298 views

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, ...
1
vote
1answer
433 views

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 ...
1
vote
1answer
68 views

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 ...
1
vote
0answers
56 views

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 ...
1
vote
0answers
48 views

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 ...
1
vote
0answers
102 views

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 ...
1
vote
0answers
65 views

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. ...
1
vote
0answers
348 views

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 ...
0
votes
0answers
32 views

Computationally Feasible Wavelet transform algorithms for 1-D data with many samples

I am doing multi resolution analysis on a 1-d Dataset with large amount of samples (few millions). Currently I am experimenting with pywavelets in python but it gets incredibly intensive on ...
0
votes
0answers
38 views

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 ...