# Tagged Questions

For questions related to wavelets and wavelet theory

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### What mathematical background is preliminary for reading and understanding books/papers on wavelets?

Please excuse my english. I have had the following math courses for mechatronics engineering education: Calculus (single and multivariable) Linear algebra (introductory) Differential equations (ode'...
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### Why is this true about MRA-wavelets?

In the article Characterization of wavelets and MRA wavelets on local fields of positive characteristic, in page 11, As seen in the picture, The author refers to 16(Multiresolution analysis on local ...
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### How theorem 3.1 is a consequence of lemmas 3.2-3.4?

In the article "Tight wavelet frames on local fields", the author states that "Theorem 3.1 is an easy consequence of lemmas 3.2-3.4". How?
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### The range of the coefficients of 2 level Wavelet LeGall 5/3 2D transform

As in the title, I am confused about the range of the coefficients of Wavelet LeGall 5/3 (has to be exact this filter) 2D transform (only for a 8*8 block) if the value of the input matrix are within ...
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### Wavelet or FFT for Transient signal analysis?

For now I use FFT to analyze the response of an electrical system to some transient signal. The transient signal is $x(t)$, which translates to $X(w)$ in the frenquency domain. On the other hand I ...
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### Undecimated Wavelet Transform (a trous algorithm) - how to determine 'anchor'/'center' of convolution filter

i am currently implementing the 'Undecimated Wavelet Transform' with the 'a trous' algorithm. See e.g. http://www.znu.ac.ir/data/members/fazli_saeid/DIP/Paper/ISSUE2/04060954_2.pdf, section II-A. As ...
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### What is the precise mathematical definition of what a wavelet is and what is its relation to linear algebra?

I was reading on wavelets and it seems that its hard to find a precise mathematical definition of what this concept is. My confusion first arose due to Gilbert Stang's linear algebra book. In ...
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### Significance of orthonormal basis in wavelet analysis

I've recently been looking into wavelet analysis and I have the question: What is the importance of wavelets having an orthogonal basis, say as opposed to a bi-orthogonal basis or otherwise? I'm ...
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### How to prove that $f(t)=t\sin (\frac{1}{t})$ is 1-Hölder continuous for fixed $t_0 \in [-1,1]$?

How to prove that $f(t)=t\sin (\frac{1}{t})$ is 1-Hölder continuous (Lipschitz continuous) for fixed $t_0 \in [-1,1]$? $f(t)$ is defined as $0$ at $t_0 =0$. That is, for $t_0 \in [-1,1]$, there ...
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### How is the study of wavelets not just a special case of Fourier analysis?

As far as I can tell, "wavelets" is just a neologism for certain "non-smooth" families of functions which constitute orthonormal bases/families for $L^2[0,1]$. How is wavelet analysis anything new ...
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### Wavelet reference for PDE

Can anyone recommend a very readable introduction to wavelets for use in theoretical PDE/harmonic analysis? I'm frustrated with the account in Lemarie-Rieusset's Navier-Stokes book since he provides ...
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### Is there any approach to computer vision that doesn't make use of geometry?

I've long been interested in applying my background in functional analysis (especially wavelets) and other related areas to actually create something with "real world" value (not that I don't enjoy ...
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### What different between huffman and EBCOT?

I have a question about entropy coding and Image compression. Huffman coding and EBCOT coding are entropy coding. correct or not? I knew about huffman coding but I don't know EBCOT, How it working?...
Let $\mathbb{K}$ be a local field. Definition of local field: Let $\mathbb{K}$ be a field and a topological space. Then $\mathbb{K}$ is called a locally compact field if both $\mathbb{K}^+$ ...