Wavelet Analysis: A notation problem in this paper
$begingroup$
Because of my research work, I am reading this paper: PDE net. But I ran into a notation problem: In definition 2.1, I do not understand how $textbf{q}[ textbf{k} ]$ yields a real number. Therefore, I could not verify the authors' claims about the order of sum rules of the Haar wavelet frame filter bank and also the filter
begin{equation*}
textbf{q} = begin{pmatrix}
1 & 0 & -1 \
2 & 0 & -2 \
1 & 0 & -1
end{pmatrix}
end{equation*}
I checked their citations and some other literatures, but most of them just said ${textbf{q}[textbf{k}]}$ is a sequence of real numbers, which does not help me to understand the order of sum rules at all. I am grateful if anyone could give me some hint about this notation.
wavelets
asked Jan 14 at 7:39
BM YoonBM Yoon
283
$endgroup$
add a comment |
$begingroup$
Because of my research work, I am reading this paper: PDE net. But I ran into a notation problem: In definition 2.1, I do not understand how $textbf{q}[ textbf{k} ]$ yields a real number. Therefore, I could not verify the authors' claims about the order of sum rules of the Haar wavelet frame filter bank and also the filter
begin{equation*}
textbf{q} = begin{pmatrix}
1 & 0 & -1 \
2 & 0 & -2 \
1 & 0 & -1
end{pmatrix}
end{equation*}
I checked their citations and some other literatures, but most of them just said ${textbf{q}[textbf{k}]}$ is a sequence of real numbers, which does not help me to understand the order of sum rules at all. I am grateful if anyone could give me some hint about this notation.
wavelets
asked Jan 14 at 7:39
BM YoonBM Yoon
283
$endgroup$
1
$begingroup$
Since $k in mathbb{Z}^2$, the obvious guess is to take $k$ as a pair of indices into the matrix, and 0 if it's outside the bounds of the matrix. Does not that work?
$endgroup$
– Ted
Jan 14 at 8:14
$begingroup$
It works! I can't believe the authors put it in this way! I have been guessing it is about convolution at $textbf{k}$. Thank you so much.
$endgroup$
– BM Yoon
Jan 14 at 8:29
add a comment |
$begingroup$
Because of my research work, I am reading this paper: PDE net. But I ran into a notation problem: In definition 2.1, I do not understand how $textbf{q}[ textbf{k} ]$ yields a real number. Therefore, I could not verify the authors' claims about the order of sum rules of the Haar wavelet frame filter bank and also the filter
begin{equation*}
textbf{q} = begin{pmatrix}
1 & 0 & -1 \
2 & 0 & -2 \
1 & 0 & -1
end{pmatrix}
end{equation*}
I checked their citations and some other literatures, but most of them just said ${textbf{q}[textbf{k}]}$ is a sequence of real numbers, which does not help me to understand the order of sum rules at all. I am grateful if anyone could give me some hint about this notation.
wavelets
asked Jan 14 at 7:39
BM YoonBM Yoon
283
$endgroup$
Because of my research work, I am reading this paper: PDE net. But I ran into a notation problem: In definition 2.1, I do not understand how $textbf{q}[ textbf{k} ]$ yields a real number. Therefore, I could not verify the authors' claims about the order of sum rules of the Haar wavelet frame filter bank and also the filter
begin{equation*}
textbf{q} = begin{pmatrix}
1 & 0 & -1 \
2 & 0 & -2 \
1 & 0 & -1
end{pmatrix}
end{equation*}
I checked their citations and some other literatures, but most of them just said ${textbf{q}[textbf{k}]}$ is a sequence of real numbers, which does not help me to understand the order of sum rules at all. I am grateful if anyone could give me some hint about this notation.
wavelets
wavelets
asked Jan 14 at 7:39
BM YoonBM Yoon
283
asked Jan 14 at 7:39
BM YoonBM Yoon
283
asked Jan 14 at 7:39
BM YoonBM Yoon
283
asked Jan 14 at 7:39
BM YoonBM Yoon
283
asked Jan 14 at 7:39
BM YoonBM Yoon
283
283
1
$begingroup$
Since $k in mathbb{Z}^2$, the obvious guess is to take $k$ as a pair of indices into the matrix, and 0 if it's outside the bounds of the matrix. Does not that work?
$endgroup$
– Ted
Jan 14 at 8:14
$begingroup$
It works! I can't believe the authors put it in this way! I have been guessing it is about convolution at $textbf{k}$. Thank you so much.
$endgroup$
– BM Yoon
Jan 14 at 8:29
add a comment |
1
$begingroup$
Since $k in mathbb{Z}^2$, the obvious guess is to take $k$ as a pair of indices into the matrix, and 0 if it's outside the bounds of the matrix. Does not that work?
$endgroup$
– Ted
Jan 14 at 8:14
$begingroup$
It works! I can't believe the authors put it in this way! I have been guessing it is about convolution at $textbf{k}$. Thank you so much.
$endgroup$
– BM Yoon
Jan 14 at 8:29
1
1
$begingroup$
Since $k in mathbb{Z}^2$, the obvious guess is to take $k$ as a pair of indices into the matrix, and 0 if it's outside the bounds of the matrix. Does not that work?
$endgroup$
– Ted
Jan 14 at 8:14
$begingroup$
Since $k in mathbb{Z}^2$, the obvious guess is to take $k$ as a pair of indices into the matrix, and 0 if it's outside the bounds of the matrix. Does not that work?
$endgroup$
– Ted
Jan 14 at 8:14
$begingroup$
It works! I can't believe the authors put it in this way! I have been guessing it is about convolution at $textbf{k}$. Thank you so much.
$endgroup$
– BM Yoon
Jan 14 at 8:29
$begingroup$
It works! I can't believe the authors put it in this way! I have been guessing it is about convolution at $textbf{k}$. Thank you so much.
$endgroup$
– BM Yoon
Jan 14 at 8:29
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3072953%2fwavelet-analysis-a-notation-problem-in-this-paper%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3072953%2fwavelet-analysis-a-notation-problem-in-this-paper%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
$begingroup$
Since $k in mathbb{Z}^2$, the obvious guess is to take $k$ as a pair of indices into the matrix, and 0 if it's outside the bounds of the matrix. Does not that work?
$endgroup$
– Ted
Jan 14 at 8:14
$begingroup$
It works! I can't believe the authors put it in this way! I have been guessing it is about convolution at $textbf{k}$. Thank you so much.
$endgroup$
– BM Yoon
Jan 14 at 8:29