Dear all, Wavelet is really hard to learn and master. However I need to learn it by self-study. I have read Martin Vetterli's book and Mallat's book. For both books I can only understand the first 1/3 part of the books. I always understand the Haar example, but after that, math becomes dominant and horrible. I understand that in order to understand the books and learn/master wavelet well, I should have knowledge about Real Analysis, Functional Analysis, Harmonic Analysis, Approximation Thoery. But I have not learned these yet. But I need wavelet for my research and I should understand those papers using multiscale analysis and wavelet. I would appreciate if anybody can provide the following information: 1) any reference books/notes/chapters on wavelet that goes beyond the level of simple Haar example, and including working knowledge of Real Analysis, Functional Analysis, Harmonic Analysis, Approximation Thoery that can let me embark my journey on wavelet. I mean, I know these Real Analysis, Functional Analysis, Harmonic Analysis, Approximation Thoery are important; but I cannot wait only several semesters later after I learned these subjects then I come back to learn wavelet, right? So I am looking for some references that including minimal working knowledge of all these math background in order to understand wavelet. I want a fast yet still good understanding of wavelet math. 2) any reference books/notes/chapters on wavelet that goes beyond the level of simple Haar example, and including worked example on multiscale image processing, etc. I found a problem, in books they always give simple examples such as Haar, and also show some code for wavelet denoising by thresholding, but these are really simple; In reality when people write research paper using wavelet, they often write very concisely about the wavelet part and how it is used in aid of analysis and show only simulation results but no implementation details, not to say source codes, etc. So there are two extreme: either too simple example in books/tutorials or too concise in real world research papers... The above two problems have perplexed me for quite long. I hope the math gurus and wavelet veterans in this forum can give me some pointers and share with me some of your experiences... Thank you very much and I really appreciate your help! -Joenyim

# seeking advice on study wavelet -- any good wavelet learning material

Started by ●March 23, 2004

Reply by ●March 23, 20042004-03-23

Joenyim Kim wrote:> Dear all, > > Wavelet is really hard to learn and master. However I need to learn it by > self-study.Have you looked at http://mathforum.org/library/view/16414.html or http://www.amara.com/current/wavelet.html ? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������

Reply by ●March 24, 20042004-03-24

Joenyim Kim wrote:> Dear all, > > Wavelet is really hard to learn and master. However I need to learn it by > self-study. I have read Martin Vetterli's book and Mallat's book. For both > books I can only understand the first 1/3 part of the books. I always > understand the Haar example, but after that, math becomes dominant and > horrible. > > I understand that in order to understand the books and learn/master wavelet > well, I should have knowledge about Real Analysis, Functional Analysis, > Harmonic Analysis, Approximation Thoery. But I have not learned these yet. > But I need wavelet for my research and I should understand those papers > using multiscale analysis and wavelet.You have my sympathy (not that it'll do you much good). My experience has been very similar to yours. The Wavelet module in Matlab helps by showing examples of input and output. Gib

Reply by ●March 24, 20042004-03-24

Hi Joenyim, There is a really good book (at least in my opinion) on the subject by Gilbert Strang and Truong Nguyen. It's called Wavelets and Filter Banks. If you are have good DSP bkgd, you can also reference the book by P.P. Vaidyanathan called Multirate Systems and Filter Banks. Reading these two, I found I can better understand the material in the other two books you've mentioned. hth, cf Joenyim Kim wrote:> > Dear all, > > Wavelet is really hard to learn and master. However I need to learn it by > self-study. I have read Martin Vetterli's book and Mallat's book. For both > books I can only understand the first 1/3 part of the books. I always > understand the Haar example, but after that, math becomes dominant and > horrible. > > I understand that in order to understand the books and learn/master wavelet > well, I should have knowledge about Real Analysis, Functional Analysis, > Harmonic Analysis, Approximation Thoery. But I have not learned these yet. > But I need wavelet for my research and I should understand those papers > using multiscale analysis and wavelet. > > I would appreciate if anybody can provide the following information: > > 1) any reference books/notes/chapters on wavelet that goes beyond the level > of simple Haar example, and including working knowledge of Real Analysis, > Functional Analysis, Harmonic Analysis, Approximation Thoery that can let me > embark my journey on wavelet. > > I mean, I know these Real Analysis, Functional Analysis, Harmonic Analysis, > Approximation Thoery are important; but I cannot wait only several semesters > later after I learned these subjects then I come back to learn wavelet, > right? > > So I am looking for some references that including minimal working knowledge > of all these math background in order to understand wavelet. I want a fast > yet still good understanding of wavelet math. > > 2) any reference books/notes/chapters on wavelet that goes beyond the level > of simple Haar example, and including worked example on multiscale image > processing, etc. > > I found a problem, in books they always give simple examples such as Haar, > and also show some code for wavelet denoising by thresholding, but these are > really simple; > > In reality when people write research paper using wavelet, they often write > very concisely about the wavelet part and how it is used in aid of analysis > and show only simulation results but no implementation details, not to say > source codes, etc. > > So there are two extreme: either too simple example in books/tutorials or > too concise in real world research papers... > > The above two problems have perplexed me for quite long. I hope the math > gurus and wavelet veterans in this forum can give me some pointers and share > with me some of your experiences... > > Thank you very much and I really appreciate your help! > > -Joenyim

Reply by ●March 24, 20042004-03-24

On Tue, 23 Mar 2004 19:38:19 -0500, "Joenyim Kim" <jeonyimkim80@yahoo.com> wrote:>Dear all, > >Wavelet is really hard to learn and master. However I need to learn it by >self-study. I have read Martin Vetterli's book and Mallat's book. For both >books I can only understand the first 1/3 part of the books. I always >understand the Haar example, but after that, math becomes dominant and >horrible. > >I understand that in order to understand the books and learn/master wavelet >well, I should have knowledge about Real Analysis, Functional Analysis, >Harmonic Analysis, Approximation Thoery. But I have not learned these yet. >But I need wavelet for my research and I should understand those papers >using multiscale analysis and wavelet. >[...]> >I mean, I know these Real Analysis, Functional Analysis, Harmonic Analysis, >Approximation Thoery are important; but I cannot wait only several semesters >later after I learned these subjects then I come back to learn wavelet, >right?This is like you say you need to learn calculus, but you don't have time to learn algebra and trigonometry yet... People have already given you various references - depending on what _sort_ of reasearch you're talking about they may suffice to show you how to use wavelets without really understanding them. But if you actually want to _understand_ how wavelets work you _need_ to learn some of the prerequisites, that's just the way it is! (What sort of research are you doing?) ************************ David C. Ullrich

Reply by ●March 25, 20042004-03-25

David C. Ullrich <ullrich@math.okstate.edu> wrote in message news:<h813601i2lm2mbrh8n8j1f9cor9bvrkq11@4ax.com>...> On Tue, 23 Mar 2004 19:38:19 -0500, "Joenyim Kim" > <jeonyimkim80@yahoo.com> wrote: > > >Dear all, > > > >Wavelet is really hard to learn and master. However I need to learn it by > >self-study. I have read Martin Vetterli's book and Mallat's book. For both > >books I can only understand the first 1/3 part of the books. I always > >understand the Haar example, but after that, math becomes dominant and > >horrible. > > > >I understand that in order to understand the books and learn/master wavelet > >well, I should have knowledge about Real Analysis, Functional Analysis, > >Harmonic Analysis, Approximation Thoery. But I have not learned these yet. > >But I need wavelet for my research and I should understand those papers > >using multiscale analysis and wavelet. > > > [...] > > > >I mean, I know these Real Analysis, Functional Analysis, Harmonic Analysis, > >Approximation Thoery are important; but I cannot wait only several semesters > >later after I learned these subjects then I come back to learn wavelet, > >right? > > This is like you say you need to learn calculus, but you don't have > time to learn algebra and trigonometry yet... > > People have already given you various references - depending on > what _sort_ of reasearch you're talking about they may suffice > to show you how to use wavelets without really understanding > them. But if you actually want to _understand_ how wavelets > work you _need_ to learn some of the prerequisites, that's > just the way it is! (What sort of research are you doing?) > > > > ************************ > > David C. UllrichHi, I just want to have a one-stop reference giving enough background information whenever neccessary to understand the wavelet itself. The ideal reference will have just enough comprehensive background information for understanding wavelet. I know I finally need to learn functional analysis, harmonic stuff... but the only problem is timing, if I don't do selfstudy now but wait until next course offering of those courses, I guess my boss will fire me before I get the chance to finish those classes... Any help? Thank you!

Reply by ●March 25, 20042004-03-25

cf <cf@nospam.org> wrote in message news:<406133D3.2583F3CE@nospam.org>...> Hi Joenyim, > > There is a really good book (at least in my opinion) on the subject > by Gilbert Strang and Truong Nguyen. It's called Wavelets and Filter > Banks. If you are have good DSP bkgd, you can also reference > the book by P.P. Vaidyanathan called Multirate Systems and Filter Banks. > Reading these two, I found I can better understand the material > in the other two books you've mentioned. > > hth, > > cf >That's great. I went to library and read the Strang's book for several hours without sleeping. That's good indicator. Strang's luanguage is clear and sentences are clear. I like it. God, please monitor me to finish that book! :=) Thank you very much!

Reply by ●March 25, 20042004-03-25

Jeonyim, I am also curious on what kind of research you are working on since wavelet can be applied to many areas. For example, coding, pattern recognition, radar, .... We can probably give you some better idea on what you need to reference so you don't get fired by your boss. cf Jeonyim Kim wrote:> > > > > > This is like you say you need to learn calculus, but you don't have > > time to learn algebra and trigonometry yet... > > > > People have already given you various references - depending on > > what _sort_ of reasearch you're talking about they may suffice > > to show you how to use wavelets without really understanding > > them. But if you actually want to _understand_ how wavelets > > work you _need_ to learn some of the prerequisites, that's > > just the way it is! (What sort of research are you doing?) > > > > > > > > ************************ > > > > David C. Ullrich > > Hi, I just want to have a one-stop reference giving enough background > information whenever neccessary to understand the wavelet itself. The > ideal reference will have just enough comprehensive background > information for understanding wavelet. > > I know I finally need to learn functional analysis, harmonic stuff... > but the only problem is timing, if I don't do selfstudy now but wait > until next course offering of those courses, I guess my boss will fire > me before I get the chance to finish those classes... > > Any help? Thank you!

Reply by ●March 25, 20042004-03-25

On 24 Mar 2004 20:52:16 -0800, jeonyimkim80@yahoo.com (Jeonyim Kim) wrote:>David C. Ullrich <ullrich@math.okstate.edu> wrote in message news:<h813601i2lm2mbrh8n8j1f9cor9bvrkq11@4ax.com>... >> On Tue, 23 Mar 2004 19:38:19 -0500, "Joenyim Kim" >> <jeonyimkim80@yahoo.com> wrote: >> >> >Dear all, >> > >> >Wavelet is really hard to learn and master. However I need to learn it by >> >self-study. I have read Martin Vetterli's book and Mallat's book. For both >> >books I can only understand the first 1/3 part of the books. I always >> >understand the Haar example, but after that, math becomes dominant and >> >horrible. >> > >> >I understand that in order to understand the books and learn/master wavelet >> >well, I should have knowledge about Real Analysis, Functional Analysis, >> >Harmonic Analysis, Approximation Thoery. But I have not learned these yet. >> >But I need wavelet for my research and I should understand those papers >> >using multiscale analysis and wavelet. >> > >> [...] >> > >> >I mean, I know these Real Analysis, Functional Analysis, Harmonic Analysis, >> >Approximation Thoery are important; but I cannot wait only several semesters >> >later after I learned these subjects then I come back to learn wavelet, >> >right? >> >> This is like you say you need to learn calculus, but you don't have >> time to learn algebra and trigonometry yet... >> >> People have already given you various references - depending on >> what _sort_ of reasearch you're talking about they may suffice >> to show you how to use wavelets without really understanding >> them. But if you actually want to _understand_ how wavelets >> work you _need_ to learn some of the prerequisites, that's >> just the way it is! (What sort of research are you doing?) >> >> >> >> ************************ >> >> David C. Ullrich > > >Hi, I just want to have a one-stop reference giving enough background >information whenever neccessary to understand the wavelet itself. The >ideal reference will have just enough comprehensive background >information for understanding wavelet. > >I know I finally need to learn functional analysis, harmonic stuff... >but the only problem is timing, if I don't do selfstudy now but wait >until next course offering of those courses, I guess my boss will fire >me before I get the chance to finish those classes... > >Any help?What sort of help is appropriate depends on the answer to the question I asked: what sort of "research" are we talking about? You could try answering the question - it's not hard. For some sorts of research the idea of trying to learn about wavelets before learning that other stuff is utterly ridiculous - for some other sorts of research it might not be nearly so ridiculous. So: What sort of research are we talking about here? ???>Thank you!************************ David C. Ullrich

Reply by ●March 25, 20042004-03-25

"cf" <cf@nospam.org> wrote in message news:40626EFF.80CB2BF@nospam.org...> Jeonyim, > > I am also curious on what kind of research you are working on > since wavelet can be applied to many areas. For example, coding, > pattern recognition, radar, .... We can probably give you some > better idea on what you need to reference so you don't get fired > by your boss. > > cf > > Jeonyim Kim wrote: > > > > Hi, I just want to have a one-stop reference giving enough background > > information whenever neccessary to understand the wavelet itself. The > > ideal reference will have just enough comprehensive background > > information for understanding wavelet. > > > > I know I finally need to learn functional analysis, harmonic stuff... > > but the only problem is timing, if I don't do selfstudy now but wait > > until next course offering of those courses, I guess my boss will fire > > me before I get the chance to finish those classes... > > > > Any help? Thank you!I am reading papers on multiresolution motion tracking, etc. I am quite newbie. Image processing is my interesting... I found wavelet is in almost all papers I read... but I don't understand them...