"David C. Ullrich" <ullrich@math.okstate.edu> wrote in message news:lqf560peombp3bvnlg4m2bbsfpe3jl86in@4ax.com...> On 24 Mar 2004 20:52:16 -0800, jeonyimkim80@yahoo.com (Jeonyim Kim) > wrote: > > >David C. Ullrich <ullrich@math.okstate.edu> wrote in messagenews:<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 itby> >> >self-study. I have read Martin Vetterli's book and Mallat's book. Forboth> >> >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/masterwavelet> >> >well, I should have knowledge about Real Analysis, FunctionalAnalysis,> >> >Harmonic Analysis, Approximation Thoery. But I have not learned theseyet.> >> >But I need wavelet for my research and I should understand thosepapers> >> >using multiscale analysis and wavelet. > >> > > >> [...] > >> > > >> >I mean, I know these Real Analysis, Functional Analysis, HarmonicAnalysis,> >> >Approximation Thoery are important; but I cannot wait only severalsemesters> >> >later after I learned these subjects then I come back to learnwavelet,> >> >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. UllrichI am reading papers on multiresolution motion tracking, etc. I am quite newbie. Image processing is my interest... I found wavelet is in almost all papers I read... but I don't understand them...

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

Started by ●March 23, 2004

Reply by ●March 25, 20042004-03-25

Reply by ●March 25, 20042004-03-25

On Thu, 25 Mar 2004 14:10:28 -0500, "Joenyim Kim" <jeonyimkim80@yahoo.com> wrote:> >"David C. Ullrich" <ullrich@math.okstate.edu> wrote in message >news:lqf560peombp3bvnlg4m2bbsfpe3jl86in@4ax.com... >> 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 > > >I am reading papers on multiresolution motion tracking, etc. I am quite >newbie. Image processing is my interest... I found wavelet is in almost >all papers I read... but I don't understand them...Not sure whether that answers the question or not. I thought maybe your research was going to be in a field where you'd just be using someone's canned wavelets. If you're doing research in image processing (as opposed to just _using_ image processing for research in biology or whatever) then you need to learn the math. ************************ David C. Ullrich

Reply by ●March 25, 20042004-03-25

There are several ways to learn wavelets, multiresolution analysis, or multirate filter banks whatever the hell it is. If you are good at math so you can get physical meanings out of math theorems then try Ingrid Daubechies's "Ten Lectures on Wavelets". If you have good background in signal processing then try Vetterli and Kovačević's "Wavelets and Subband Coding". Or you can try Strang and Nguyen's "wavelets and filter banks" if you like the first authors' style (He is an author of "Linear Algebra and Its Applications," one of few favorite math books of mine.). This book is organized very uniquely. For smooth start, I recommend Ch.7 of Woods and Gonzalez's Digital Image Processing, 2nd ed.. If none of above works, don't worry. This is not easy stuff.

Reply by ●March 26, 20042004-03-26

I think motion tracking is more inline with image analysis rather than image processing. I will start off by reading about optical flow before diving into multiresolution stuff. Remember, don't try to fit a particular algorithm to a problem, instead, try to define the problem first and then think about how you can solve it. Here are two references that might be of use to you: Klaus, Berthold and Horn, Paul, "Chapter 12: Motion Field & Optical Flow", Robot Vision, The MIT Press, ISBN: 0-262-08159-8, p. 453-474, 1989. Anandan, P., "A Computational Framework and an Algorithm for the Measurement of Visual Motion", International Journal of Compter Vision, 2, p.283-310, 1989. Good luck. cf Joenyim Kim wrote:> > 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...

Reply by ●March 26, 20042004-03-26

Gib Bogle <bogle@too.much.spam.ihug.co.nz> wrote in message news:<c3r8dj$na1$2@lust.ihug.co.nz>...> 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.Nobody really knows why people do that though. Discrete wavelets are even harder to solve than continuous wavelets.> > Gib

Reply by ●March 27, 20042004-03-27

Dear Joenyim (and others), I'm adding a somewhat philosophical and long view to this discussion. I hope you find it interesting :-) Joenyim, you have also all my sympathy (yes, someone already said the same), and I'm fighting still with the same problems. For me personally, I *have* good math and signal processing background, and I still cannot understand what are the wavelets. I've been on a course of wavelets, I've read several survey papers etc... But still the field doesn't open to me. I've tried to ask from people from our applied mathematics department could you please explain what is the essential difference between "Filterbank analysis" and "Wavelet analysis", and I really haven't had an asnwer that would satisfy me. The answers have been something like: "I suggest you first study functional analysis in order to understand....". This is, in my opinion, a wrong answer. Of course I probably have much deeper view of a subject X after going to N courses that are "basic material" for the subject X. Still, I know several good teachers who have taught me some very complex issue without assuming you have first gone to courses X1,X2, ... There are also good books and bad books. What I'm trying to say, I know that it is possible to explain very complex issues with minimal amount of previous knowledge of math, statistics, or signal processing (or whatever else), but still giving a good ground for more advanced studies of the subject... Multiresolution learning, he he. To me, the problem with wavelets teaching seems to be exactly what Joenyim describes: the first examples (Haar) are simple and intuitive, and suddently *TSUUP!* we are deep in the theory of function spaces without any _intuitive notion_ of these subjects. I think the issue here is more higher-level and general question, it is something to do with the philosophy of teaching mathematics. It also seems that people working on wavelet theory think they solve every problem in this world [sorry, wavelet theoretians!] - they are "optimal" in whatever sense depending on the context - compression, detection, analysis. And old tools like windowed Fourier transform should be immediately replaced by this Optimal Method. If this is really so, why I'm not still very convinced? Well, easy - I haven't understand what the wavelets can offer that traditional signal analysis doesn't. My very own definition of a "guru" is something like: Guru = A person who masters his/her subject, AND he knows how to teach this subject to others as well. Finally I'd like to say that I've also found the Strang & Nguyen book very good - that was what I was looking for. I've just not finished it yet 8-) -Tomi