Reply by Tomi Kinnunen 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
Reply by ZZBunker 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 cf 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 Jay Liu 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
Kova&#269;evi&#263;'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 David C. Ullrich 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 Joenyim Kim March 25, 20042004-03-25
"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...
Reply by Joenyim Kim 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...
Reply by David C. Ullrich 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 cf 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 Jeonyim Kim 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!