Wavelets with improved frequency

Hi to all!!!
I'am Intersted in digital image processing, using wavelets.

So, i must get wavelets with improved resolution in frequency.
Not H - [0;0.5], G - [0.5;1], but may be
H - [0;0.4], G - [0.6;1], where H - low pass filter, G - high pass
filter.

At current time i use wavelt packets and m-band wavelet transform
to solve this task.

Has anyone some ideas aboit such problem?

Please, adivce me.

Vasilii Gai.

Giper wrote:

> I'am Intersted in digital image processing, using wavelets.

What kind of processing?

> 
> So, i must get wavelets with improved resolution in frequency.

Why?


> Not H - [0;0.5], G - [0.5;1], but may be
> H - [0;0.4], G - [0.6;1], where H - low pass filter, G - high pass
> filter.

May be.

> At current time i use wavelt packets and m-band wavelet transform
> to solve this task.

What is the task?

> Has anyone some ideas aboit such problem?

What is the problem?

> Please, adivce me.

First, you need to figure out what do you want.


Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

"""Vladimir Vassilevsky �����(�):
"""
> Giper wrote:
>
> > I'am Intersted in digital image processing, using wavelets.
>
> What kind of processing?
>
> >
> > So, i must get wavelets with improved resolution in frequency.
>
> Why?
>
>
> > Not H - [0;0.5], G - [0.5;1], but may be
> > H - [0;0.4], G - [0.6;1], where H - low pass filter, G - high pass
> > filter.
>
> May be.
>
> > At current time i use wavelt packets and m-band wavelet transform
> > to solve this task.
>
> What is the task?
>
> > Has anyone some ideas aboit such problem?
>
> What is the problem?
>
> > Please, adivce me.
>
> First, you need to figure out what do you want.
>
>
> Vladimir Vassilevsky
>
> DSP and Mixed Signal Design Consultant
>
> http://www.abvolt.com

>>>>>>>>>
>> I'am Intersted in digital image processing, using wavelets.

> What kind of processing?

using wavelets i must solve different tasks:
- image segmentation
- image filtration
- edge detecion
>>
>> So, i must get wavelets with improved resolution in frequency.

>Why?

I must get such wavelts because standard wavelet transform very
quickly divide frequency band of source image.
I need to perfome more percise analysis of image. I suppose that it
leads to improving in results of, for example, image segmentation.

>> At current time i use wavelt packets and m-band wavelet transform
>> to solve this task.

> What is the task?

The task is to perfome more percise analysis in frequency domain,
using wavelets.

Thx.

Vasilii Gai.

Giper skrev:
> """Vladimir Vassilevsky =D0=C9=D3=C1=CC(=C1):

> >> I'am Intersted in digital image processing, using wavelets.
>
> > What kind of processing?
>
> using wavelets i must solve different tasks:
> - image segmentation
> - image filtration
> - edge detecion

>From a general point of view, it is usually a bad starting point to say

that "I will use technique A to solve problem B". Better starting
points
are "In what problems are technique A useful?" or "What techniques
are applicable for solving problem B?"

A compromise could be to ask "Can technique A be used to solve
problem B?" and be prepared for the possibility that the answer is
"No".

Wavelets is basically a particular type of filter bank that has two
main properties that do not generally hold for filter banks:

1) The computations are recursive
2) The frequency/time resolution is optimum with respect to
    the Heisenberg inequality.

Time-frequency analysis by classical methods (i.e. filter banks)
are goverened by the Heisenberg inequality,

 T*dF >=3D 2*pi                     (*)

or something like that. Given a target frequency resolution dF
equation (*) says that you need an observation of duration

  T >=3D 2*pi / dF     (**)

Now, equation (*) is a lower limit, most implementations of
time-frequency analysis perform worse:

  T > 2*pi / dF       (***)

Wavelets distinguish themselves with that they meet the lower
limit:

   T =3D 2*pi/dF.       (****)

The bottom line is that, in all likelihood, your wavelets are
already optimal with respect to frequency resolution. If they
are not good enough for your application, chances are that
the wavelet filtering techique might not suit the problem
at hand.

Of course, don't take my word for any of this. Check out the
theory of wavelets in general and the wavelet functions
you use in particular, and see whether I am right. If your
wavelet functions do not obey the equality (****) above,
you can do somewhat better by choosing a different
wavelet function. But that's about all you can do. =20

Rune

Giper wrote:

> """Vladimir Vassilevsky =D0=C9=D3=C1=CC(=C1):
> """


> using wavelets i must solve different tasks:
> - image segmentation
> - image filtration
> - edge detecion

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 =E2=F0=E6, =CE=C1=D0=D2=C9=CD=C5=D2?

>=20

>=20
> I must get such wavelts because standard wavelet transform very
> quickly divide frequency band of source image.
> I need to perfome more percise analysis of image. I suppose that it
> leads to improving in results of, for example, image segmentation.
 > The task is to perfome more percise analysis in frequency domain,
 > using wavelets.


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=CF=D0=D2=C5=C4=C5=CC=C5=CE=C9=C0. =EE=C5=D7=CF=DA=CD=CF=D6=CE=CF =D0=CF=CC=
=D5=DE=C9=D4=D8 =CE=C9=CB=C1=CB=CF=CA=20
=C4=CF=D0=CF=CC=CE=C9=D4=C5=CC=D8=CE=CF=CA =C9=CE=C6=CF=D2=CD=C1=C3=C9=C9=
=2E

VLV