DWT and Data Compression

Hello

About the DWT:
The DWT provides data compression by setting a threshold value and all
coefficients that are less than the choosen value will be reduced to zero
or eliminated and the signal can be reconstructed from the thresholded
coefficients. 
Therefore, I would like to ask about the lossless compression , does this
involve just the DWT and IDWT without setting any threshold value? or does
it involve more than that?

Thanks in advance

Umutesi Faith wrote:
> Hello
>
> About the DWT:
> The DWT provides data compression by setting a threshold value and all
> coefficients that are less than the choosen value will be reduced to zero
> or eliminated and the signal can be reconstructed from the thresholded
> coefficients.
> Therefore, I would like to ask about the lossless compression , does this
> involve just the DWT and IDWT without setting any threshold value? or does
> it involve more than that?
>
> Thanks in advance

Lossless compression algorithms might or might not use a discrete
wavelet transform. Here's a good source for you:

http://en.wikipedia.org/wiki/Lossless_compression

Cheers! --M

"mlimber" <mlimber@gmail.com> writes:

> Umutesi Faith wrote:
>> Hello
>>
>> About the DWT:
>> The DWT provides data compression by setting a threshold value and all
>> coefficients that are less than the choosen value will be reduced to zero
>> or eliminated and the signal can be reconstructed from the thresholded
>> coefficients.
>> Therefore, I would like to ask about the lossless compression , does this
>> involve just the DWT and IDWT without setting any threshold value? or does
>> it involve more than that?
>>
>> Thanks in advance
>
> Lossless compression algorithms might or might not use a discrete
> wavelet transform. Here's a good source for you:
>
> http://en.wikipedia.org/wiki/Lossless_compression
>
> Cheers! --M

A the strings "wavelet" and "dwt" do not occur in that page. Can
you give a pointer to an example of lossless compression based on
wavelets?
-- 
%  Randy Yates                  % "Watching all the days go by...    
%% Fuquay-Varina, NC            %  Who are you and who am I?"
%%% 919-577-9882                % 'Mission (A World Record)', 
%%%% <yates@ieee.org>           % *A New World Record*, ELO
http://home.earthlink.net/~yatescr

For lossless compression, you would typically use reversible integer to
integer wavelet transforms (keywords for googling). One of the papers
that might be helpful is:

Reversible Integer-to-Integer Wavelet Transforms for Image Compression:
Performance Evaluation and Analysis
Michael D. Adams, Faouzi Kossentini, IEEE TRANSACTIONS ON IMAGE
PROCESSING, VOL. 9, NO. 6, JUNE 2000

Hope this helps
Raja

Umutesi Faith wrote:
> Hello
>
> About the DWT:
> The DWT provides data compression by setting a threshold value and all
> coefficients that are less than the choosen value will be reduced to zero
> or eliminated and the signal can be reconstructed from the thresholded
> coefficients.
> Therefore, I would like to ask about the lossless compression , does this
> involve just the DWT and IDWT without setting any threshold value? or does
> it involve more than that?
> 
> Thanks in advance

ysriraja@gmail.com writes:

> For lossless compression, you would typically use reversible integer to
> integer wavelet transforms (keywords for googling). One of the papers
> that might be helpful is:
>
> Reversible Integer-to-Integer Wavelet Transforms for Image Compression:
> Performance Evaluation and Analysis
> Michael D. Adams, Faouzi Kossentini, IEEE TRANSACTIONS ON IMAGE
> PROCESSING, VOL. 9, NO. 6, JUNE 2000
>
> Hope this helps
> Raja

If you're not quantizing the wavelet coefficients, then how does
a DWT help? At least from the 30,000-foot level? Seems like there's
as little entropy in the transformed data as the original data, no?
-- 
%  Randy Yates                  % "Midnight, on the water... 
%% Fuquay-Varina, NC            %  I saw...  the ocean's daughter." 
%%% 919-577-9882                % 'Can't Get It Out Of My Head' 
%%%% <yates@ieee.org>           % *El Dorado*, Electric Light Orchestra
http://home.earthlink.net/~yatescr

You're right. The wavelet transform cannot be guaranteed to decrease
the entropy by itself. However, by subband partitioning one has the
luxury of defining different context models (As the low frequency and
high frequency subbands have different pdf's) for each subband to be
used for arithmetic coding.

So maybe applying the wavelet transform just provides more flexibility
in the pre-processing prior to entropy coding.


Randy Yates wrote:

> If you're not quantizing the wavelet coefficients, then how does
> a DWT help? At least from the 30,000-foot level? Seems like there's
> as little entropy in the transformed data as the original data, no?
> --
> %  Randy Yates                  % "Midnight, on the water...
> %% Fuquay-Varina, NC            %  I saw...  the ocean's daughter."
> %%% 919-577-9882                % 'Can't Get It Out Of My Head'
> %%%% <yates@ieee.org>           % *El Dorado*, Electric Light Orchestra
> http://home.earthlink.net/~yatescr

Hello,

Thanks for the reply. I guess this was just my straight approach about
lossless data compression with wavelet as i was referring to the data
compression concept of dwt with matlab programme! 

However, by performing the DWT , using the quadrature mirror filters (ex:
daubechies,...), and digital filtering mechamism (FIR filtering), do we
speak in this particular case about the wavelet window, as we have at hand
just the discrete signal and the filters that will just do the transform??
In fact this works perfectly but i don't see how this is related to any
kind of window? could these filters be the window? in continuous wavelet
transform(CWT) the window concept is quite clear as it is referred to as
the mother wavelet!!
thanks !