Wavelet data compression

[Umutesi Faith]

Hello

I am trying to do some data compression using the DWT techniques but
have encoutered some problems. Once i have set the threshold values, al
the DWT coefficients that were less than the chosen value were reduced t
zero which was the purpose. But on the other hand i would like t
reconstruct the signal using only the remained coefficients without usin
those coefficients replaced with zeroes. This also will affect the lengt
of the signal ( the number of samples). IS it possible (or correct) t
just reconstruct the signal with the remained samples?

Thanks

[Jani Huhtanen]

Umutesi Faith wrote:

>
> Hello
>
> I am trying to do some data compression using the DWT techniques but i
> have encoutered some problems. Once i have set the threshold values, all
> the DWT coefficients that were less than the chosen value were reduced to
> zero which was the purpose. But on the other hand i would like to
> reconstruct the signal using only the remained coefficients without using
> those coefficients replaced with zeroes. This also will affect the length
> of the signal ( the number of samples). IS it possible (or correct) to
> just reconstruct the signal with the remained samples?
>
> Thanks

Yes. Reconstruction will lead to least squares sense optimal reconstruction
when those coefficients set to zero are not available.

--
Jani Huhtanen

[Umutesi Faith]

Ok, i will try and see what results i get! By the way i did not understan
what you meant by "least squares sense optimal reconstruction"!
Thanks!

************************************************** ****************


>Yes. Reconstruction will lead to least squares sense optima
reconstruction
>when those coefficients set to zero are not available.
>
>--
>Jani Huhtanen
>
>

[Jani Huhtanen]

Umutesi Faith wrote:

> Ok, i will try and see what results i get! By the way i did not understand
> what you meant by "least squares sense optimal reconstruction"!
> Thanks!
>
> ************************************************** ****************
>
>
>>Yes. Reconstruction will lead to least squares sense optimal
> reconstruction
>>when those coefficients set to zero are not available.
>>
>>--
>>Jani Huhtanen
>>
>>

If one considers the zeroed coefficients as missing, then straightforward
reconstruction leads to minimum error in least squares sense. This, because
we are dealing with orthogonal projection (well, actually this might not
hold for biorthogonal case).

--
Jani Huhtanen
Tampere University of Technology, Pori