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deconvolution techniques

Started by skaspok June 13, 2007
In dielectric samples, a pulse of electric field makes charge plans moving,
creating an acoustic wave transformed in tension, using a piezo transducer.
I have a signal to deconvolute to recover the space charge profile. I know
the impulse response.
Today, the only thing working is to divide and filter the low frequencies
with a gaussian. I tried Wiener, richardson-lucy, doesn't work.

I'm looking for an overview of déconvolution technics so that I can do it
properly and justifie my choices. of course any advises will be welcome.

thanks

adrien



skaspok wrote:
> In dielectric samples, a pulse of electric field makes charge plans movin=
g,
> creating an acoustic wave transformed in tension, using a piezo transduce=
r=2E
> I have a signal to deconvolute to recover the space charge profile. I know > the impulse response. > Today, the only thing working is to divide and filter the low frequencies > with a gaussian. I tried Wiener, richardson-lucy, doesn't work. > > I'm looking for an overview of d=E9convolution technics so that I can do =
it
> properly and justifie my choices. of course any advises will be welcome. > > thanks > > adrien
While I do not entirely understand what you need deconvolution for, and neither do I understand what you have tried so far, I think I can tell you how to deconvolve properly. Well, the only technique I know is the following one : add zeroes at the end of both signals so that their new length enquals the length of the first signal plus the length of the second signal (the impulse response) minus 1 (just as for when you perform plain old convolution). Then, perform a FFT on both signals, and perform a complex division between both signals (the FFT of the original signal behind divided by the FFT of the impulse response). Just take a look at the impulse response in the frequency domain to make sure that there are no areas of frequency that are a bit too near zero (we all know how ugly the results of divisions by zero can be). As far as I know, that's the only way to perform deconvolution, as it can only be performed in the frequency domain, and through complex division. If there's anything you don't understand, feel free to ask me to explain in french, as I'm french as well.
Have you tried Least Squares Deconvolution? Least squares deconvolution
with Tikhonov regularization may solve your  problem. 

>Have you tried Least Squares Deconvolution? Least squares deconvolution >with Tikhonov regularization may solve your problem. > >
Yes i'm currently trying to find good regularisations for the algorithm, I tried the derivative operator to avoid high frequencies but I still have waves on the result. My signal should be composed of Gaussians maybe I should add a constraint going that way but I don't exactly know how. If someone knows what I'm speaking about I would be interested by any suggestion bye