Inverse autoconvolution (autocorrelation) solutions space

Hi !

I need to define the space of all the solutions of an inverse autoconvolution.

Is there an known way to do that ? Is there a parametric way to define that space ?

I thought about using the convolution theorem: f=invFourier(sqrt(Fourier(f*f)))

But I don't know how to define the non-symmetrical solutions.

Thanks

Answer 1

[Youssef Khmou]

Dear Jonathan,

Do you mean 1/autocorrelation(X)? you have to define the system X, is it 1D,2D signal?

Based on the Wiener theorem you mentioned, you can check my submission based on that theorem (2d signal ) :

http://www.mathworks.com/matlabcentral/fileexchange/37624-2d-autocorrelation-function

Answer 2

[Jonathan]

Hi !

I found new information on the subject. What i'm trying to do is a deautoconvolution of a nonnegative 1D function. There's a lot of info on the subject in the following paper:

An Iterative deautoconvolution algorithm for nonnegative functions

I will try implementing the algorithm contain in that article and maybe try the one contain in this article:

Deblurring subject to nonnegativity constraints