# Blind deconvolution using by maximizing kurtosis

I am trying to solve a 1D blind deconvolution to find a source signal, s(n), given only x(n) which is s(n) corrupted by additive white noise signal.

By CLT, we can assume that x(n) is more gaussian than s(n).

I understand that to find the filter coefficients, we are to maximize kurtosis and use the update equation $f_{k} = f_{k-1} + \mu\triangle$ where $\triangle$ is the gradient that has the kurtosis as well as cross correlation between the output of the filter and x(n).

I was wondering how is it possible to find the output of the filter without first establishing the filter? How do we also find maximize the kurtosis without finishing the update equation as well?

Much thanks!

• Just initialize the weight with random numbers. – Creator Mar 16 '18 at 18:33
• @Creator the weight? – Jacob Mar 16 '18 at 23:18
• sorry, sometime filter coefficients are termed as weight. – Creator Mar 17 '18 at 3:49
• @creator I intialized it with a vector of zero with the center = 1, somehow the update equation gave me a 24000x300 vector. I chose a 300 filter size and 24000 comes from the cross correlation between output signal and input signal. Did I do something wrong? – Jacob Mar 18 '18 at 21:18
• I am not sure what you mean by 24000x300 as a vector? This is a matrix not a vector. If you work on 1D signal with a filter, after the convolution or the filter operation you still get a vector. A vector is nx1 or 1xn type of matrix where n can be any number. The convergence of the filter will be an issue in your case anyway. – Creator Mar 18 '18 at 21:41