Blind deconvolution application issues

Blind deconvolution application issues

I have the output from an inverse filter
b = y- (FIR filter)
where y is corrupted with eta as the gaussian noise and b is the measured
output signal;
y is the received signal corrupted with gaussian noise of unknown varaince
and mean.
Let the FIR filter be Hx. A are the unknown parameters and x is the true
signal that is unknown. b is projected to a higher dimensional space ie,
embedded into a higher dimensional space. where the objective function is
min Z= ||b||_2 ^2. In pg 3 of the pdf the Gauss Newton example is
provided. Following from the paper
http://www.optimization-online.org/DB_FILE/2012/02/3351.pdf .
I have not understood anything and having a tough time to do the coding.
So, can somebody please explain how I may apply Gauss Newton method in my
case?