Speech dereverbaration via maximum kurtosis adaptive filtering
As was advised to me  by A_A in the comment section I will close this thread with a "self-answer".
The code present in the question is a code for a speech signal de-reverberation adaptive filter based on the Kurtosis signal of the signal's Lp residual. The original idea isn't mine (the reference is in the question). But the problem I faced was mainly due to the fact that my sensor did not convert to the desired result. I drastically increased the number of iterations the adaptive filter does and the result converged.(from n=500 to n=2000) There are others parameters that can be tweaked too (like mu) but I haven't had the time recently to thoroughly evaluate their effects. 

Here's a link to download the code hope it helps. (expires by April 18th)

Code download link

Here's the link for the RIR code I used, I did not write the code though. I downloaded the file from matlab file exchange. The original author is Stephen G. McGovern, he also wrote a paper with the theoretical explanations for the RIR filter.

RIR code