Should you include division by coefficient of variation in WV reconstruction for its normed 1D signal? I make a new ECG time series from WV spectrum of original signal and its L2 energy normalisation. 
I am thinking if the reconstruction step benefits from covariance at each time point. 
I take later a norm of the matrix, which creates the new time series. 


result there is no benefit of adding cov postop into the L2 new signal - verified, strong evidence
now, testing if the application of cov on the initial energy spectrum helps 


Nonlinearity

I think the coefficient of variation should not be applied to the initial spectrum because there exists a bijection between the two data sets, although a nonlinear one.


  The problem here is that neither sensor is better in this case, because the data sets are direct conversions of each other, but the CV of each data set is different: 0.79 versus 0.42.


Hovever, I am not sure if the nonlineary of the problem case makes the thing different. 

Source: https://en.wikipedia.org/wiki/Coefficient_of_variation
There is no benefit of dividing the new improved signal by the covariance of the original ECG and its improved signal like the following code; by the two decimal accuracy in Corrgrams and other more precise tools (eigen cor)

% Covariance http://dsp.stackexchange.com/q/35291/5633
% https://en.wikipedia.org/wiki/Coefficient_of_variation
utp = utp / sum( cov(u,utp) )'; 


Fig. 1 Left-hand-side figure without division by covariance and Right-hand-side figure with division by covariance - about marginal dependence and independence of the cases



Other inspected methods where I see no difference


Eigen cor matirx of the two
-M^{-1} about conditional independence and dependence


Please, let me know how to get more decimal digits in R corrgram panel.cor; I am trying to replace the problem by Didzis' p-value corrgram discussed there but having problems with finding the upper bound for the amount of points to maintain significant p-value.