For a frame of t=0,1,...,N-1
Partial j of source k is
And the observed mixture is
The model of complete-incomplete data relationship
The incomplete data y
The complete data x are the sources s + noise v
where the noises sum to the observed additive noise v(t)
For convenience, all the noise compoenents are assumed to be statistically independent, zero-mean, white and Gaussian with variance 
associated with each of them where 
is the fraction of actual noise power assigned to the component.
Also
The convenience will be apparent later