MMSE whitening and subspace whitening

This correspondence develops a linear whitening transformation that minimizes the mean-squared error (MSE) between the original and whitened data, i.e., one that results in a white output that is as close as possible to the input, in an MSE sense. When the covariance matrix of the data is not invertible, the whitening transformation is designed,to optimally whiten the data on a subspace in which it is contained. The optimal whitening transformation is developed both for the case of finite-length data vectors and infinite-length signals.