Subspace learning and innovation characterization in generalized Gaussian noise

This paper formulates the problem of maximum likelihood subspace learning and innovation characterization in the presence of generalized Gaussian noise. This approach leads to a set of necessary conditions that are a nonlinear generalization of the Gaussian eigenvalue decomposition of the sample covariance matrix. To address the innovation problem, a class of jointly generalized Gaussian random variables is introduced using a generalized correlation matrix. Necessary condition for the maximum likelihood estimate of that matrix are derived, whose solution would permit the recovery of the innovation.