Speech enhancement is a classical problem in signal processing, yet still largely unsolved. Two of the conventional approaches for solving this problem are linear filtering, like the classical Wiener filter, and subspace methods. These approaches have traditionally been treated as different classes of methods and have been introduced in somewhat different contexts. Linear filtering methods originate in stochastic processes, while subspace methods have largely been based on developments in numerical linear algebra and matrix approximation theory. This book bridges the gap between the