 
Summary: 1
A Unified Framework for Designing Optimal
STSA Estimators Assuming Maximum
Likelihood Phase Equivalence of Speech and
Noise
Bengt J. Borgstršom, Member, IEEE, and Abeer Alwan, IEEE Fellow
Abstract
In this paper, we present a stochastic framework for designing optimal shorttime spectral amplitude
(STSA) estimators for speech enhancement assuming phase equivalence of speech and noise. By
assuming additive superposition of speech and noise, which is implied by the maximum likelihood (ML)
phase estimate [6], we effectively project the optimal spectral amplitude estimation problem onto a 1
dimensional subspace of the complex spectral plane, thus simplifying the problem formulation. Assuming
generalized Gamma distributions (GGDs) for a priori distributions of both speech and noise STSAs,
we derive separate families of novel estimators according to either the maximum likelihood (ML), the
minimum meansquare error (MMSE), or the maximum a posteriori (MAP) criterion. The use of GGDs
allows optimal estimators to be determined in a generalized form, so that particular solutions can be
obtained by substituting statistical shape parameters corresponding to expected speech and noise priors.
It is interesting to note that several of the proposed estimators exhibit strong similarities to wellknown
STSA solutions. For example, the magnitude spectral subtracter (MSS) [2] and Wiener filter (WF) [1]
are obtained for specific cases of GGD shape parameters. Quantitative analysis of a selected subset of the
