3 research outputs found
Square root-based multi-source early PSD estimation and recursive RETF update in reverberant environments by means of the orthogonal Procrustes problem
Multi-channel short-time Fourier transform (STFT) domain-based processing of
reverberant microphone signals commonly relies on power-spectral-density (PSD)
estimates of early source images, where early refers to reflections contained
within the same STFT frame. State-of-the-art approaches to multi-source early
PSD estimation, given an estimate of the associated relative early transfer
functions (RETFs), conventionally minimize the approximation error defined with
respect to the early correlation matrix, requiring non-negative inequality
constraints on the PSDs. Instead, we here propose to factorize the early
correlation matrix and minimize the approximation error defined with respect to
the early-correlation-matrix square root. The proposed minimization problem --
constituting a generalization of the so-called orthogonal Procrustes problem --
seeks a unitary matrix and the square roots of the early PSDs up to an
arbitrary complex argument, making non-negative inequality constraints
redundant. A solution is obtained iteratively, requiring one singular value
decomposition (SVD) per iteration. The estimated unitary matrix and early PSD
square roots further allow to recursively update the RETF estimate, which is
not inherently possible in the conventional approach. An estimate of the said
early-correlation-matrix square root itself is obtained by means of the
generalized eigenvalue decomposition (GEVD), where we further propose to
restore non-stationarities by desmoothing the generalized eigenvalues in order
to compensate for inevitable recursive averaging. Simulation results indicate
fast convergence of the proposed multi-source early PSD estimation approach in
only one iteration if initialized appropriately, and better performance as
compared to the conventional approach
Instantaneous PSD Estimation for Speech Enhancement based on Generalized Principal Components
Power spectral density (PSD) estimates of various microphone signal
components are essential to many speech enhancement procedures. As speech is
highly non-nonstationary, performance improvements may be gained by maintaining
time-variations in PSD estimates. In this paper, we propose an instantaneous
PSD estimation approach based on generalized principal components. Similarly to
other eigenspace-based PSD estimation approaches, we rely on recursive
averaging in order to obtain a microphone signal correlation matrix estimate to
be decomposed. However, instead of estimating the PSDs directly from the
temporally smooth generalized eigenvalues of this matrix, yielding temporally
smooth PSD estimates, we propose to estimate the PSDs from newly defined
instantaneous generalized eigenvalues, yielding instantaneous PSD estimates.
The instantaneous generalized eigenvalues are defined from the generalized
principal components, i.e. a generalized eigenvector-based transform of the
microphone signals. We further show that the smooth generalized eigenvalues can
be understood as a recursive average of the instantaneous generalized
eigenvalues. Simulation results comparing the multi-channel Wiener filter (MWF)
with smooth and instantaneous PSD estimates indicate better speech enhancement
performance for the latter. A MATLAB implementation is available online