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Series in
Signal and Information Processing, Vol. 14
edited by Hans-Andrea Loeliger
Markus
Hofbauer,
Optimal Linear Separation and Deconvolution
of Acoustical Convolutive Mixtures.
1. Auflage/1st edition 2005, XX, 182 Seiten/pages, € 64,00.
ISBN 3-89649-996-3
This thesis addresses the problem of the optimal inversion of a linear
acoustical convolutive mixing process by means of multichannel linear
filtering. In most real-world acoustical scenarios, a number of sound emitting
sources are encountered, which may be simultaneously active. When perceiving
the sound of these sources by direct listening or from microphone recordings,
the original undistorted signal of a single source is not accessible, but
rather a mixture of the superposed sources. Furthermore, the source signals are
reverberated due to multipath propagation. Propagation and mixing of the
sources is characterized by a convolutive mixing process and can be completely
described by a matrix of acoustical impulse-responses (AIRs).
Reverberation, the superposition of several sources, and additive background
noise account for a reduced speech intelligibility in case of speech sources,
and for a reduced sound fidelity in general. Several multichannel algorithms
exist which aim at a separation and deconvolution (dereverberation) of the
sources. The most prevalent linear multichannel filtering techniques are
beamforming and blind algorithms. In adverse and highly reverberant
environments the performance of these methods is limited, and it is not clear,
whether the limitations arise from the particular linear algorithm, or if the
setup and physical environment fundamentally limits the performance of any
linear filtering method.
A theoretical and practical `best-case' performance analysis for linear
multichannel filtering methods in the least-squares optimal sense is presented
in this thesis. The term `best-case' implies that the convolutive mixing
process is known, i.e., the matrix of AIRs are given. Insights gained by the
analysis may serve as an upper bound for any practical linear filtering
algorithm with less knowledge.
AIRs in real-world environments are complex in the sense that they are
typically non-minimum phase, with lengths of thousands of taps. A direct
single-channel inversion of an AIR requires a non-causal filter of infinite
length (IIR) and is infeasible. Hence, it is not apparent that effective
inverse filters of finite length (FIR) can be found for real-world acoustical
convolutive mixing systems, and be reasonably applied.
In this thesis it is demonstrated that in the multichannel case and \emph{under
certain conditions} a perfect separation and deconvolution is achievable with
FIR filters, in theory and practice, even in adverse environments. In the more
applicable general case, where these conditions do not apply, a least-squares
solution still yields a significant source enhancement.
A versatile theoretical framework for a `best-case' analysis is developed to
determine the filters which yield a least-squares optimal inverse of the
convolutive mixing process. Each source is embedded in a block-Toeplitz matrix
equation (BTME) according to its propagation model. A general weighing function
allows to control the filtering task: The BTME can be arbitrarily weighted to
specify confined problems, and to influence the least-squares solution as
desired. Lower bounds for the FIR-filter lengths and conditions are derived
that guarantee an exact deconvolution and separation, or either one at a time.
A measurement system is established, which allows the measurement of the AIRs
and the assessment of the `best-case' performance with a maximum of eight
sources and eight sensors, and background noise. The insights of the
theoretical analysis are confirmed by real-world experiments in representative
environments -- a quiet office, a noisy cafeteria, and a highly reverberant
hallway. It is demonstrated that inverse filtering is indeed possible in
adverse real-world conditions. Dependencies on important eligible parameters as
the system latency and filter length are analyzed. An AIR sensitivity analysis
shows the importance of an accurate AIR estimation.
The presented `best-case' analysis framework and measurement system may be
utilized when designing an application or multichannel algorithm: For a
particular setup and environment, parameters can be optimized and results
assessed in listening tests. Finally, the analysis framework reveals the
complexity of the convolutive mixing process in a particular environment, and
imparts a deeper understanding thereof.
Markus Hofbauer was born in Basel, Switzerland, on July 10, 1972.
After the compulsory education in Peru and Germany, he attended the Gymnasium
in Weil am Rhein, Germany, where he obtained the Abitur. He spent an interim
high-school year in Tacoma, WA, USA and received the high-school Diploma. In
1993 he joined the Swiss Federal Institute of Technology Zurich (ETH) to study
electrical engineering and graduated with a Diploma degree in electrical engineering
in 1998. Subsequently, he started as a research and teaching assistant at the
Signal and Information Processing Laboratory (ISI) at ETH. In parallel with his
work on his Ph.D., he was an appointed lecturer of the graduate course
`Adaptive Filters' at ETH from 1999-2004. He is co-author of the textbook
`Adaptive Filter'. In March 2005 he completed the thesis entitled `Optimal
Linear Separation and Deconvolution of Acoustical Convolutive Mixtures' and
received the Ph.D. degree from ETH. In May 2005 he joined SIEMENS Zurich as an
R&D engineer in a technological consulting team.
Keywords:
Acoustical convolutive mixtures, acoustic impulse-response, beamforming, blind
source separation, block-Toeplitz matrix, deconvolution, dereverberation,
multichannel filtering, noise suppression, polynomial matrix, optimal
filtering, room acoustics, speech enhancement, Sylvester matrix.
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