ICA基础盲源分离：理论与应用

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《盲语音分离》(Blind Speech Separation)是由Shoji Makino、Te-Won Lee和Hiroshi Sawada共同编著的一本专业书籍，于2007年出版。该书是世界上第一部关于基于独立成分分析（Independent Component Analysis, ICA）的盲源分离（Blind Source Separation, BSS）在语音混响环境中的应用的专著。它集合了少数顶尖研究者的智慧，旨在提供深入浅出、全面权威且易于理解的教程式内容，为当前及未来研究者提供关于ICA在语音信号处理领域的最新、最详尽的参考资料。书中探讨的主要内容包括但不限于：ICA理论基础、语音信号的混合模型、非线性盲分离方法（如FastICA算法）、以及如何处理语音混响中的时间相关性问题，这些都是实际应用中遇到的关键挑战。此外，书中还涵盖了性能评估和实际案例研究，以便读者能将所学应用于实际场景中进行语音增强、噪声抑制或多通道语音识别等任务。盲语音分离技术的重要性在于其能在复杂的环境中，如嘈杂的会议、电话通话或者背景噪音背景下，有效地分离出目标说话人声音，这对于语音通信、音频处理和多媒体系统具有重要意义。作者们强调，尽管这项技术面临着诸如计算复杂度和实时性的挑战，但通过不断的研究和优化，ICA已经在语音增强系统中取得了显著的进步。本书不仅适合已深入研究ICA的学者，也适合对语音信号处理感兴趣的技术人员和工程师，以及研究生和博士生作为参考教材。为了确保信息的准确性和版权， Springer出版社遵循严格的出版规范，要求所有复制和传播行为都必须得到出版商的书面许可。读者可以通过Springer官网获取电子版或印刷版，并获得ISBN号码以进行查找和引用。《盲语音分离》是一本极具价值的资源，它不仅提供了理论深度，而且提供了实际操作指导，对于提升在噪声环境下语音处理的能力有着不可替代的作用。对于任何希望在这个领域取得突破或深化理解的人来说，这本书无疑是一本值得珍藏和深入学习的宝典。

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1 Convolutive Blind Source Separation

for Audio Signals

Scott C. Douglas and Malay Gupta

Department of Electrical Engineering

Southern Methodist University

Dallas, Texas 75275 USA

Abstract. In this era of ever-improving communications technologies, we have

become used to conversing with others across the globe. Invariably, a real-time

telephone conversation begins with a microphone or other audio recording device.

Noise in the environment can corrupt our speech signal as it is being recorded,

making it harder to both use and understand further down the communications

pathway. Other talkers in the environment add their own auditory interference

to the conversation. Recent work in advanced signal processing has resulted in

new and promising technologies for recovering speech signals that have been

corrupted by speech-like and other types of interference. Termed blind source

separation methods, or BSS methods for short, these techniques rely on the diversity

provided by the collection of multichannel data by an array of distant micro-

phones (sensors) in room environments. The practical goal of these methods is

to produce a set of output signals which are much more intelligible and lis-

tenable than the mixture signals, without any prior information about the sig-

nals being separated, the room reverberation characteristics, or the room impulse

response.

The main goal of this chapter is to describe several current approaches for

the convolutive BSS task as they relate to speech processing applications. Novel

methods and results that are described in this chapter include:

1. Block-based extensions of the natural gradient algorithm using robust gradient

scaling.

2. Spatio-temporal extensions of the well-known FastICA algorithm to convolutive

speech separation.

3. A performance comparison of several speech separation methods in real room

environments and with diﬀerent microphone array conﬁgurations.

4. Performance evaluations of various algorithms under the practical situation of

an input signal power mismatch at the sensors.

5. A study of the importance of aprioriroom acoustics and direction-of-arrival

information on algorithm convergence.

1.1 Historical Perspective

The BSS task has its roots in communication theory, in which man-made

signals pass through a convolutive transmission medium that can alter the

spectral and temporal characteristics of the signal to an extent such that

S. Makino et al. (eds.), Blind Speech Separation, 3–45.

4 Scott C. Douglas and Malay Gupta

the received signal shape is completely diﬀerent from that of the originally-

transmitted signal. It also has connections to human perception, in that

human hearing system is able to focus attention on particular sound sources

in the presence of signiﬁcant noise and interference. It is not surprising

that early contributions in the development of BSS techniques were made

in two diﬀerent areas of study: blind equalization/deconvolution in sig-

nal processing, and the analysis of neurological structures in the brain in

medicine.

1.1.1 Blind Equalization and Deconvolution

Blind equalization and deconvolution originally arose in the context of com-

munication systems involving symbols that are transmitted using modulated

analog waveforms. Since the goal of communications is signal recovery, the

channel eﬀects must be removed from the observed signal, leading to the con-

cept of channel identiﬁcation to guide the design of a second system applied

to the received signals that reverses the channel’s eﬀects. Training signals

are often transmitted periodically to aid in this recovery, and these trans-

mitted symbols lower the eﬀective data rate of the communications link.

In the blind counterpart to the above communications task, termed blind

equalization or deconvolution, no training data is used, and the goal is to

recover the original transmitted symbols based only on the received signal

measurements.

Blind signal recovery is possible due to certain structural or statistical

constraints that are often placed on the transmitted sources in communica-

tions tasks. This structural constraint can be on the amplitude of the signals

being transmitted, as in the case of the constant modulus algorithm [2] and

the Sato algorithm [1]. Alternatively, a constraint on the probability density

function (p.d.f.) of the sources, such as their non-Gaussianity [3], can also be

used, in which case the goal of signal recovery is to match the density of the

equalized signal to that of the transmitted symbols. Further simpliﬁcations

to this approach were suggested in [4], in which higher-order statistics are

exploited for the equalization task. A similar method was originally proposed

by Wiggins [5]. This work illustrates that non-Gaussian statistics have played

an important role in many blind signal recovery algorithms.

In BSS, multiple unknown sources are transmitted through an unknown

multiple-input, multiple-output channel. Recovery of the sources is hampered

by an additional diﬃculty not present in the blind equalization or deconvo-

lution task: the source distributions may diﬀer from one another.

1.1.2 Neurological Structures and Information Representation

The study of brain function naturally leads one to consider the coding strategies

employed by neurological structures such as the brains of higher animals in

1 Convolutive Blind Source Separation 5

storing information [6]. Interestingly, concepts in information theory, con-

cerned with study of randomness and structure in arbitrary data [7] became

a key concept used in these studies, along with the speciﬁc concept of mu-

tual information. These connections led Linsker [8, 9] to propose unsupervised

information-theoretic learning rules to maximize the mutual information be-

tween the inputs and outputs of a nonlinear computational neural network.

Previously, in the context of linear networks, it had already been shown that an

application of a Hebbian-type learning rule extracts the principal component

of stationary input data. Linsker observed that if linear units in the network

were replaced by nonlinear units (neurons), similar learning rules extract in-

dependent components instead of principal components. This fact led several

to postulate the information maximization (INFOMAX) principle [8, 10, 11]

which states that, in a network of nonlinear computational units, maximum

information ﬂow can reduce the redundancy between the data at the output of

the system. These studies were later linked to the term independent component

analysis, which has as its goal the representation of a data set such that the

components of the representation have a joint density that factors into products

of marginal densities. Under linear mixing conditions and the constraint that

the source signals are statistically-independent, ICA becomes a viable criterion

by which to perform BSS, although technically these two ﬁelds of study are

diﬀerent, with diﬀerent overall goals.

1.2 Mixture and Separation Models

The diﬃculty of the blind source separation task strongly depends on the way

in which the signals are mixed within the physical environment. The simplest

mixing scenario is termed instantaneous mixing, for which most early BSS

algorithms were designed. Although useful for theoretical derivations, such

algorithms have limited practical applicability in speech separation problems

unless additional eﬀort is spent on the system implementation. Real-world

acoustical paths lead to convolutive mixing of the sources when measured at

the acoustic sensors, and the degree of mixing is signiﬁcant when the reverber-

ation time (RT) of the room is large. Additional diﬃculties are encountered

when the number of talkers is large; our experience indicates that separation

of four or more talkers can be challenging in the presence of signiﬁcant room

reverberation.

1.2.1 Instantaneous Mixture and Separation Models

In instantaneous mixing, m unknown source signals {s

(k)}, 1 ≤ i ≤ m are

combined to yield the n measured sensor signals {x

(k)}, 1 ≤ j ≤ n as

1 Convolutive Blind Source Separation 7

Separating System

s(k)

v(k)

y(k)

x(k)

A(z) B(z,k)

Mixing System

Fig. 1.2. Block diagram of the convolutive BSS task. A(z)=



∞

l=−∞

−l

and

B(z, k)=



∞

l=−∞

(k)z

−l

denote the z transform of the sequence of the systems

} and {B

(k)}, respectively.

assumed bandlimited signals such that sampled signals can take the place

of continuous-times ones. The block diagram for the convolutive BSS in the

discrete-time or z-domain is shown in Fig. 1.2.

Reverberant environments, in which sounds undergo hundreds or thou-

sands of reﬂections as they propagate within the acoustical space, introduce

time dependencies in the signal mixtures beyond those already present in the

original source signals. For this reason, designers of convolutive BSS algo-

rithms must consider both (i) spatial unmixing and (ii) the temporal changes

introduced by the mixing system. Ideally, the temporal structure of the orig-

inal sources would be preserved in the outputs of the separation system,

although this feature requires some knowledge of the temporal structures of

the source signals. Convolutive BSS algorithms must exploit both spatial and

temporal signal characteristics to function properly, which is why they are

sometimes referred to as spatio-temporal BSS algorithms.

Without any additional constraints, a convolutive BSS system processes

the signal mixtures x

(k) such that

(k)=

∞



l=−∞



j=1

ijl

(k)x

(k − l) (1.4)

contains a ﬁltered estimate of one of the sources s



(k) for some index assign-

ment i ⇒ i



without repetition.

The relation in (1.4) is in the form of a multichannel convolution, where

the coeﬃcients {b

ijl

}(k) represent the impulse response of the multichannel

separation system ﬁlter. Using well-known Fourier transform properties, it

is possible to express the above demixing system in the frequency-domain,

where the Fourier coeﬃcients of the multichannel separation system ﬁlter are

the unknown parameters. This parametrization of the separation system is

discussed in more detail in a later section, where issues regarding the dimen-

sionality of the model are dealt with explicitly.

The number of unknown sources m plays an important role in BSS

algorithms in that, under reasonable constraints on the mixing system, the

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