Speech Enhancement for Nonstationary Noise Environments

Signal & Image Processing : An International Journal (SIPIJ) Vol.2, No.4, December 2011
DOI : 10.5121/sipij.2011.2411 129
Speech Enhancement for Nonstationary Noise
Environments
Sandhya Hawaldar1
and Manasi Dixit2
Department of Electronics, KIT’s College of Engineering, Shivaji University, Kolhapur,
416234, India
santell2007@gmail.com
Abstract
In this paper, we present a simultaneous detection and estimation approach for speech enhancement in
nonstationary noise environments. A detector for speech presence in the short-time Fourier transform
domain is combined with an estimator, which jointly minimizes a cost function that takes into account both
detection and estimation errors. Under speech-presence, the cost is proportional to a quadratic spectral
amplitude error, while under speech-absence, the distortion depends on a certain attenuation factor.
Experimental results demonstrate the advantage of using the proposed simultaneous detection and
estimation approach which facilitate suppression of nonstationary noise with a controlled level of speech
distortion.
Keywords
Estimation, Nonstationary noise, Spectral analysis, Speech enhancement, Decision rule.
1. Introduction
A practical speech enhancement system generally consists of two major components: the
estimation of noise power spectrum, and the estimation of speech. The estimation of noise, when
only one microphone source is provided, is based on the assumption of a slowly varying noise
environment. In particular, the noise spectrum remains virtually stationary during speech activity.
The estimation of speech is based on the assumed statistical model, distortion measure, and the
estimated noise. A commonly used approach for estimating the noise power spectrum is to
average the noisy signal over sections which do not contain speech. Existing algorithms often
focus on estimating the spectral coefficients rather than detecting their existence. The spectral-
subtraction algorithm [1] [2] contains an elementary detector for speech activity in the time–
frequency domain, but it generates musical noise caused by falsely detecting noise peaks as bins
that contain speech, which are randomly scattered in the STFT domain. Subspace approaches for
speech enhancement [3] [4] decompose the vector of the noisy signal into a signal-plus-noise
subspace and a noise subspace, and the speech spectral coefficients are estimated after removing
the noise subspace. Accordingly, these algorithms are aimed at detecting the speech coefficients
and subsequently estimating their values. McAulay and Malpass [5] were the first to propose a
speech spectral estimator under a two-state model. They derived a maximum-likelihood (ML)
estimator for the speech spectral amplitude under speech-presence uncertainty. Ephraim and
Malah followed this approach of signal estimation under speech presence uncertainty and derived
an estimator which minimizes the mean-square error (MSE) of the short-term spectral amplitude
(STSA) [6]. In [7], speech presence probability is evaluated to improve the minimum MSE
(MMSE) of the log-spectral amplitude (LSA) estimator, and in [8] a further improvement of the

130
MMSE-LSA estimator is achieved based on a two-state model. Under speech absence hypothesis,
Cohen and Berdugo [8] considered a constant attenuation factor to enable a more natural residual
noise, characterized by reduced musicality. Under slowly time-varying noise conditions, an
estimator which minimizes theMSE of the STSA or the LSA under speech presence uncertainty
may yield reasonable results [11].However, under quickly time-varying noise conditions, abrupt
transients may not be sufficiently attenuated, since speech is falsely detected with some positive
probability. Reliable detectors for speech activity and noise transients are necessary to further
attenuate noise transients without much degrading the speech components. Despite the sparsity of
speech coefficients in the time–frequency domain and the importance of signal detection for noise
suppression performance, common speech enhancement algorithms deal with speech detection
independently of speech estimation. Even when a voice activity detector is available in the STFT
domain ,it is not straightforward to consider the detection errors when designing the optimal
speech estimator.
High attenuation of speech spectral coefficients due to missed detection errors may significantly
degrade speech quality and intelligibility, while falsely detecting noise transients as speech-
contained bins, may produce annoying musical noise. In this paper, we present a simultaneous
detection and estimation approach for speech enhancement in nonstationary noise environments.
A detector for speech presence in the short-time Fourier transform domain is combined with an
estimator, which jointly minimizes a cost function that takes into account both detection and
estimation errors. Cost parameters control the tradeoff between speech distortion, caused by
missed detection of speech components and residual musical noise resulting from false-detection.
Under speech-presence, the cost is proportional to quadratic spectral amplitude (QSA) error [6],
while under speech-absence, the distortion depends on a certain attenuation factor [2], [8], [9].
The noise spectrum is estimated by recursively averaging past spectral power values, using a
smoothing parameter that is adjusted by the speech presence probability in subbands [13].
This paper is organized as follows. In Section 2 review of classical speech enhancement. In
Section 3, proposed approach for speech enhancement. In Section 4 we compare the performance
of the proposed approach to existing algorithms, both under stationary and nonstationary
environments. In section 5, we conclude the advantages of simultaneous detection & estimation
approach with modified speech absence estimate.
2. Classical Speech Enhancement
Let ( )
x n and ( )
d n denote speech and uncorrelated additive noise signals, and let
( ) ( ) ( )
y n x n d n
= +
= +
= +
= + be the observed signal.
Applying the STFT to the observed signal, we have,
lk lk lk
Y X D
= +
= +
= +
= + (1)
where 0 1
, ,...
l =
=
=
= is the time frame index and 0 1 1
, ,...,
k K
= −
= −
= −
= − is the frequency-bin index.
Let 1
lk
H and 0
lk
H denote, respectively, speech presence and absence hypotheses in the time–
frequency bin(l, k) , i.e.,
1 :
lk
lk lk lk
H Y X D
= +
= +
= +
= +
(2)
0 :
lk
lk lk
H Y D
=
=
=
=
Assume that the noise expansion coefficients can be represented as the sum of two uncorrelated
noise components: s t
lk lk lk
D D D
= +
= +
= +
= + where s
lk
D denotes a quasi-stationary noise component,
and t
lk
D denotes a highly nonstationary transient component. The transient components are

131
generally rare, but they may be of high energy and thus cause significant degradation to speech
quality and intelligibility. But in many applications, a reliable indicator for the transient noise
activity may be available in the system. For example, in an emergency vehicle (e.g., police or
ambulance) the engine noise may be considered as quasi-stationary, but activating a siren results
in a highly nonstationary noise which is perceptually very annoying. Given that a transient noise
source is active, a detector for the transient noise in the STFT domain may be designed and its
spectrum can be estimated based on training data.
The objective of a speech enhancement system is to reconstruct the spectral coefficients of the
speech signal such that under speech-presence a certain distortion measure between the spectral
coefficient and its estimate, ˆ
( , )
ij
d X X , is minimized, and under speech-absence a constant
attenuation of the noisy coefficient would be desired to maintain a natural background noise [6],
[9]. Most classical speech enhancement algorithms try to estimate the spectral coefficients rather
than detecting their existence, or try to independently design detectors and estimators. The well-
known spectral subtraction algorithm estimates the speech spectrum by subtracting the estimated
noise spectrum from the noisy squared absolute coefficients [1], [2], and thresholding the result
by some desired residual noise level. Thresholding the spectral coefficients is in fact a detection
operation in the time–frequency domain, in the sense that speech coefficients are assumed to be
absent in the low-energy time–frequency bins and present in noisy coefficients whose energy is
above the threshold. McAulay and Malpass were the first to propose a two-state model for the
speech signal in the time–frequency domain [5].The resulting estimator does not detect speech
components, but rather, a soft-decision is performed to further attenuate the signal estimate by the
a posteriori speech presence probability.
If an indicator for the presence of transient noise components is available in a highly
nonstationary noise environment, then high-energy transients may be attenuated by using OM-
LSA estimator [8] and setting the a priori speech presence probability to a sufficiently small
value. Unfortunately, an estimation-only approach under signal presence uncertainty produces
larger speech degradation, since the optimal estimate is attenuated by the a posteriori speech
presence probability. On the other hand, increasing a priori speech presence probability prevents
the estimator from sufficiently attenuating noise components. Integrating a jointly detector and
estimator into the speech enhancement system may significantly improve the speech
enhancement performance under nonstationary noise environments and allow further reduction of
transient components without much degradation of the desired signal.
3. Proposed Approach for Speech Enhancement
Let (
(
(
( )
)
)
) 0
ˆ
,
j
C X X ≥
≥
≥
≥ denote the cost of making a decision j
η
η
η
η and choosing an estimator ˆ
j
X
where X is the desired signal. Then, the Bayes risk of the two operations associated with
simultaneous detection and estimation is defined by [11] and [12]
(
(
(
( )
)
)
) (
(
(
( )
)
)
) (
(
(
( )
)
)
) (
(
(
( )
)
)
)
1
0
ˆ
, | |
y x
j j
j
R C X X p Y p Y X p X d X d Y
η
η
η
η
=
=
=
= Ω Ω
Ω Ω
Ω Ω
Ω Ω
=
=
=
= ∑
∑
∑
∑ ∫ ∫
∫ ∫
∫ ∫
∫ ∫
(3)
where x
Ω
Ω
Ω
Ω and y
Ω
Ω
Ω
Ω are the spaces of the speech and noisy signals, respectively. The simultaneous
detection and estimation approach is aimed at jointly minimizing the Bayes risk over both the
decision rule and the corresponding signal estimate. Let 1
( )
q p H denote the a priori speech
presence probability and let R
X and I
X denote the real and imaginary parts of the expansion
coefficient X . Then, the a priori distribution of the speech expansion coefficient follows:
1 0
( ) ( | ) (1 ) ( | )
p X q p X H q p X H
= + −
= + −
= + −
= + − (4)

132
where 0
( | ) ( )
p X H X
δ
δ
δ
δ
=
=
=
= and ( ) ( , )
R I
X X X
δ δ
δ δ
δ δ
δ δ denotes the Dirac-delta function.
The cost function ˆ
( , )
j
C X X may be defined differently whether 1
H or 0
H is true. Therefore, we
let ˆ ˆ
( , ) ( , | )
ij j i
C X X C X X H denote the cost which is conditioned on the true hypothesis.1
The cost function depends on both the true signal value and its estimate under the decision and
therefore couples the operations of detection and estimation.
The cost function associated with the pair {
{
{
{ }
}
}
}
,
j j
H η
η
η
η is generally defined by,
ˆ ˆ
( , ) ( , )
ij ij ij
C X X b d X X
=
=
=
= (5)
where ˆ
( , )
ij
d X X is an appropriate distortion measure and the cost parameters ij
b control the
tradeoff between the costs associated with the pairs {
{
{
{ }
}
}
}
,
j j
H η
η
η
η .That is, a high-valued 01
b raises
the cost of a false alarm, (i.e., decision of speech presence when speech is actually absent) which
may result in residual musical noise. Similarly, 10
b is associated with the cost of missed detection
of a signal component, which may cause perceptual signal distortion. Under a correct
classification, 00 11 1
b b
= =
= =
= =
= = normalized cost parameters are generally used. However (.,.)
ij
d is
not necessarily zero since estimation errors are still possible even when there is no detection
error. When speech is indeed absent, the distortion function is defined to allow some natural
background noise level such that under 0
H , the attenuation factor will be lower bounded by a
constant gain floor 1
f
G as proposed in [2], [8], [9].
The distortion measure of the QSA cost function is defined by,
2
2
ˆ
(| | |) , 1
ˆ
( , )
ˆ
( | | |) , 0
j
ij
f j
X X i
d X X
G Y X i



 − =
− =
− =
− =




=
=
=
= 



− =
− =
− =
− =








(6)
and is related to the STSA suppression rule of Ephraim and Malah [6].Assume that both X and
D are statistically independent, zero-mean, complex-valued Gaussian random variables with
variances x
λ
λ
λ
λ and d
λ
λ
λ
λ , respectively. Let /
x d
ξ λ λ
ξ λ λ
ξ λ λ
ξ λ λ , denote the a priori SNR under hypothesis
1
H , let 2
| | / d
Y
γ λ
γ λ
γ λ
γ λ ,denote the a posteriori SNR and let / (1 )
υ γξ ξ
υ γξ ξ
υ γξ ξ
υ γξ ξ
+
+
+
+ . For evaluating the
optimal detector and estimator under the QSA cost function we denote by j
X ae α
α
α
α
and Re j
Y θ
θ
θ
θ
the clean and noisy spectral coefficients, respectively, where | |
a X
=
=
=
=
and | |
R Y
=
=
=
= .Accordingly, the pdf of the speech expansion coefficient under 1
H satisfies,
2
1
( , | ) exp( )
x x
a a
p a H
α
α
α
α
πλ λ
πλ λ
πλ λ
πλ λ
= −
= −
= −
= − (7)
As proposed in [14], the optimal estimation under the decision 0 1
, { , }
j j
η
η
η
η ∈
∈
∈
∈
1
1 0
ˆ ( , ) ( , ) ( , )
j j STSA j f j
X b G b G Y
ξ γ ξ γ φ ξ γ
ξ γ ξ γ φ ξ γ −
−
−
−
 
 
 
 
= Λ +
= Λ +
= Λ +
= Λ +
 
 
 
  (8)
( , )
j
G Y
ξ γ
ξ γ
ξ γ
ξ γ
The optimal estimator under decision 0
η
η
η
η is modified with certain attenuation factor based on
noise variance lk
d
λ
λ
λ
λ and Noisy speech power lk
S ,

133
0 0
X̂ G Y
= ×
= ×
= ×
= × (9)
Where 10 1/2
0 ( / )
lk
f d lk
G G S e
λ
λ
λ
λ −
−
−
−
= × +
= × +
= × +
= × + and
To obtain lk
S recursive averaging is employed such that
2
1, (1 ) | |
lk s l k s lk
S S Y
ξ ξ
ξ ξ
ξ ξ
ξ ξ
−
−
−
−
= + −
= + −
= + −
= + −
where ζs (0 < ζs < 1) is a smoothing parameter.
This modification reduces greatly the nonstationary noise from Noisy speech as it considers noisy
speech power along with its variance.
The decision rule [14] under the QSA cost function is,
1
2 2
10 0 1 10 2 2
01 1 0
1 10 0
0
(1 )( 1)
(1 )
( , ) ( ) ( )
2( )
f f
STSA
b G G b
b G G G G
G b G G
η
η
η
η
ξ
ξ
ξ
ξ
υ
υ
υ
υ
ξ γ
ξ γ
ξ γ
ξ γ
ξ γ
ξ γ
ξ γ
ξ γ
η
η
η
η
 
 
 
 
− + + − +
− + + − +
− + + − +
− + + − + >
>
>
>
 
 
 
 
+
+
+
+
Λ − − −
Λ − − −
Λ − − −
Λ − − −
 
 
 
 
<
<
<
<
 
 
 
 
−
−
−
−
 
 
 
 
(10)
Fig.1. shows a block diagram of the simultaneous detection and estimation system, the estimator
is obtained by (8) and (9) and the interrelated decision rule (10) chooses the appropriate estimator
for minimizing the combined Bayes risk.
Fig.1. Simultaneous Detection and Estimation System.
4. Experimental Results
In our experimental study we consider the problem of hands free communication in an emergency
vehicle and demonstrate the advantage of the simultaneous detection and estimation approach
under stationary & nonstationary noise environments. Speech signals are recorded with sampling
frequency at 8 kHz and degraded by different stationary & nonstationary additive noise.
Nonstationary noise like siren noise is added with car noise for different levels of input SNR. The
test signals include 12 speech utterances from 12 different speakers, half male and half female.
The noisy signals are transformed into the STFT domain using half-overlapping Hamming
windows of 32-ms length, and the background-noise spectrum is estimated by using the IMCRA
algorithm[13] .The performance evaluation includes objective quality measure- SNR defined, in
dB, a subjective study of spectrograms, and informal listening tests.
The proposed approach is compared with the OM-LSA algorithm [8]. The speech presence
probability required for the OM-LSA estimator as well as for the simultaneous detection and
estimation approach is estimated as proposed in [8]. For the OM-LSA algorithm, the decision-
directed estimator with 0.92
α
α
α
α =
=
=
= is implemented as specified in [8], and the gain floor

134
is 20
f
G dB
= −
= −
= −
= − . Fig. 2 shows waveforms and spectrograms of a clean signal, noisy signal, and
enhanced signals for Speech degraded by car and siren noise with SNR of 5 dB. The speech
enhanced by using the OM-LSA algorithm & the simultaneous detection and estimation approach
are shown in Fig. 2.(c) and 2.(d), respectively. However, the simultaneous detection and
estimation approach with modified speech absence estimate yields greater reduction of transient
noise without affecting the quality of the enhanced speech signal.
Fig. 2. Speech waveforms and spectrograms. (a) Clean speech signal: “kamal naman kar.” in Marathi
uttered by a male subject (b) Speech degraded by car noise and siren noise with SNR of 5dB. (c) Speech
enhanced by using the OM-LSA estimator. (d) Speech enhanced by using the simultaneous detection and
estimation approach with modified speech absence estimate using, b01 = b10 = 2.5 as proposed by authors.
Quality measures for the different input SNRs are shown in Table 1 & Table 2.The results from
Table 1 demonstrate improved speech quality obtained by the simultaneous detection and
estimation approach for stationary noise environments.

135
TABLE 1
Output SNR (in dB) By Using The OM-LSA Estimator & Simultaneous Detection And
Estimation Approach for Different Stationary Noise Environments with Varying Input SNR
Between 15dB to -5dB.
Noise Input SNR OM-LSA
Estimator
Proposed
Simultaneous
Detection &
Estimation approach
White Gaussian Noise 15 18.0290 21.1937
10 15.0292 18.7496
5 11.9830 9.7287
0 8.5279 7.7648
-5 5.9435 7.3687
Car 15 15.5912 20.8507
10 12.9320 16.3415
5 10.5166 13.8647
0 8.3231 10.3499
-5 6.0857 7.6548
The results from Table 2 demonstrate improved speech quality obtained by the simultaneous
detection and estimation approach with modified speech absence estimate for nonstationary noise
environments (car with siren noise).
TABLE 2
Output SNR (in dB) By Using The OM-LSA Estimator & Simultaneous Detection And
Estimation Approach for Different Nonstationary Noise Environments with Varying Input SNR
Between 15dB to -5dB.
Noise Input SNR OM-LSA
Estimator
Proposed
Simultaneous
Detection &
Estimation approach
Car(with siren noise) 15 16.1622 19.7296
10 12.8231 16.0058
5 12.3619 12.4352
0 3.0348 4.9814
-5 -3.9558 -2.3462
Train 15 17.6705 21.6112
10 15.5157 17.0405
5 14.9869 16.2158
0 12.2862 13.4268
-5 6.8280 7.7332
Subjective listening tests confirm that the speech quality improvement achieved by using the
proposed method.
5. Conclusion
We have presented a single-channel speech enhancement approach in the time–frequency domain
for nonstationary noise environments. A detector for the speech coefficients and a corresponding

136
estimator with modified speech absence estimate for their values is jointly designed to minimize a
combined Bayes risk. In addition, cost parameters enable to control the tradeoff between speech
quality, noise reduction, and residual musical noise. Experimental results show greater noise
reduction with improved speech quality when compared with the OM-LSA suppression rules
under stationary and nonstationary noise. It is demonstrated that under nonstationary noise
environment, greater reduction of nonstationary noise components may be achieved by exploiting
reliable information with simultaneous detection and estimation approach.
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Nov.2007

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