ADAPTIVE WIENER FILTERING APPROACH FOR SPEECH ENHANCEMENT - Ubiquitous Computing and Communication Journal

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					    ADAPTIVE WIENER FILTERING APPROACH FOR SPEECH
                    ENHANCEMENT

            M. A. Abd El-Fattah*, M. I. Dessouky , S. M. Diab and F. E. Abd El-samie #
           Department of Electronics and Electrical communications, Faculty of Electronic Engineering
                                  Menoufia University, Menouf, Egypt
                   E-mails: * maro_zizo2010@yahoo.com , # fathi_sayed@yahoo.com



                                                ABSTRACT
                   This paper proposes the application of the Wiener filter in an adaptive manner in
           speech enhancement. The proposed adaptive Wiener filter depends on the adaptation of the
           filter transfer function from sample to sample based on the speech signal statistics(mean
           and variance). The adaptive Wiener filter is implemented in time domain rather than in
           frequency domain to accommodate for the varying nature of the speech signal. The
           proposed method is compared to the traditional Wiener filter and spectral subtraction
           methods and the results reveal its superiority.

                Keywords: Speech Enhancement, Spectral Subtraction, Adaptive Wiener Filter



1   INTRODUCTION

     Speech enhancement is one of the most              is removed first. Decomposition of the vector space
important topics in speech signal processing.           of the noisy signal is performed by applying an
Several techniques have been proposed for this          eigenvalue or singular value decomposition or by
purpose like the spectral subtraction approach, the     applying the Karhunen-Loeve transform (KLT)[8].
signal subspace approach, adaptive noise canceling      Mi. et. al. have proposed the signal / noise KLT
and     the iterative Wiener filter[1-5] . The          based approach for colored noise removal[9]. The
performances of these techniques depend on              idea of this approach is that noisy speech frames
quality and intelligibility of the processed speech     are classified into speech-dominated frames and
signal. The improvement of the speech signal-to-        noise-dominated frames. In the speech-dominated
noise ratio (SNR) is the target of most techniques.     frames, the signal KLT matrix is used and in the
                                                        noise-dominated frames, the noise KLT matrix is
      Spectral subtraction is the earliest method for   used.
enhancing speech degraded by additive noise[1].               In this paper, we present a new technique to
This technique estimates the spectrum of the clean      improve the signal-to-noise ratio in the enhanced
(noise-free) signal by the subtraction of the           speech signal by using an adaptive implementation
estimated noise magnitude spectrum from the noisy       of the Wiener filter. This implementation is
signal magnitude spectrum while keeping the phase       performed in time domain to accommodate for the
spectrum of the noisy signal. The drawback of this      varying nature of the signal.
technique is the residual noise.
                                                               The paper is organized as follows: in section
      Another technique is a signal subspace            II, a review of the spectral subtraction technique is
approach [3]. It is used for enhancing a speech         presented. In section III, the traditional Wiener
signal degraded by uncorrelated additive noise or       filter in frequency domain is revisited. Section IV,
colored noise [6,7]. The idea of this algorithm is      proposes the adaptive Wiener filtering approach for
based on the fact that the vector space of the noisy    speech enhancement. In section V, a comparative
signal can be decomposed into a signal plus noise       study between the proposed adaptive Wiener filter,
subspace and an orthogonal noise subspace.              the Wiener filter in frequency domain and the
Processing is performed on the vectors in the signal    spectral subtraction approach is presented.
plus noise subspace only, while the noise subspace


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2     SPECTRAL SUBTRACTION
                                                         A noise-free signal estimate can then be obtained
      Spectral subtraction can be categorized as a       with the inverse Fourier transform. This noise
non-parametric approach, which simply needs an           reduction method is a specific case of the general
estimate of the noise spectrum. It is assume that        technique given by Weiss, et al. and extended by
there is an estimate of the noise spectrum that is       Berouti , et al.[2,12].
typically estimated during periods of speaker                  The spectral subtraction approach can be
silence. Let x(n) be a noisy speech signal :             viewed as a filtering operation where high SNR
                                                         regions of the measured spectrum are attenuated
          x ( n) = s ( n) + v ( n)                 (1)   less than low SNR regions. This formulation can be
                                                         given in terms of the SNR defined as:
where s(n) is the clean (the noise-free) signal, and                              2
v(n) is the white gaussian noise. Assume that the                          X (ω )
noise and the clean signals are uncorrelated. By                     SNR =                                (5)
                                                                            ˆ
                                                                           Pv (ω )
applying the spectral subtraction approach that
estimates the short term magnitude spectrum of the
                                                         Thus, equation (3) can be rewritten as:
noise-free signal S (ω ) by subtraction of the
                                                                   2          2 ˆ
                                    ˆ                         ˆ
                                                             S (ω ) = X (ω ) − Pv (ω )
estimated noise magnitude spectrum V (ω ) from
                                                                                                 −1       (6)
the noisy signal magnitude spectrum X (ω ) . It is                           2⎡           1  ⎤
                                                                     ≈ X (ω ) 1 +
sufficient to use the noisy signal phase spectrum as                              ⎢
                                                                                  ⎣      SNR ⎥
                                                                                             ⎦
an estimate of the clean speech phase
spectrum,[10]:
                                                               An important property of noise suppression
                                                         using spectral subtraction is that the attenuation
ˆ                ˆ
S(ω) = ( X (ω) − N(ω) ) exp(j∠X (ω))               (2)   characteristics change with the length of the
                                                         analysis window. A common problem for using
The estimated time-domain speech signal is               spectral subtraction is the musicality that results
obtained as the inverse Fourier transform of             from the rapid coming and going of waves over
 ˆ                                                       successive frames [13].
 S (ω ) .
       Another way to recover a clean signal s(n)        3   WIENER FILTER IN FREQUNCY
from the noisy signal x(n) using the spectral                DOMAIN
subtraction approach is performed by assuming
that there is an the estimate of the power spectrum              The Wiener filter is a popular technique that
of the noise Pv (ω ) , that is obtained by averaging     has been used in many signal enhancement
over multiple frames of a known noise segment.           methods. The basic principle of the Wiener filter is
An estimate of the clean signal short-time squared       to obtain a clean signal from that corrupted by
magnitude spectrum can be obtained as follow [8]:        additive noise. It is required estimate an optimal
                                                         filter for the noisy input speech by minimizing the
           ⎧X(ω) 2 −Pv(ω), if X(ω) 2 −Pv(ω) ≥0           Mean Square Error (MSE) between the desired
                    ˆ                 ˆ
        2 ⎪                                                                                        ˆ
                                                         signal s(n) and the estimated signal s ( n) . The
    ˆ
    S(ω) = ⎨
                                                   (3)   frequency domain solution to this optimization
           ⎪ 0,                        otherwise         problem is given by[13]:
           ⎩
                                                                              Psω)
                                                                               (
                                                                  H(ω) =                                  (7)
It is possible combine this magnitude spectrum                             Psω) + Pvω)
                                                                            (      (
estimate with the measured phase and then get the
Short Time Fourier Transform (STFT) estimate as          where Ps (ω ) and Pv (ω ) are the power spectral
follows:                                                 densities of the clean and the noise signals,
                                                         respectively. This formula can be derived
          ˆ        ˆ        j∠X (ω )                     considering the signal s and the noise signal v as
          S (ω ) = S (ω ) e                        (4)


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uncorrelated and stationary signals. The signal-to-                                   Pv (ω ) =σv2
noise ratio is defined by[13]:                                                                                                                   (10)

                           Ps (ω )                                   Consider a small segment of the speech
                  SNR =                             (8)     signal in which the signal x(n) is assumed to be
                           ˆ
                           Pv (ω )                          stationary, The signal x(n) can be modeled by:

This definition can be incorporated to the Wiener                 x(n) = mx + σxw(n)                   (11)
filter equation as follows:
                                                            where mx and σx are the local mean and standard
                                                            deviation of x(n). w(n) is a unit variance noise.
                                     −1
                   ⎡      1 ⎤                                        Within this small segment of speech, the
         H ( ω ) = ⎢1 +                               (9)
                        SNR ⎥
                                                            Wiener filter transfer function can be approximated
                   ⎣        ⎦                               by:

      The drawback of the Wiener filter is the fixed
                                                                                     Ps (ω )                            σs
                                                                                                                                2

frequency response at all frequencies and the                    H (ω ) =                                      =
                                                                            Ps (ω ) + Pv (ω )                       σs + σv
                                                                                                                        2               2
requirement to estimate the power spectral density
of the clean signal and noise prior to filtering.                                                        (12)
                                                            From Eq.(12), because H (ω ) is constant over the
4        THE PROPOSED ADAPTIVE WIENER
                                                            small segment of speech, the impulse response of
         FILTER
                                                            the Wiener filter can be obtained by:
      This section presents and adaptive
implementation of the Wiener filter which benefits
                                                                            σs
                                                                                 2
from the varying local statistics of the speech             h( n) =                       δ ( n)                                                 (13)
signal. A block diagram of the proposed approach                       σs + σv
                                                                            2         2

is illustrated in Fig. (1). In this approach, the
estimated speech signal mean mx and variance
                                                                                                  ˆ
                                                            From Eq.(13), the enhanced speech s ( n) within
                                                            this local segment can be expressed as:
σx   2
         are exploited.

                                                                                                                    σs
                                                                                                                            2
                    A priori knowledge                      s (n) = mx + ( x(n) - mx ) ∗
                                                            ˆ                                                                           δ ( n)
                                                                                                                σs + σv
                                                                                                                    2               2




                Space-
                                                                                      σs
                                                                                           2
Degraded speech variant                    Enhanced
 x(n)                                           speech
                                                                    = mx +                                 ( x(n) − mx )
                                                                                 σs + σv
                                                                                      2            2
                  h(n)
                                                    ˆ
                                            signal s ( n)                                                                                     (14)
                                                            If it is assumed that mx and                                σs          are updated at
                                                            each sample, we can say:

                      Measure of
                                                                                            σs (n) ( x(n) − mx(n))
                                                                                                       2

                      Local speech                          s (n) = mx (n) +
                                                            ˆ
                                                                                          σs (n) + σv
                                                                                               2                2
     A priori         statistics
    knowledge                                                                                                                                    (15)

                                                            In    Eq.(15),           the           local        mean                    mx(n)    and
Figure 1: Typical adaptive speech enhancement system
                 for additive noise reduction               ( x(n) − mx (n)) are modified separately from
                                                            segment to segment and then the results are
                                                            combined. If σs is much larger than σv the
                                                                               2                             2


         It is assumed that the additive noise v(n) is                     ˆ
                                                            output signal s ( n) is assumed to be primarily due
of zero mean and has a white nature with variance
                                                            to x(n) and the input signal x(n) is not attenuated. If
of σv .Thus, the power spectrum Pv (ω ) can be
       2


                                                            σs is smaller than σv , the filtering effect is
                                                               2                       2

approximated by:
                                                            performed.

                          Ubiquitous Computing and Communication Journal                                                                            3
     Notice that mx is identical to ms when                  In the first experiment , all the above-
                                                        mentioned algorithms are carried out on the Handle
 mv is zero. So, we can estimate mx (n) in Eq.(15)      signal with different SNRs and the output PSNR
from x(n) by:
                                                        results are shown in Fig. (2). The same experiment
                                 n+M
                                                        is repeated for the Laughter and Gong signals and
                        1
ms (n) = mx (n) =
ˆ        ˆ                       ∑ x(k )                the results are shown in Figs.(3) and (4),
                                                        respectively.
                    (2 M +1)    k =n−M
                                                             From these figures, it is clear that the proposed
                                                 (16)   adaptive Wiener filter approach has the best
                                                        performance for different SNRs. The adaptive
where ( 2 M + 1) is the number of samples in the        Wiener filter approach gives about 3-5 dB
                                                        improvement at different values of SNR. The non-
short segment used in the estimation.                   linearity between input SNR and output PSNR is
                                                        due to the adaptive nature of the filter.
           To measure the local signal statistics in
the system of Figure 1, the algorithm developed
uses the signal variance σs . The specific method
                           2


used to designing the space-variant h(n) is given by
(17.b).
     Since σx = σs + σv may be estimated
                2      2     2
                                                                                80
from x(n) by:
                                                                                70

         ⎧σx (n) − σv , if σx (n) > σv
           ˆ2       ˆ2      ˆ2       ˆ2
σs (n) = ⎨
 ˆ  2                                                                           60
         ⎩0,            otherwise
                                                           O u tp u t P S N R (d B )



                                                                                50

                                              (17.a)
        Where                                                                   40

                                                                                30
                        n+ M
             1
σx (n) =
 ˆ  2

         (2 M + 1)
                        ∑ ( x(k ) − m (n))
                       k =n−M
                                    ˆ    x
                                             2
                                                                                20
                                                                                                                       Spectral Subtraction
                                             (17.b)
                                                                                10                                     Wiener Filter
      By this proposed method, we guarantee that                                                                       Adaptive Wiener Filter
the filter transfer function is adapted from sample
to sample based on the speech signal statistics.                                       0
                                                                                       -10   -5   0   5     10      15 20      25      30       35
                                                                                                          Input SNR (dB)
5       EXPERIMENTAL RESULTS

      For evaluation purposes, we use different                 Figure 2: PSNR results for white noise
speech signals like the handel, laughter and gong        case at-10 dB to +35 dB SNR levels for Handle signal
signals. White Gaussian noise is added to each
speech signal with different SNRs. The different
speech enhancement algorithms such as the
spectral subtraction method, the Weiner filter in
frequency domain and the proposed adaptive
Wiener filter are carried out on the noisy speech
signals. The peak signal to noise ratio (PSNR)
results for each enhancement algorithm are
compared.



                    Ubiquitous Computing and Communication Journal                                                                          4
                                                                                                               reveal that the best performance is that of the
                      60                                                                                       proposed adaptive Wiener filter.

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Figure 3: PSNR results for white noise case at -10 dB
                                to +35 dB SNR levels for Laughter signal                                       Figure 5: Time domain results of the Handel sig. at
                                                                                                               SNR = +5dB (a) original sig. (b) noisy sig. (c) spectral
                                                                                                               subtraction. (d) Wiener filtering. (e) adaptive Wiener
                                                                                                               filtering.
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Figure 4: PSNR results for white noise case at -10 dB                                                                                                                                  ) re .(H
                                                                                                                                                                                     (e F q z)
                                     to +35 dB SNR levels for Gong signal

      The results of the different enhancement                                                                 Figure 6:The spectrum of the Handel sig. in Fig.(5) (a)
                                                                                                               original sig. (b) noisy sig. (c) spectral subtraction. (d)
algorithms for the handle signal with SNRs of 5,
                                                                                                               Wiener filtering. (e) adaptive Wiener filtering.
10,15 and 20 dB in the both time and frequency
domain are given in Figs. (5) to (12). These results


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                                                                                       (e) Time (msec)                                                                                                                                                             (e) Time(msec)

Figure 7: Time domain results of the Handel sig. at
SNR = 10 dB (a) original sig. (b) noisy sig. (c) spectral                                                                                                  Figure 9: Time domain results of the Handel sig. at
subtraction. (d) Wiener filtering. (e) adaptive Wiener                                                                                                     SNR = 15 dB (a) original sig. (b) noisy sig. (c) spectral
filtering.                                                                                                                                                 subtraction. (d) Wiener filtering. (e) adaptive Wiener
                                                                                                                                                           filtering.
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                                                                                ) re. z
                                                                              (e F q (H)                                                                                                                                                                          ) re. z
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Figure 8: The spectrum of the Handel sig. in Fig.(7)                                                                                                       Figure 10: The spectrum of the Handel sig. in Fig.(9)
(a) original sig. (b) noisy sig. (c) spectral subtraction. (d)                                                                                             (a) original sig. (b) noisy sig. (c) spectral subtraction. (d)
Wiener filtering. (e) adaptive Wiener filtering.                                                                                                           Wiener filtering. (e) adaptive Wiener filtering.




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                                                                                                                                                    6   CONCLUSION
                                   1                                                                                  1

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                                                                                                    A m p lit u d e
                                                                                                                                                           An adaptive Wiener filter approach for
                                   0                                                                                  0                             speech enhancement is proposed in this papaper.
                                                                                                                                                    This approach depends on the adaptation of the
                             -1                                                                                 -1
                                       0   2000 4000 6000 8000                                                            0   2000 4000 6000 8000   filter transfer function from sample to sample
                                                 (a)                                                                                (b)             based on the speech signal statistics(mean and
                                                                                                                                                    variance). This results indicates that the proposed
                                   1                                                                                  1                             approach provides the best SNR improvement
                 A m p lit u d e




                                                                                                    A m p lit u d e
                                   0                                                                                  0                             among the spectral subtraction approach and the
                                                                                                                                                    traditional Wiener filter approach in frequency
                             -1                                                                                 -1                                  domain. The results also indicate that the proposed
                                       0   2000 4000 6000 8000                                                            0   2000 4000 6000 8000   approach can treat musical noise better than the
                                                 (c)                                                                                (d)             spectral subtraction approach and it can avoid the
                                                                               1                                                                    drawbacks of Wiener filter in frequency domain .
                                                             A m p lit u d e




                                                                               0                                                                    REFERENCES

                                                                         -1                                                                         [1] S. F. Boll: Suppression of acoustic noise in
                                                                                   0    2000 4000 6000 8000                                         speech using spectral subtraction, IEEE Trans.
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                                                                                                                                                    pp. 113-120 (1979).
Figure 11: Time domain results of the Handel sig. at                                                                                                 [2] M. Berouti, R. Schwartz, and J. Makhoul:
SNR = 20 dB (a) original sig. (b) noisy sig. (c) spectral                                                                                           Enhancement of speech corrupted by acoustic
subtraction. (d) Wiener filtering. (e) adaptive Wiener                                                                                              noise, Proc. IEEE Int. Conf. Acoust., Speech
filtering.                                                                                                                                          Signal Processing, pp. 208-211 (1979).
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                                                                                                             0
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                  0
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                  0                                                                                          0                                      [5] J. S. Lim and A. V. Oppenheim.: All-pole
           -20                                                                                         -20                                          Modelling of Degraded Speech, IEEE Trans.
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                                                                                                                                                    based signal subspace        approach for speech
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                                                             0                                                                                      enhancement, in IEEE ICASSP, pp. 804-807
                                                                                                                                                    (1995).
                                                       -20                                                                                          [7] Y. Hu and P. Loizou: A subspace approach
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                                                          0                        00 00 00 00
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