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The problem of noise reduction has attracted a considerable amount of research attention over the past several decades. Numerous techniques were developed, and among them is the optimal Wiener filter, which is the most fundamental approach, and has been delineated in different forms and adopted in diversified applications. It is not a secret that the Wiener filter achieves noise reduction with some integrity loss of the speech signal. However, few efforts have been reported to show the inherent relationship between noise reduction and speech distortion. By defining a speech-distortion index and a noise-reduction factor, this chapter studies the quantitative performance behavior of the Wiener filter in the context of noise reduction. We show that for a single-channel Wiener filter, the amount of noise attenuation is in general proportionate to the amount of speech degradation. In other words, the more the noise is reduced, the more the speech is distorted. This may seem discouraging as we always expect an algorithm to have maximal noise attenuation without much speech distortion. Fortunately, we show that the speech distortion can be better managed by properly manipulating the Wiener filter, or by considering some knowledge of the speech signal. The former leads to a sub-optimal Wiener filter where a parameter is introduced to control the tradeoff between speech distortion and noise reduction, and the latter leads to the well-known parametric-model-based noise reduction technique. We also show that speech distortion can even be avoided if we have multiple realizations of the speech signal.

Speech signals are frequently disturbed by statistically independent additive noise signals. When the power fluctuation of the noise signal is significantly slower than that of the speech signal, a single-microphone approach may be successfully used to reduce the level of the disturbing noise. This chapter outlines algorithms for noise reduction which are based on short term spectral representations of speech and on optimal estimation techniques. We present some of the more prominent estimation methods for complex spectral coefficients, for the amplitude and phase of spectral coefficients, and for related parameters such as the a priori signal-to-noise ratio. We interpret these algorithms in terms of their input-output characteristics. Some recent developments such as the use of super-Gaussian speech models and the properties of the resulting estimators are highlighted. Furthermore, we discuss the estimation of the background noise power and the application of these techniques in conjunction with a low bit rate speech coder.

In this contribution, MAP spectral amplitude estimators for speech enhancement are presented. For single-microphone applications, efficient MAP estimators with a super-Gaussian speech model, that can be adapted with high accuracy towards the real distribution in a given system, are introduced. For multi-microphone applications, joint MAP estimators that also exploit spatial properties of speech and noise are derived. Both the integration of the more accurate speech model as well as the multi-microphone joint spectral amplitude estimation improve the performance of a common DFT domain speech enhancement system.

Modeling speech signals in the short-time Fourier transform (STFT) domain is a fundamental problem in designing speech enhancement systems. This chapter introduces a novel modeling approach, which is based on generalized autoregressive conditional heteroscedasticity (GARCH). GARCH is widely-used for volatility modeling of financial time-series such as exchange rates and stock returns. GARCH models take into account the heavy tailed distribution and volatility clustering characteristics of financial time-series. Spectral analysis shows that speech signals in the STFT domain are also characterized by heavy tailed distributions and volatility clustering. We demonstrate the application of GARCH modeling to speech enhancement, and show its advantage compared to using the conventional decision-directed method.

A noise suppression algorithm with high speech quality based on weighted noise estimation is presented. This algorithm continuously updates the estimated noise by weighted noisy speech in accordance with an estimated SNR. With a better noise estimate, a more correct SNR is obtained, resulting in the enhanced speech with low distortion. Subjective evaluation results show that five-grade mean opinion scores of this algorithm with a speech codec is improved by as much as 0.35, compared with either the MMSE-STSA or the EVRC noise suppression algorithm. A noise suppressor based on a later version of this noise suppression algorithm satisfies all the 3GPP minimum performance requirements. It is employed in the world’s first 3G handset equipped with a 3GPP-endorsed noise suppressor.

In this chapter, we present the signal subspace approach (SSA) for speech enhancement. The SSA is becoming a serious competitor to its already widely used frequency-domain counterparts since it seems to offer a better compromise between signal distortion and the level of the residual noise. We provide a detailed description of the technique in terms of its underlying theory as well as the implementation issues. We also discuss the methods, proposed in the literature, to deal with the colored noise case and to cope with the complexity concerns usually associated with the SSA. In addition to that, we provide a filterbank interpretation to the SSA which allows it to be viewed from a frequency-domain perspective which is a more intuitive domain as far as speech signals are concerned. Finally, we present some of the latest variations and extensions to the SSA found in the literature which also serve as suggestions to further research in this area.

The application of the Kalman filter to the single-microphone speech enhancement task is presented in this chapter. Among numerous published algorithms, an important sub-group employs the estimate-maximize (EM) procedure to iteratively estimate the spectral parameters of the speech and noise signals. We elaborate on a specific member of this sub-group. In the E-step, the Kalman smoother is applied and in the M-step, a non-standard Yule-Walker equation set is solved. An approximated EM algorithm is derived by applying the gradient-descent method to the likelihood function. We obtain a sequential, computationally efficient, algorithm. It is then shown, that the sequential parameter estimation can be replaced by a Kalman filter to obtain a dual speech and parameters Kalman filter. A natural generalization to the dual scheme is an estimation scheme in which both speech and parameters are jointly estimated by applying a nonlinear extension to the Kalman filter, namely the unscented Kalman filter . Extensive experimental study, using real speech and noise signals is provided to compare the proposed methods with alternative speech enhancement algorithms. Kalman filter based algorithms are shown to maintain the natural speech quality. However, their noise reduction ability is limited.

In many speech communication applications a microphone array is available nowadays, such that multi-microphone speech enhancement techniques can be used instead of single-microphone speech enhancement techniques. A wellknown multi-microphone speech enhancement technique is the generalized sidelobe canceller (GSC), which is however quite sensitive to signal model errors, such as microphone mismatch. This chapter discusses a more robust technique called the spatially pre-processed speech distortion weighted multichannel Wiener filter (SPSDW-MWF), which takes speech distortion due to signal model errors explicitly into account in its design criterion, and which encompasses the standard GSC as a special case. In addition, a novel frequency-domain criterion for the SDW-MWF is presented, from which several — existing and novel — adaptive frequency-domain algorithms can be derived for implementing the SDW-MWF. The noise reduction performance and the robustness of these adaptive algorithms is investigated for a hearing aid application. Using experimental results with a small-sized microphone array, it is shown that the SP-SDW-MWF is more robust against signal model errors than the GSC, both in stationary and in changing noise scenarios.

The convenience and the ease of use provided by hands-free operation of speech communication devices mean that speech enhancement schemes are becoming indispensable. In this chapter, two subband adaptive microphone array schemes are presented, which aim to provide good speech enhancement capability in poor signal to noise ratio situations. The basic commonality of the adaptive microphone array schemes is that they approximate the Wiener solution in an adaptive manner as new data comes in. Furthermore, both schemes include a quadratic constraint to prevent the trivial zero solution of the weights and to avoid suppression of the source of interest. The constraint is included to provide robustness against model mismatch and good spatial capture of the target signal. Furthermore, by using a subband structure the processing allows a time-frequency operation for each channel. As such, both schemes utilize the spatial, spectral, and temporal domains in an efficient and concise manner allowing a computational effective processing while maintaining high performance speech enhancement. Evaluations on the same data set, gathered from a car, show that the proposed schemes achieve good noise suppression up to 20 dB while experiencing very low levels of speech distortion.