The problem of noise reduction has attracted a considerable amount of research attention over the past several decades. Among the numerous techniques that were developed, the optimal Wiener filter can be considered as one of the most fundamental noise reduction approaches, which has been delineated in different forms and adopted in various applications. Although it is not a secret that the Wiener filter may cause some detrimental effects to the speech signal (appreciable or even significant degradation in quality or intelligibility), few efforts have been reported to show the inherent relationship between noise reduction and speech distortion. By defining a speech-distortion index to measure the degree to which the speech signal is deformed and two noise-reduction factors to quantify the amount of noise being attenuated, this paper studies the quantitative performance behavior of the Wiener filter in the context of noise reduction. We show that in the single-channel case the a posteriori signal-to-noise ratio (SNR) (defined after the Wiener filter) is greater than or equal to the a priori SNR (defined before the Wiener filter), indicating that the Wiener filter is always able to achieve noise reduction. However, the amount of noise reduction is in general proportional to the amount of speech degradation. This may seem discouraging as we always expect an algorithm to have maximal noise reduction without much speech distortion. Fortunately, we show that speech distortion can be better managed in three different ways. If we have some a priori knowledge (such as the linear prediction coefficients) of the clean speech signal, this a priori knowledge can be exploited to achieve noise reduction while maintaining a low level of speech distortion. When no a priori knowledge is available, we can still achieve a better control of noise reduction and speech distortion by properly manipulating the Wiener filter, resulting in a suboptimal Wiener filter. In case that we have multiple microphone sensors, the multiple observations of the speech signal can be used to reduce noise with less or even no speech distortion

A generalized singular value decomposition (GSVD) based algorithm is proposed for enhancing multimicrophone speech signals degraded by additive colored noise. This GSVD-based multimicrophone algorithm can be considered to be an extension of the single-microphone signal subspace algorithms for enhancing noisy speech signals and amounts to a specific optimal filtering problem when the desired response signal cannot be observed. The optimal filter can be written as a function of the generalized singular vectors and singular values of a speech and noise data matrix. A number of symmetry properties are derived for the single-microphone and multimicrophone optimal filter, which are valid for the white noise case as well as for the colored noise case. In addition, the averaging step of some single-microphone signal subspace algorithms is examined, leading to the conclusion that this averaging operation is unnecessary and even suboptimal. For simple situations, where we consider localized sources and no multipath propagation, the GSVD-based optimal filtering technique exhibits the spatial directivity pattern of a beamformer. When comparing the noise reduction performance for realistic situations, simulations show that the GSVD-based optimal filtering technique has a better performance than standard fixed and adaptive beamforming techniques for all reverberation times and that it is more robust to deviations from the nominal situation, as, e.g., encountered in uncalibrated microphone arrays.

In everyday environments, we are frequently immersed by unwanted acoustic noise and interference while we want to listen to acoustic signals, most often speech. Technology for assisted listening is then desired to increase the efficiency of speech communication, reduce listener fatigue, or just allow for enjoying undisturbed sounds (e.g., music). For people with normal hearing, assisted listening devices (ALDs) mainly aim to achieve hearing protection or increase listening comfort; however, for hearing-impaired individuals, as the most prominent user group so far, further progress of assisted listening technology is crucial for better inclusion into our world of pervasive acoustic communication.

Fixed superdirective beamformers using small-sized microphone arrays are known to be highly sensitive to errors in the assumed microphone array characteristics (gain, phase, position). This paper discusses the design of robust superdirective beamformers by taking into account the statistics of the microphone characteristics. Different design procedures are considered: applying a white noise gain constraint, trading off the mean noise and distortion energy, minimizing the mean deviation from the desired superdirective directivity pattern, and maximizing the mean or the worst case directivity factor. When computational complexity is not an issue, maximizing the mean or the worst case directivity factor is the preferred design procedure. In addition, it is shown how to determine a suitable parameter range for the other design procedures such that both a high directivity and a high level of robustness are obtained

Fixed broadband beamformers using small-size microphone arrays are known to be highly sensitive to errors in the microphone array characteristics. The paper describes two design procedures for designing broadband beamformers with an arbitrary spatial directivity pattern, which are robust against gain and phase errors in the microphone array characteristics. The first design procedure optimizes the mean performance of the broadband beamformer and requires knowledge of the gain and the phase probability density functions, whereas the second design procedure optimizes the worst-case performance by using a minimax criterion. Simulations with a small-size microphone array show the performance improvement that can be obtained by using a robust broadband beamformer design procedure.