Simon Doclo

New insights into the noise reduction Wiener filter

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

GSVD-based optimal filtering for single and multimicrophone speech enhancement

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.

Design of broadband beamformers robust against gain and phase errors in the microphone array characteristics

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.

Frequency-domain criterion for the speech distortion weighted multichannel Wiener filter for robust noise reduction

Recently, a generalized multi-microphone noise reduction scheme, referred to as the spatially pre-processed speech distortion weighted multichannel Wiener filter (SP-SDW-MWF), has been presented. This scheme consists of a fixed spatial pre-processor and a multichannel adaptive noise canceler (ANC) optimizing the SDW-MWF cost function. By taking speech distortion explicitly into account in the design criterion of the multichannel ANC, the SP-SDW-MWF adds robustness to the standard generalized sidelobe canceler (GSC). In this paper, we present a multichannel frequency-domain criterion for the SDW-MWF, from which several - existing and novel - adaptive frequency-domain algorithms can be derived. The main difference between these adaptive algorithms consists in the calculation of the step size matrix (constrained vs. unconstrained, block-structured vs. diagonal) used in the update formula for the multichannel adaptive filter. We investigate the noise reduction performance, the robustness and the tracking performance of these adaptive algorithms, using a perfect voice activity detection (VAD) mechanism and using an energy-based VAD. Using experimental results with a small-sized microphone array in a hearing aid, it is shown that the SP-SDW-MWF is more robust against signal model errors than the GSC, and that the block-structured step size matrix gives rise to a faster convergence and a better tracking performance than the diagonal step size matrix, only at a slightly higher computational cost.

Reduced-Bandwidth and Distributed MWF-Based Noise Reduction Algorithms for Binaural Hearing Aids

In a binaural hearing aid system, output signals need to be generated for the left and the right ear. Using the binaural multichannel Wiener filter (MWF), which exploits all microphone signals from both hearing aids, a significant reduction of background noise can be achieved. However, due to power and bandwidth limitations of the binaural link, it is typically not possible to transmit all microphone signals between the hearing aids. To limit the amount of transmitted information, this paper presents reduced-bandwidth MWF-based noise reduction algorithms, where a filtered combination of the contralateral microphone signals is transmitted. A first scheme uses a signal-independent beamformer, whereas a second scheme uses the output of a monaural MWF on the contralateral microphone signals and a third scheme involves an iterative distributed MWF (DB-MWF) procedure. It is shown that in the case of a rank-1 speech correlation matrix, corresponding to a single speech source, the DB-MWF procedure converges to the binaural MWF solution. Experimental results compare the noise reduction performance of the reduced-bandwidth algorithms with respect to the benchmark binaural MWF. It is shown that the best performance of the reduced-bandwidth algorithms is obtained by the DB-MWF procedure and that the performance of the DB-MWF procedure approaches quite well the optimal performance of the binaural MWF.

Speech enhancement with multichannel Wiener filter techniques in multimicrophone binaural hearing aids

This paper evaluates speech enhancement in binaural multimicrophone hearing aids by noise reduction algorithms based on the multichannel Wiener filter (MWF) and the MWF with partial noise estimate (MWF-N). Both algorithms are specifically developed to combine noise reduction with the preservation of binaural cues. Objective and perceptual evaluations were performed with different speech-in-multitalker-babble configurations in two different acoustic environments. The main conclusions are as follows: (a) A bilateral MWF with perfect voice activity detection equals or outperforms a bilateral adaptive directional microphone in terms of speech enhancement while preserving the binaural cues of the speech component. (b) A significant gain in speech enhancement is found when transmitting one contralateral microphone signal to the MWF active at the ipsilateral hearing aid. Adding a second contralateral microphone showed a significant improvement during the objective evaluations but not in the subset of scenarios tested during the perceptual evaluations. (c) Adding the partial noise estimate to the MWF, done to improve the spatial awareness of the hearing aid user, reduces the amount of speech enhancement in a limited way. In some conditions the MWF-N even outperformed the MWF possibly due to an improved spatial release from masking.

Theoretical Analysis of Binaural Multimicrophone Noise Reduction Techniques

Binaural hearing aids use microphone signals from both left and right hearing aid to generate an output signal for each ear. The microphone signals can be processed by a procedure based on speech distortion weighted multichannel Wiener filtering (SDW-MWF) to achieve significant noise reduction in a speech + noise scenario. In binaural procedures, it is also desirable to preserve binaural cues, in particular the interaural time difference (ITD) and interaural level difference (ILD), which are used to localize sounds. It has been shown in previous work that the binaural SDW-MWF procedure only preserves these binaural cues for the desired speech source, but distorts the noise binaural cues. Two extensions of the binaural SDW-MWF have therefore been proposed to improve the binaural cue preservation, namely the MWF with partial noise estimation (MWF-eta) and MWF with interaural transfer function extension (MWF-ITF). In this paper, the binaural cue preservation of these extensions is analyzed theoretically and tested based on objective performance measures. Both extensions are able to preserve binaural cues for the speech and noise sources, while still achieving significant noise reduction performance.

Superdirective Beamforming Robust Against Microphone Mismatch

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

Design of far-field and near-field broadband beamformers using eigenfilters

This paper discusses two novel non-iterative design procedures based on eigenfilters for designing broadband beamformers with an arbitrary spatial directivity pattern for an arbitrary microphone configuration. In the conventional eigenfilter technique a reference frequency-angle point is required, whereas in the eigenfilter technique based on a TLS (total least squares) error criterion, no reference point is required. It is shown how to design broadband beamformers in the far-field, near-field and mixed near-field far-field of the microphone array. Both eigenfilter techniques are compared with other broadband beamformer design procedures (least-squares, maximum energy array, non-linear criterion). It will be shown by simulations that among the considered non-iterative design procedures the TLS eigenfilter technique has the best performance, i.e. best resembling the performance of the non-linear design procedure but having a significantly lower computational complexity.

Robust adaptive time delay estimation for speaker localization in noisy and reverberant acoustic environments

Two adaptive algorithms are presented for robust time delay estimation (TDE) in acoustic environments with a large amount of background noise and reverberation. Recently, an adaptive eigenvalue decomposition (EVD) algorithm has been developed for TDE in highly reverberant acoustic environments. In this paper, we extend the adaptive EVD algorithm to noisy and reverberant acoustic environments, by deriving an adaptive stochastic gradient algorithm for the generalized eigenvalue decomposition (GEVD) or by prewhitening the noisy microphone signals. We have performed simulations using a localized and a diffuse noise source for several SNRs, showing that the time delays can be estimated more accurately using the adaptive GEVD algorithm than using the adaptive EVD algorithm. In addition, we have analyzed the sensitivity of the adaptive GEVD algorithm with respect to the accuracy of the noise correlation matrix estimate, showing that its performance may be quite sensitive, especially for low SNR scenarios.