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

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New insights into the noise reduction Wiener filter

Since the statistics of the speech signal as well as of the noise are not explicitly available, and the most perceptually meaningful distortion measure is not known, model-based approaches have recently been extensively studied and applied to the three basic problems of speech enhancement: signal estimation from a given sample function of noisy speech, signal coding when only noisy speech is available, and recognition of noisy speech signals in man-machine communication. Research on the model-based approach is integrated and put into perspective with other more traditional approaches for speech enhancement. A unified statistical approach for the three basic problems of speech enhancement is developed, using composite source models for the signal and noise and a fairly large set of distortion measures. >

Statistical-model-based speech enhancement systems

The importance of phase in speech enhancement

Scalar and vector Kalman filters are implemented for filtering speech contaminated by additive white noise or colored noise, and an iterative signal and parameter estimator which can be used for both noise types is presented. Particular emphasis is placed on the removal of colored noise, such as helicopter noise, by using state-of-the-art colored-noise-assumption Kalman filters. The results indicate that the colored noise Kalman filters provide a significant gain in signal-to-noise ratio (SNR), a visible improvement in the sound spectrogram, and an audible improvement in output speech quality, none of which are available with white-noise-assumption Kalman and Wiener filters. When the filter is used as a prefilter for linear predictive coding, the coded output speech quality and intelligibility are enhanced in comparison to direct coding of the noisy speech. >

Filtering of colored noise for speech enhancement and coding

With the advent of `multimedia', digital signal processing (DSP) of sound has emerged from the shadow of bandwidth limited speech processing to become a research field of its own. To date, most research in DSP applied to sound has been concentrated on speech, which is bandwidth limited to about 4 kilohertz. Speech processing is also limited by the low fidelity typically expected in the telephone network. Today, the main applications of audio DSP are high quality audio coding and the digital generation and manipulation of music signals. They share common research topics including perceptual measurement techniques and analysis/synthesis methods. Additional important topics are hearing aids using signal processing technology and hardware architectures for digital signal processing of audio. In all these areas the last decade has seen a significant amount of application-oriented research. The frequency range of wideband audio has an upper limit of 20 kilohertz and the resulting difference in frequency range and Signal to Noise Ratio (SNR) due to sample size must be taken into account when designing DSP algorithms. There are whole classes of algorithms that the speech community is not interested in pursuing or using. These algorithms and techniques are revealed in this book. This book is suitable for advanced level courses and serves as a valuable reference for researchers in the field. Interested and informed engineers will also find the book useful in their work.

Applications of digital signal processing to audio and acoustics

In this paper, the problem of speech enhancement when only corrupted speech signal is available for processing is considered. For this, the Kalman filtering method is studied and compared with the Wiener filtering method. Its performance is found to be significantly better than the Wiener filtering method. A delayed-Kalman filtering method is also proposed which improves the speech enhancement performance of Kalman filter further.

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A speech enhancement method based on Kalman filtering

The problem of robust estimation of autoregressive parameters in the presence of outliers is considered. The least squares estimate lacks efficiency robustness when innovation outliers are present. Several M-estimates (maximum likelihood type) corresponding to different cost functions show good efficiency robustness against innovation outliers. The M-estimate with Welsch cost function is found to be the best in a comparative simulation study. However, in the case of additive outliers, M-estimates are not robust and they give large bias errors. Generalized M-estimates are recommended for the additive outlier case. A simulation study shows that a combination of Welsch function as the weight function and Andrews or Welsch function as the cost function produces the best performance in generalized M-estimates. >

Robust M-estimates and generalized M-estimates for autoregressive parameter estimation

The problem of adaptive estimation of linear prediction (LP) coefficients from noisy speech is considered. Performance of three adaptive ARMA spectral estimation algorithms are studied for this purpose: the recursive extended least squares (RELS) algorithm, the recursive maximum likelihood (RML) algorithm, and the overdetermined recursive instrumental variable (ORIV) algorithm. To put them in proper perspective, the normalized LMS (NLMS) has also been considered. The ORIV algorithm is found to be the best in terms of Itakura distance from the ideal LP coefficients and the power spectral density estimation. The RML algorithm is found to be robust in highly noisy cases. >

A. Basu

Papers

A speech enhancement method based on Kalman filtering

Robust M-estimates and generalized M-estimates for autoregressive parameter estimation

A comparative performance evaluation of adaptive ARMA spectral estimation methods for noisy speech