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Binaural noise reduction with a stereophonic (or simply stereo) setup has become a very important problem as stereo sound systems and devices are being more and more deployed in modern voice communications. This problem is very challenging since it requires not only the reduction of the noise at the stereo inputs, but also the preservation of the spatial information embodied in the two channels so that after noise reduction the listener can still localize the sound source from the binaural outputs. As a result, simply applying a traditional single-channel noise reduction technique to each channel individually may not work as the spatial effects may be destroyed. In this paper, we present a new formulation of the binaural noise reduction problem in stereo systems. We first form a complex signal from the stereo inputs with one channel being its real part and the other being its imaginary part. By doing so, the binaural noise reduction problem can be processed by a single-channel widely linear filter. The widely linear estimation theory is then used to derive optimal noise reduction filters that can fully take advantage of the noncircularity of the complex speech signal to achieve noise reduction while preserving the desired signal (speech) and spatial information. With this new formulation, the Wiener, minimum variance distortionless response (MVDR), maximum signal-to-noise ratio (SNR), and tradeoff filters are derived. Experiments are provided to justify the effectiveness of these filters. [ABSTRACT FROM AUTHOR]

Abstract: Noise reduction is often formulated as a linear filtering problem in the frequency domain. With this formulation, the core issue of noise reduction becomes how to design an optimal frequency-domain filter that can significantly suppress noise without introducing perceptually noticeable speech distortion. While higher-order information can be used, most existing approaches use only second-order statistics to design the noise-reduction filter because they are relatively easier to estimate and are more reliable. When we transform non-stationary speech signals into the frequency domain and work with the short-time discrete Fourier transform coefficients, there are two types of second-order statistics, i.e., the variance and the so-called pseudo-variance due to the noncircularity of the signal. So far, only the variance information has been exploited in designing different noise-reduction filters while the pseudo-variance has been neglected. In this paper, we attempt to shed some light on how to use noncircularity in the context of noise reduction. We will discuss the design of optimal and suboptimal noise reduction filters using both the variance and pseudo-variance and answer the basic question whether noncircularity can be used to improve the noise-reduction performance. [Copyright &y& Elsevier]

Noise reduction, which aims at estimating a clean speech from noisy observations, has attracted a considerable amount of research and engineering attention over the past few decades. In the single-channel scenario, an estimate of the clean speech can be obtained by passing the noisy signal picked up by the microphone through a linear filter/transformation. The core issue, then, is how to find an optimal filter/transformation such that, after the filtering process, the signal-to-noise ratio (SNR) is improved but the desired speech signal is not noticeably distorted. Most of the existing optimal filters (such as the Wiener filter and subspace transformation) are formulated from the mean-square error (MSE) criterion. However, with the MSE formulation, many desired properties of the optimal noise-reduction filters such as the SNR behavior cannot be seen. In this paper, we present a new criterion based on the Pearson correlation coefficient (PCC). We show that in the context of noise reduction the squared PCC (SPCC) has many appealing properties and can be used as an optimization cost function to derive many optimal and suboptimal noise-reduction filters. The clear advantage of using the SPCC over the MSE is that the noise-reduction performance (in terms of the SNR improvement and speech distortion) of the resulting optimal filters can be easily analyzed. This shows that, as far as noise reduction is concerned, the SPCC-based cost function serves as a more natural criterion to optimize as compared to the MSE. [ABSTRACT FROM AUTHOR]

The widely studied subspace and linear filtering methods for noise reduction require the noise correlation matrix to be invertible. In certain application scenarios, however, this matrix is either rank deficient or very ill conditioned, so this requirement cannot be fulfilled. In this paper, we investigate possible solutions to this important problem based on subspace techniques for single-channel time-domain noise reduction. The eigenvalue decomposition is applied to both the speech and noise correlation matrices to separate the null and nonnull subspaces. Then, a set of optimal and suboptimal filters are derived from the nullspace of the noise signal. Through simulations, we observe that the proposed filters are able to significantly reduce noise without introducing much distortion to the desired signal. In comparison with the conventional Wiener approach, the developed filters perform significantly better in improving both the signal-to-noise ratio (SNR) and the perceptual evaluation of speech quality (PESQ) score when the noise correlation matrix is rank deficient. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of single-channel noise reduction in the time domain. The objective is to find a lower dimensional filter that can yield a noise reduction performance as close as possible to or even better than that obtained by the full-rank solution. This is achieved in three steps. First, we transform the observation signal vector sequence, through a semi-orthogonal matrix, into a sequence of transformed signal vectors with a reduced dimension. Second, a reduced-rank filter is applied to get an estimate of the clean speech in the transformed domain. Third, the estimate of the clean speech in the time domain is obtained by an inverse semi-orthogonal transformation. The focus of this paper is on the derivation of semi-orthogonal transformations under certain estimation criteria in the first step and the design of the reduced-rank optimal filters that can be used in the second step. We show how noise reduction using the principle of rank reduction can be cast as an optimal filtering problem, and how different semi-orthogonal transformations affect the noise reduction performance. Simulations are performed under various conditions to validate the deduced filters for noise reduction. [ABSTRACT FROM AUTHOR]

Abstract: Conventional multichannel noise reduction techniques are formulated by splitting the processed microphone observations into two terms: filtered noise-free speech and residual additive noise. The first term is treated as desired signal while the second is a nuisance. Then, the objective has typically been to reduce the nuisance while keeping the filtered speech as similar as possible to the clean speech. It turns out that this treatment of the overall filtered speech as the desired signal is inappropriate as will become clear soon. In this paper, we present a new study of the multichannel time-domain noise reduction filters. We decompose the noise-free microphone array observations into two components where the first is correlated with the target signal and perfectly coherent across the sensors while the second consists of residual interference. Then, well-known time-domain filters including the minimum variance distortionless response (MVDR), the space–time (ST) prediction, the maximum signal-to-noise ratio (SNR), the linearly constrained minimum variance (LCMV), the multichannel tradeoff, and Wiener filters are derived. Besides, the analytical performance evaluation of these time-domain filters is provided and new insights into their functioning are presented. Numerical results are finally given to corroborate our study. [Copyright &y& Elsevier]