On the importance of the Pearson correlation coefficient in noise reduction
On the importance of the Pearson correlation coefficient in noise reduction
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DOI：
10.1109/tasl.2008.919072
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发表时间：
2008-05-01
影响因子：
--
通讯作者：
Huang, Yiteng (Arden)
中科院分区：
文献类型：
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作者：
Benesty, Jacob;Chen, Jingdong;Huang, Yiteng (Arden)
降噪旨在从嘈杂的观察中估计出干净的语音，在过去的几十年里吸引了大量的研究和工程关注。在单通道场景中，可以通过将麦克风拾取的噪声信号传递通过线性滤波器/变换来获得干净语音的估计。那么，核心问题是如何找到最佳的滤波器/变换，使得经过滤波处理后，信噪比（SNR）得到改善，但所需的语音信号不会明显失真。大多数现有的最优滤波器（例如维纳滤波器和子空间变换）都是根据均方误差（MSE）准则制定的。然而，使用 MSE 公式，无法看到最佳降噪滤波器的许多所需属性，例如 SNR 行为。在本文中，我们提出了一种基于皮尔逊相关系数（PCC）的新标准。我们表明，在降噪的背景下，平方 PCC (SPCC) 具有许多吸引人的特性。可以用作优化成本函数来导出许多最优和次优降噪滤波器。与 MSE 相比，使用 SPCC 的明显优势是可以轻松分析所得最佳滤波器的降噪性能（在 SNR 改进和语音失真方面）。这表明，就降噪而言，与 MSE 相比，基于 SPCC 的成本函数可以作为更自然的优化标准。
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.