In this paper, we introduce a quadratic approach for single-channel noise reduction. The desired signal magnitude is estimated by applying a linear filter to a modified version of the observations’ vector. The modified version is constructed from a Kronecker product of the observations’ vector with its complex conjugate. The estimated signal magnitude is multiplied by a complex exponential whose phase is obtained using a conventional linear filtering approach. We focus on the linear and quadratic maximum signal-to-noise ratio (SNR) filters and demonstrate that the quadratic filter is superior in terms of subband SNR gains. In addition, in the context of speech enhancement, we show that the quadratic filter is ideally preferable in terms of perceptual evaluation of speech quality (PESQ) and short-time objective intelligibility (STOI) scores. The advantages, compared to the conventional linear filtering approach, are particularly significant for low input SNRs, at the expanse of a higher computational complexity. The results are verified in practical scenarios with nonstationary noise and in comparison to well-known speech enhancement methods. We demonstrate that the quadratic maximum SNR filter may be superior, depending on the nonstationary noise type.

中文翻译：

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用于单通道降噪的二次方法

在本文中，我们介绍了一种用于单通道降噪的二次方法。通过将线性滤波器应用于观测向量的修改版本来估计所需的信号幅度。修改后的版本由观测向量与其复共轭的 Kronecker 积构成。估计的信号幅度乘以复指数，其相位是使用传统线性滤波方法获得的。我们专注于线性和二次最大信噪比 (SNR) 滤波器，并证明二次滤波器在子带 SNR 增益方面更胜一筹。此外，在语音增强的背景下，我们表明二次滤波器在语音质量的感知评估 (PESQ) 和短时客观可懂度 (STOI) 分数方面是理想的首选。与传统的线性滤波方法相比，这些优势对于低输入 SNR 尤其显着，但计算复杂度更高。结果在具有非平稳噪声的实际场景中得到了验证，并与众所周知的语音增强方法进行了比较。我们证明了二次最大 SNR 滤波器可能更好，具体取决于非平稳噪声类型。