In this paper, we address the speech denoising problem, where white Gaussian additive noise is to be removed from a given speech signal. Our approach is based on a redundant, analysis-sparse representation of the original speech signal. We pick an eigenvector of the Zauner unitary matrix and -- under certain assumptions on the ambient dimension -- we use it as window vector to generate a spark deficient Gabor frame. The analysis operator associated with such a frame, is a (highly) redundant Gabor transform, which we use as a sparsifying transform in denoising procedure. We conduct computational experiments on real-world speech data, solving the analysis basis pursuit denoising problem, with four different choices of analysis operators, including our Gabor analysis operator. The results show that our proposed redundant Gabor transform outperforms -- in all cases -- Gabor transforms generated by state-of-the-art window vectors of time-frequency analysis.

中文翻译：

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Star DGT：用于语音降噪的鲁棒Gabor变换

在本文中，我们解决了语音降噪问题，即从给定的语音信号中去除高斯白噪声。我们的方法基于原始语音信号的冗余，分析稀疏表示。我们选择Zauner ary矩阵的特征向量，并且-在某些环境尺寸假设下-将其用作窗口向量以生成火花不足的Gabor框架。与这样的帧相关联的分析运算符是（高度）冗余的Gabor变换，在降噪过程中我们将其用作稀疏变换。我们对现实世界中的语音数据进行了计算实验，解决了分析基准追踪降噪问题，并选择了包括Gabor分析算子在内的四种分析算子。