Abstract: This paper proposes a speech enhancement algorithm putting the theory of Alternating Direction Method of Multipliers（ADMM） into the algorithm of sparse nonnegative matrix factorization, which can solve the problems such as slow convergence and poor local optima in the traditional speech enhancement based Nonnegative Matrix Factorization（NMF）. It mainly consists of a training stage and an enhancement stage. During the training stage, the dictionaries of the noise are constructed as the prior information by using the ADMM based nonnegative matrix factorization. In the enhancement stage, the spectrum of noisy speech is analyzed by the sparse nonnegative matrix factorization algorithm. After that, the noise dictionary is combined with iterative formulation to evaluate the speech dictionary and the coding matrix of speech. The clean part of the speech is finally reconstructed from the noisy speech. Compared with the traditional speech enhancement methods of NMF, extensive experiments indicate that this algorithm not only has faster speed but also gets better noise suppression performance especially under instantaneous noise environment.

Key words: speech enhancement, sparse nonnegative matrix factorization, alternating direction method of multipliers

摘要： 提出一种基于交替方向乘子法的（Alternating Direction Method of Multipliers，ADMM）稀疏非负矩阵分解语音增强算法，该算法既能克服经典非负矩阵分解（Nonnegative Matrix Factorization，NMF）语音增强算法存在收敛速度慢、易陷入局部最优等问题，也能发挥ADMM分解矩阵具有的强稀疏性。算法分为训练和增强两个阶段：训练时，采用基于ADMM非负矩阵分解算法对噪声频谱进行训练，提取噪声字典，保存其作为增强阶段的先验信息；增强时，通过稀疏非负矩阵分解算法，从带噪语音频谱中对语音字典和语音编码进行估计，重构原始干净的语音，实现语音增强。实验表明，该算法速度更快，增强后语音的失真更小，尤其在瞬时噪声环境下效果显著。

关键词: 语音增强, 稀疏非负矩阵分解, 交替方向乘子法