IEEE Trans Neural Netw Learn Syst. 2017 Dec;28(12):3102-3108. doi: 10.1109/TNNLS.2016.2610960. Epub 2016 Oct 5.
In an underdetermined mixture system with unknown sources, it is a challenging task to separate these sources from their observed mixture signals, where . By exploiting the technique of sparse coding, we propose an effective approach to discover some 1-D subspaces from the set consisting of all the time-frequency (TF) representation vectors of observed mixture signals. We show that these 1-D subspaces are associated with TF points where only single source possesses dominant energy. By grouping the vectors in these subspaces via hierarchical clustering algorithm, we obtain the estimation of the mixing matrix. Finally, the source signals could be recovered by solving a series of least squares problems. Since the sparse coding strategy considers the linear representation relations among all the TF representation vectors of mixing signals, the proposed algorithm can provide an accurate estimation of the mixing matrix and is robust to the noises compared with the existing underdetermined blind source separation approaches. Theoretical analysis and experimental results demonstrate the effectiveness of the proposed method.
在一个具有未知源的欠定混合系统中，从观察到的混合信号中分离这些源是一项具有挑战性的任务，其中 。通过利用稀疏编码技术，我们提出了一种有效的方法，从由观察到的混合信号的所有时频 (TF) 表示向量组成的集合中发现一些 1-D 子空间。我们表明，这些 1-D 子空间与仅单个源具有主导能量的 TF 点相关联。通过通过层次聚类算法对这些子空间中的向量进行分组，我们获得了混合矩阵的估计。最后，通过求解一系列最小二乘问题可以恢复源信号。由于稀疏编码策略考虑了混合信号的所有 TF 表示向量之间的线性表示关系，因此与现有的欠定盲源分离方法相比，所提出的算法可以提供混合矩阵的准确估计，并且对噪声具有鲁棒性。理论分析和实验结果证明了所提出方法的有效性。
