基于CS与K-SVD的欠定盲源分离稀疏分量分析

Sparse presentation of underdetermined blind source separation based on compressed sensing and K-SVD

为了提高盲源分离的准确率,提出了结合压缩感知(CS)与K均值奇异值分解(K-SVD)的稀疏分量分析方法进行盲源分离.首先,分析欠定盲源分离估计源信号与压缩感知问题的等价性,建立压缩感知框架;其次,在此框架下利用K-SVD方法训练稀疏字典;最后利用经典追踪算法计算得到稀疏分量,结合传统的两步法,进行盲源分离.大量实验表明,该算法与其他稀疏表示方法相比获得了较好的分离效果.与传统两步法不同的是,该算法在压缩感知框架下利用K-SVD方法自适应地训练稀疏字典,求出混合信号的稀疏表示,稀疏分量分析方法的改进对盲源分离的准确率起到直接的影响作用.

To improve the precision of blind source separation,a method based on the compressed sensing（CS） and K-means singular value decomposition（K-SVD） is proposed.First,the equivalence between the problem of estimating the source in underdetermined blind source separation and the compressed sensing is analyzed and the framework of compressed sensing is built.Then K-SVD is used to train sparse dictionary self-adaptive under the framework.Finally the sparse component is computed using classic basis pursuit algorithm.Through lots of experiments the algorithm is proved to be a better algorithm,which inherits the advantages of sparse presentation ability and can significantly improve the precision of blind source separation.Different from traditional two steps methods,the algorithm proposed gets sparse presentation of signal taking a new way that combine CS and K-SVD,it shows that sparse presentation influences the result of blind resource separation directly.