基于压缩感知和优化算法的欠定盲源信号分离

Underdetermined Blind Source Separation Based on Compressed Sensing and Optimization Algorithm

针对目前欠定盲源信号分离在源信号不充分稀疏的情况下分离精度较低的问题,提出一种基于压缩感知和优化算法的欠定盲源信号分离方法.首先分析了欠定盲源信号分离和压缩感知问题的等价性,并建立基于压缩感知的欠定盲源信号分离的数学模型;然后以分离信号的稀疏性和互相关性来建立目标函数,并通过使用压缩感知和优化算法来实现欠定盲源信号的分离;最后对语音信号进行了仿真实验.实验结果表明,在源信号不充分稀疏的情况下,利用这种方法得到的分离信号与源信号的平均相似系数为0.990 3,由此可见这种方法是一种有效的、分离精度较高的分离方法.这也为欠定盲源信号分离问题的研究提供了一种新的途径和手段.

In view of low accuracy of the present underdetermined blind source separation under the condition that the source signal is not fully sparse, a method of underdetermined blind source separation based on Compressed Sensing （CS） and optimization algorithm is put forward. Firstly, the equivalence between underdetermined blind source separation and Compressed Sensing is analyzed, and the separation model of underdetermined blind source is established;Secondly, the objective function is established by the sparsity and cross correlation of the separate signal, and the underdetermined blind source separation is realized by Compression Sensing and optimization algorithm;Finally, the simulation experiments of speech signals are carded out. The experiment results have shown that the average correlation coefficient of the separated signals using this method and source signals is 0. 990 3. So it is a method of underdetermined blind source separation with high efficiency and accuracy, which also provides a new method and means for underdetermined blind source separation.