基于势函数与压缩感知的欠定盲源分离

传统的基于K均值聚类算法及最小路径法的欠定盲源分离两步法存在K值难以确定，对初始值敏感，噪声和奇异点难以排除以及相对缺乏理论依据等诸多不足，针对以上问题，提出了基于势函数及压缩感知理论的新型两步算法。该算法首先利用多峰值粒子群寻优算法改进的势函数法来估计混合矩阵，然后利用估计矩阵来构建传感矩阵，并将基于正交匹配追踪的压缩感知算法引入欠定盲源分离过程中，最终实现源信号的重构。仿真实验结果表明，混合矩阵最高估计精度达到99.13%，重构信号干扰比均高于10dB，很好的满足了重构精度的要求，验证了本文算法的有效性。所提算法对一维混合信号的欠定盲源分离具有良好的普适性和较高的准确率。

Under-determined blind source separation based on potential function and compressive sensing

There are some deficiencies in traditional two-step algorithm for under-determined blind source separation, such as the value of K is difficult to be determined, the algorithm is sensitive to the initial value, noises and singular points are difficult to be excluded, the algorithm is lacking theory basis, etcetera. In order to solve these problems, a new two-step algorithm based on the potential function algorithm and compressive sensing theory was proposed. Firstly, the mixing matrix was estimated by improved potential function algorithm based on multi-peak value particle swarm optimization algorithm, after the sensing matrix was constructed by the estimated mixing matrix, the sensing compressive algorithm based on orthogonal matching pursuit was introduced in the process of under-determined blind source separation to realize the signal reconstruction. The simulation results show that the highest estimation precision of the mixing matrix can reach 99.13%, and all the signal reconstruction interference ratios can be higher than 10dB, which meets the reconstruction accuracy requirements well and confirms the effectiveness of the proposed algorithm. This algorithm is of good universality and high accuracy for under-determined blind source separation of one-dimensional mixing signals.