盲信号压缩重构——模型与方法

通过分析欠定盲信号分离模型和压缩感知模型本质内涵和内在联系，建立了基于压缩感知的欠定盲信号重构问题的数学模型，该模型对于欠定盲信号分离的实现提供了一个新的解决途径。基于该模型的压缩重构方法通过两步来实现：分别利用源信号稀疏域性质实现对盲估计欠定混合矩阵的估计；利用压缩感知的重构稀疏源信号的方法，实现对欠定稀疏盲信号的分离和重构。提出的算法根据实际应用场合，具有一定扩展能力。最后通过模拟实验验证了提出模型和相应算法的有效性。

Blind signal compressed reconstruction: model and method

The model inherent connections between underdetermined blind source separation and compressed sensing is analyzed, and the mathematical model of underdetermined blind signal reconstruction problems based on the compressed sensing model is built. The mixing matrix is estimated using the structure of the time domain or transform domain of the source signals. Based on the estimated mixing matrix, the greedy  orthogonal matching pursuit method is used to realize the reconstruction of the underdetermined sparse source signals. The proposed method can be modified to satisfy different applications. Numerical experiments including the comparison with a recent underdetermined blind source separation approach are provided to show the effectiveness of the proposed method.