一种欠定盲源分离算法通用模型

A Generalized Model of Underdetermined Blind Source Separation Algorithm

针对传感器数目小于源信号数目的欠定情形,研究了基于压缩感知(CS)的欠定盲源分离(UBSS)问题。从欠定盲源分离和压缩感知的数学模型入手,在源信号具有稀疏性的前提下,将其转化为CS理论中的稀疏信号重构问题。在Sparco框架下建立了CS-UBSS两步法算法通用模型,并理论证明了该模型的有限等距特性(RIP)。仿真结果说明了该算法模型针对语音信号和图像信号的可行性与适用性,拓宽了UBSS问题的解决思路,尤其是CS理论中性能优越的重构算法可以直接应用于源信号的恢复。

In view of the underdetermined situation that the number of sensors is less than that of the source signals, we studied the Undertermined Blind Source Separation （UBSS） problem based on Compressed Sensing （CS）. Starting with the mathematical models of UBSS and CS, the source signal that has sparseness property is transformed into the issue of sparse signal reconstruction in CS theory. Then, the signal reconstruction algorithm of CS theory in the Sparco framework was applied in UBSS to construct a two-step CS-UBSS algorithm model. The Restricted Isometry Property （RIP） characteristics of the model was proved in theory. The simulation results prove the feasibility and applicability of the algorithm model for voice signals and image signals, which providing a new way for the solving the UBSS problem, especially in such a case that the reconstruction algorithm in CS theory can be applied directly in the recovery of source signals.