Comparison of source signal recovery algorithms based on compressed sensing for underdetermined blind source separation
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摘要: 构建了基于压缩感知的欠定盲源分离源信号恢复模型，比较研究了基于互补匹配追踪算法(CMP)、基于L1范数的互补匹配追踪算法(L1CMP)和基于修正牛顿的径向基函数算法(NRASR)实现欠定源信号恢复的应用效果。结果表明：源信号时域充分稀疏情况下，CMP，L1CMP和NRASR的恢复效果接近，但L1CMP算法计算复杂度最低；变换域充分稀疏情况下，CMP和L1CMP恢复效果接近，NRASR恢复效果较差；时域非充分稀疏情况下，CMP效果较差，L1CMP和NRASR效果接近。综合考虑，L1CMP算法效果最佳；在观测信号数和源数较少的情况下，算法在时域恢复信号精度会下降；稀疏表示法结合压缩感知重构能够提高源信号恢复的效果。
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关键词:
- 欠定盲源分离 /
- 源信号恢复 /
- 互补匹配追踪算法 /
- 基于L1范数的互补匹配追踪算法 /
- 基于修正牛顿的径向基函数算法
Abstract: The source signal recovery model for underdetermined blind source separation based on compressed sensing(CS) is constructed, and the recovery effect of three algorithms separately based on the complementary matching pursuit(CMP), the L1 based complementary matching pursuit(L1CMP) and modified Newton radial basis function(NRASR) are compared by simulation. Results show that as to the completely sparse source signals in time domain, the recovery effect of the three algorithms are similar, while the calculation complexity of L1CMP is the lowest. As to the completely sparse source signals in transformation domain, the recovery effects of CMP and L1CMP are similar, but that of NRASR is worse. When the source signals are incompletely sparse in time domain, the recovery effect of CMP is worse, and those of L1CMP and NRASR are similar. So based on comprehensive consideration, the L1CMP algorithm is the best in the three algorithms. As to the case of the source signal number and observation signal number are small, the recovery effect would decline in time domain. The sparse representation method combined with the CS reconstruction algorithms can get good source signal recovery effect. -
图 1 时域充分稀疏源信号恢复结果
Figure 1. Source signal recovery effect when source signals are sparse in time domain
图 2 m=6，n=8，某些时刻有多个源信号起主导作用时的源信号恢复结果
Figure 2. Source signal recovery effect when there are more than two signals playing the dominant role in time domain
图 3 m=3，n=5，源信号非充分稀疏情况下源信号恢复仿真结果
Figure 3. Source signal recovery effect when m=3, n=5, and the source signals are incompletely sparse in time domain
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