有噪ICA中最优恢复的伪欧几里德迭代法
A Pseudo-Euclidean Iteration for Optimal Recovery in Noisy ICA
摘要：
独立分量分析（ICA）是盲信号分离的一种常用模型。ICA模型假设多个独立的源信号线性混合形成观测信号。我们提出了一种新的算法，PEGI（伪欧几里德梯度迭代），可证明模型恢复的ICA高斯噪声。该算法的主要技术创新是在伪欧几里德（不定“内积”）空间中使用不动点迭代。这种不确定的“内积”的使用解决了常见的技术问题，现有的几种算法的嘈杂ICA。这导致了一个算法，这是概念上简单，有效和准确的测试。我们的第二个贡献是结合PEGI与分析的目标，在嘈杂的ICA模型的最佳恢复。已经观察到，根据自然信号与干扰加噪声比（SINR）准则，利用混合矩阵的逆进行解混合的直接方法对于信号恢复是次优的。ICA文献中提出了几种部分解决方案。事实证明，混合矩阵重构问题的任何解决方案都可以用于构建SINR最优ICA解混，尽管SINR本身无法从数据中计算。这使我们能够获得一个实用的和可证明的SINR最佳恢复方法ICA任意高斯噪声。
英文摘要：
Independent Component Analysis (ICA) is a popular model for blind signal separation. The ICA model assumes that a number of independent source signals are linearly mixed to form the observed signals. We propose a new algorithm, PEGI (for pseudo-Euclidean Gradient Iteration), for provable model recovery for ICA with Gaussian noise. The main technical innovation of the algorithm is to use a fixed point iteration in a pseudo-Euclidean (indefinite "inner product") space. The use of this indefinite "inner product" resolves technical issues common to several existing algorithms for noisy ICA. This leads to an algorithm which is conceptually simple, efficient and accurate in testing. Our second contribution is combining PEGI with the analysis of objectives for optimal recovery in the noisy ICA model. It has been observed that the direct approach of demixing with the inverse of the mixing matrix is suboptimal for signal recovery in terms of the natural Signal to Interference plus Noise Ratio (SINR) criterion. There have been several partial solutions proposed in the ICA literature. It turns out that any solution to the mixing matrix reconstruction problem can be used to construct an SINR-optimal ICA demixing, despite the fact that SINR itself cannot be computed from data. That allows us to obtain a practical and provably SINR-optimal recovery method for ICA with arbitrary Gaussian noise.
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