基于对数二次惩罚二次最小化的独立向量分析
Independent Vector Analysis via Log-Quadratically Penalized Quadratic Minimization
摘要：
提出了一种基于独立向量分析的盲源分离新算法。这是对具有迭代投影（IP）或迭代源转向（ISS）的流行的基于辅助函数的IVA（IVA）的改进。我们引入迭代投影调整（IPA），其中我们更新一个去混合滤波器，并沿其当前方向联合调整所有其他源。每次更新都涉及解决一个非凸最小化问题，我们称之为对数二次惩罚二次最小化（LQPQM），我们认为这是超出这项工作的兴趣。在一般情况下，我们表明，其全球最小值对应于一个单变量函数的最大根，让人想起修改的特征值问题。我们提出了一个简单的基于Newton-Raphson的方法来有效地计算它，数值实验证明了所提出方法的有效性。首先，我们证明了它有效地减少了代理函数的值。在进一步的实验中，我们研究了合成混合物，找到真正的分层矩阵的概率和收敛速度。我们表明，该方法结合了高成功率和快速收敛。最后，我们验证了混响盲语音分离任务的性能。我们发现，所有的基于MANIVA的方法执行类似的声学BSS度量。然而，ARIVA-IPA收敛得更快。与下一个最好的基于ARTIVA的方法相比，我们在运行时间方面测量到高达8.5倍的速度提升，这取决于通道数量和信噪比（SNR）。
英文摘要：
We propose a new algorithm for blind source separation (BSS) using independent vector analysis (IVA). This is an improvement over the popular auxiliary function based IVA (AuxIVA) with iterative projection (IP) or iterative source steering (ISS). We introduce iterative projection with adjustment (IPA), where we update one demixing filter and jointly adjust all the other sources along its current direction. Each update involves solving a non-convex minimization problem that we term log-quadratically penalized quadratic minimization (LQPQM), that we think is of interest beyond this work. In the general case, we show that its global minimum corresponds to the largest root of a univariate function, reminiscent of modified eigenvalue problems. We propose a simple procedure based on Newton-Raphson to efficiently compute it. Numerical experiments demonstrate the effectiveness of the proposed method. First, we show that it efficiently decreases the value of the surrogate function. In further experiments on synthetic mixtures, we study the probability of finding the true demixing matrix and convergence speed. We show that the proposed method combines high success rate and fast convergence. Finally, we validate the performance on a reverberant blind speech separation task. We find that all the AuxIVA-based methods perform similarly in terms of acoustic BSS metrics. However, AuxIVA-IPA converges faster. We measure up to 8.5 times speed-up in terms of runtime compared to the next best AuxIVA-based method, depending on the number of channels and the signal-to-noise ratio (SNR).
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