In this paper, we address the problem of extracting all super-Gaussian source signals from a linear mixture in which (i) the number of super-Gaussian sources $K$ is less than that of sensors $M$ , and (ii) there are up to $M - K$ stationary Gaussian noises that do not need to be extracted. To solve this problem, independent vector extraction (IVE) using a majorization minimization and block coordinate descent (BCD) algorithms has been developed, attaining robust source extraction and low computational cost. We here improve the conventional BCDs for IVE by carefully exploiting the stationarity of the Gaussian noise components. We also newly develop a BCD for a semiblind IVE in which the transfer functions for several super-Gaussian sources are given a priori. Both algorithms consist of a closed-form formula and a generalized eigenvalue decomposition. In a numerical experiment of extracting speech signals from noisy mixtures, we show that when $K = 1$ in a blind case or at least $K - 1$ transfer functions are given in a semiblind case, the convergence of our proposed BCDs is significantly faster than those of the conventional ones.

中文翻译：

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用于基于辅助函数的独立向量提取的块坐标下降算法

在本文中，我们解决了从线性混合中提取所有超高斯源信号的问题，其中 (i) 超高斯源的数量 $K$ 小于传感器 百万美元 ，和 (ii) 有多达 $M - K$不需要提取的平稳高斯噪声。为了解决这个问题，已经开发了使用主最小化和块坐标下降 (BCD) 算法的独立向量提取 (IVE)，实现了稳健的源提取和低计算成本。我们在这里通过仔细利用高斯噪声分量的平稳性来改进 IVE 的传统 BCD。我们还新开发了一种用于半盲 IVE 的 BCD，其中先验地给出了几个超高斯源的传递函数。两种算法均由封闭式公式和广义特征值分解组成。在从嘈杂的混合中提取语音信号的数值实验中，我们表明，当$K = 1$ 在盲目的情况下或至少 $K - 1$ 传递函数是在半盲情况下给出的，我们提出的 BCD 的收敛速度明显快于传统 BCD。