论文标题
ISS2：基于大型化最小化的独立向量分析的迭代源转向算法的扩展
ISS2: An Extension of Iterative Source Steering Algorithm for Majorization-Minimization-Based Independent Vector Analysis
论文作者
论文摘要
独立矢量分析的大量最小化（mm）算法优化了分离矩阵$ w = [w_1，\ ldots，w_m]^h \ in \ Mathbb {c}^{c}^{m \ times m} $，通过使形式的代孕功能$ \ mathcal {mathcal {mathcal {i = i = i = i = i = i = i = i = v_i w_i- \ log | \ det w |^2 $，其中$ m \ in \ mathbb {n} $是传感器的数量和正定确定矩阵$ v_1，\ ldots，v_m \ in \ mathbb {c}^{m \ times m} $在每个MM迭代中构造。对于$ m \ geq 3 $，尚未发现算法可获得$ \ MATHCAL {l}（w）$的全局最低。取而代之的是，已经开发了具有封闭形式更新公式的块坐标下降（BCD）方法，以最大程度地减少$ \ Mathcal {l}（w）$，并证明是有效的。这样的BCD称为迭代投影（IP），该预测在每次迭代中更新一排$ w $。另一个BCD称为迭代源转向（ISS），该转向（ISS）在每次迭代中更新混合矩阵$ a = w^{ - 1} $的一列。尽管ISS的时间复杂度比IP的时间小于$ M $倍，但常规ISS收敛速度比当前最快的IP（称为$ \ text {ip} _2 $）慢，该IP（称为$ \ text {ip} _2 $）在每种迭代中更新两行的$ W $。我们在这里将此ISS扩展到$ \ text {iss} _2 $，可以在每次迭代中更新两列$ a $，同时保持其较小的时间复杂性。为此，我们提供了一种开发新的ISS类型方法的统一方法，从中可以立即以系统的方式获得$ \ text {iss} _2 $以及常规ISS的方法。分开回响语音混合物的数值实验表明，我们的$ \ text {iss} _2 $以比传统ISS少的mm迭代收敛，并且与$ \ text {ip} _2 $相当。
A majorization-minimization (MM) algorithm for independent vector analysis optimizes a separation matrix $W = [w_1, \ldots, w_m]^h \in \mathbb{C}^{m \times m}$ by minimizing a surrogate function of the form $\mathcal{L}(W) = \sum_{i = 1}^m w_i^h V_i w_i - \log | \det W |^2$, where $m \in \mathbb{N}$ is the number of sensors and positive definite matrices $V_1,\ldots,V_m \in \mathbb{C}^{m \times m}$ are constructed in each MM iteration. For $m \geq 3$, no algorithm has been found to obtain a global minimum of $\mathcal{L}(W)$. Instead, block coordinate descent (BCD) methods with closed-form update formulas have been developed for minimizing $\mathcal{L}(W)$ and shown to be effective. One such BCD is called iterative projection (IP) that updates one or two rows of $W$ in each iteration. Another BCD is called iterative source steering (ISS) that updates one column of the mixing matrix $A = W^{-1}$ in each iteration. Although the time complexity per iteration of ISS is $m$ times smaller than that of IP, the conventional ISS converges slower than the current fastest IP (called $\text{IP}_2$) that updates two rows of $W$ in each iteration. We here extend this ISS to $\text{ISS}_2$ that can update two columns of $A$ in each iteration while maintaining its small time complexity. To this end, we provide a unified way for developing new ISS type methods from which $\text{ISS}_2$ as well as the conventional ISS can be immediately obtained in a systematic manner. Numerical experiments to separate reverberant speech mixtures show that our $\text{ISS}_2$ converges in fewer MM iterations than the conventional ISS, and is comparable to $\text{IP}_2$.
