完全逆向鞋盒镜像源方法：从脉冲响应到房间参数
Fully Reversing the Shoebox Image Source Method: From Impulse Responses to Room Parameters
AI总结：
本文提出一种完全逆向鞋盒镜像源方法的算法，结合无网格镜像源定位、房间轴恢复和一阶反射识别，从已知阵列几何的离散多通道RIR中可靠恢复声源位置、房间尺寸、6自由度位姿及6个边界吸收系数共18个参数，并通过模拟实验验证了其高精度恢复和外推能力。
摘要：
我们提出了一种算法，能够完全逆向鞋盒镜像源方法（ISM），该方法是由 Allen 和 Berkley 于 1979 年提出的、广泛使用的长方体房间脉冲响应（RIR）模拟器。更准确地说，给定由鞋盒 ISM 为已知几何结构的麦克风阵列生成的离散多通道 RIR，该算法能够可靠地恢复 18 个输入参数。这些参数包括 3D 声源位置、房间的 3 个维度、房间平移和朝向的 6 自由度，以及 6 个房间边界各自的吸收系数。该方法建立在最近提出的无网格镜像源定位技术之上，并结合了用于房间轴恢复和一阶反射识别的新程序。大量模拟实验表明，在尺寸为 2×2×2 至 10×10×5 米的房间内，使用完全随机化的输入参数，采用 32 阵元、8.4 厘米宽的球形麦克风阵列和 16 kHz 的采样率，可以实现所有参数的近似精确恢复。当增大阵列尺寸和采样率时，估计误差趋向于零。该方法还被证明显著优于一个已知基线，并展示了其在新位置外推 RIR 的能力。关键的是，该方法严格限于使用原始鞋盒 ISM 模拟的低通离散 RIR。尽管如此，据我们所知，这是首次以算法方式证明这一困难的逆问题在广泛的配置范围内原则上可以完全求解。
英文摘要：
We present an algorithm that fully reverses the shoebox image source method (ISM), a popular and widely used room impulse response (RIR) simulator for cuboid rooms introduced by Allen and Berkley in 1979. More precisely, given a discrete multichannel RIR generated by the shoebox ISM for a microphone array of known geometry, the algorithm reliably recovers the 18 input parameters. These are the 3D source position, the 3 dimensions of the room, the 6-degrees-of-freedom room translation and orientation, and an absorption coefficient for each of the 6 room boundaries. The approach builds on a recently proposed gridless image source localization technique combined with new procedures for room axes recovery and first-order-reflection identification. Extensive simulated experiments reveal that near-exact recovery of all parameters is achieved for a 32-element, 8.4-cm-wide spherical microphone array and a sampling rate of 16~kHz using fully randomized input parameters within rooms of size 2X2X2 to 10X10X5 meters. Estimation errors decay towards zero when increasing the array size and sampling rate. The method is also shown to strongly outperform a known baseline, and its ability to extrapolate RIRs at new positions is demonstrated. Crucially, the approach is strictly limited to low-passed discrete RIRs simulated using the vanilla shoebox ISM. Nonetheless, it represents to our knowledge the first algorithmic demonstration that this difficult inverse problem is in-principle fully solvable over a wide range of configurations.
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