Tian Ning, Byun Sung-Hoon, Sabra Karim, Romberg Justin
School of Electrical and Computer Engineering, Georgia Institute of Technology, North Avenue, Atlanta, Georgia 30332, USA.
Korea Research Institute of Ships and Ocean Engineering, 32 1312beon-gil Yuseong-daero, Yuseong-gu, Daejeon, 34103, Korea.
J Acoust Soc Am. 2017 May;141(5):3337. doi: 10.1121/1.4983311.
This paper presents a technique for solving the multichannel blind deconvolution problem. The authors observe the convolution of a single (unknown) source with K different (unknown) channel responses; from these channel outputs, the authors want to estimate both the source and the channel responses. The authors show how this classical signal processing problem can be viewed as solving a system of bilinear equations, and in turn can be recast as recovering a rank-1 matrix from a set of linear observations. Results of prior studies in the area of low-rank matrix recovery have identified effective convex relaxations for problems of this type and efficient, scalable heuristic solvers that enable these techniques to work with thousands of unknown variables. The authors show how a priori information about the channels can be used to build a linear model for the channels, which in turn makes solving these systems of equations well-posed. This study demonstrates the robustness of this methodology to measurement noises and parametrization errors of the channel impulse responses with several stylized and shallow water acoustic channel simulations. The performance of this methodology is also verified experimentally using shipping noise recorded on short bottom-mounted vertical line arrays.
本文提出了一种解决多通道盲反卷积问题的技术。作者观察单个（未知）源与K个不同（未知）通道响应的卷积；从这些通道输出中，作者希望估计源和通道响应。作者展示了如何将这个经典的信号处理问题视为求解一个双线性方程组系统，进而可以重铸为从一组线性观测中恢复一个秩为1的矩阵。低秩矩阵恢复领域的先前研究结果已经确定了针对此类问题的有效凸松弛方法以及高效、可扩展的启发式求解器，这些求解器使这些技术能够处理数千个未知变量。作者展示了如何利用关于通道的先验信息为通道建立一个线性模型，这反过来又使得求解这些方程组成为适定问题。这项研究通过几个风格化的浅水声学通道模拟，证明了该方法对测量噪声和通道脉冲响应参数化误差的鲁棒性。该方法的性能也通过使用短底部安装垂直线阵列记录的船舶噪声进行了实验验证。
