This paper studies the problem of jointly estimating multiple network processes driven by a common unknown input, thus effectively generalizing the classical blind multi-channel identification problem to graphs. More precisely, we model network processes as graph filters and consider the observation of multiple graph signals corresponding to outputs of different filters defined on a common graph and driven by the same input. Assuming that the underlying graph is known and the input is unknown, our goal is to recover the specifications of the network processes, namely the coefficients of the graph filters, only relying on the observation of the outputs. Being generated by the same input, these outputs are intimately related and we leverage this relationship for our estimation purposes. Two settings are considered, one where the orders of the filters are known and another one where they are not known. For the former setting, we present a least-squares approach and provide conditions for recovery. For the latter scenario, we propose a sparse recovery algorithm with theoretical performance guarantees. Numerical experiments illustrate the effectiveness of the proposed algorithms, the influence of different parameter settings on the estimation performance, and the validity of our theoretical claims.

中文翻译：

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通过多图过滤器的盲识别来估计网络进程

本文研究了由共同未知输入驱动的联合估计多个网络过程的问题，从而有效地将经典的盲多通道识别问题推广到图。更准确地说，我们将网络过程建模为图过滤器，并考虑对多个图信号的观察，这些信号对应于在公共图上定义并由相同输入驱动的不同过滤器的输出。假设底层图已知而输入未知，我们的目标是恢复网络过程的规范，即图滤波器的系数，仅依赖于对输出的观察。由于由相同的输入生成，这些输出密切相关，我们利用这种关系进行估计。考虑了两种设置，一种是已知滤波器的阶数，另一种是未知阶数。对于前一种设置，我们提出了最小二乘法并提供了恢复条件。对于后一种情况，我们提出了一种具有理论性能保证的稀疏恢复算法。数值实验说明了所提出算法的有效性，不同参数设置对估计性能的影响，以及我们理论主张的有效性。