图形上的盲解卷:精确稳定的恢复

Chang Ye, Gonzalo Mateos
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引用次数: 0

摘要

我们研究的是图上的盲解卷问题,该问题是在定位扩散到网络上的少数信号源时出现的。虽然观测值是未知图滤波器系数和稀疏输入信号的双线性函数,但对扩散滤波器可逆性的温和要求使得高效的凸松弛成为可能,从而产生了线性规划形式,可以用现成的求解器来解决。在输入的伯努利-高斯模型下,我们推导出了无噪声环境下充分的精确恢复条件。然后建立了一个稳定的恢复结果,确保即使观测数据被少量噪声破坏,估计误差仍在可控范围内。利用合成和真实世界网络数据进行的数值测试表明了所提算法的优点、对噪声的鲁棒性以及利用多个信号帮助(盲)定位扩散源的好处。从根本上讲,本文介绍的结果将(空间)时间信号的经典盲解卷范围扩大到了不规则图域。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Blind Deconvolution on Graphs: Exact and Stable Recovery
We study a blind deconvolution problem on graphs, which arises in the context of localizing a few sources that diffuse over networks. While the observations are bilinear functions of the unknown graph filter coefficients and sparse input signals, a mild requirement on invertibility of the diffusion filter enables an efficient convex relaxation leading to a linear programming formulation that can be tackled with off-the-shelf solvers. Under the Bernoulli-Gaussian model for the inputs, we derive sufficient exact recovery conditions in the noise-free setting. A stable recovery result is then established, ensuring the estimation error remains manageable even when the observations are corrupted by a small amount of noise. Numerical tests with synthetic and real-world network data illustrate the merits of the proposed algorithm, its robustness to noise as well as the benefits of leveraging multiple signals to aid the (blind) localization of sources of diffusion. At a fundamental level, the results presented here broaden the scope of classical blind deconvolution of (spatio-)temporal signals to irregular graph domains.
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