The electric network frequency (ENF) is an important and extensively researched forensic criterion to authenticate digital recordings, but currently it is still challenging to extract reliable ENF traces from recordings in uncontrollable environments. In this paper, we present a framework for robust ENF extraction from real-world audio recordings, featuring multi-tone harmonic ENF enhancement and graph-based harmonic selection. We first extend the recently developed single-tone robust filtering algorithm (RFA) to the multi-tone scenario and propose a harmonic robust filtering algorithm (HRFA). It can enhance each harmonic component without cross-component interference, thus alleviating the effects of unwanted noise and audio content. In addition, considering the fact that some harmonic components could still be severely corrupted after the HRFA, interfering rather than facilitating ENF estimation, we propose a graph-based harmonic selection algorithm (GHSA), which finds a subset of harmonic components having the overall highest mutual cross-correlation. Noticeably, the harmonic selection problem is found to be equivalent to the maximum weight clique problem in graph theory, and the Bron-Kerbosch algorithm is adopted in the GHSA. With the enhanced and carefully selected harmonic components, both the existing maximum likelihood estimator (MLE) and weighted MLE are incorporated to yield the final ENF estimation results. The proposed framework is evaluated using both synthetic signals and the ENF-WHU dataset consisting of 130 real-world audio recordings, demonstrating its advantages over both the existing single- and multi-tone competitors. This work further improves the applicability of the ENF as a forensic criterion in real-world situations.

中文翻译：

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基于谐波增强和最大权值团的鲁棒ENF估计


电网频率（ENF）是验证数字记录的重要且经过广泛研究的取证标准，但目前在不可控环境中从记录中提取可靠的 ENF 痕迹仍然具有挑战性。在本文中，我们提出了一个从现实世界的录音中稳健提取 ENF 的框架，具有多音谐波 ENF 增强和基于图形的谐波选择。我们首先将最近开发的单音鲁棒滤波算法（RFA）扩展到多音场景，并提出谐波鲁棒滤波算法（HRFA）。它可以增强每个谐波分量，而不会产生交叉分量干扰，从而减轻不需要的噪声和音频内容的影响。此外，考虑到一些谐波分量在HRFA之后仍然可能被严重破坏，从而干扰而不是促进ENF估计，我们提出了一种基于图的谐波选择算法（GHSA），该算法找到总体最高的谐波分量子集互相关。值得注意的是，调和选择问题等价于图论中的最大权团问题，并且GHSA采用了Bron-Kerbosch算法。通过增强和精心选择的谐波分量，现有的最大似然估计器 (MLE) 和加权 MLE 都被合并以产生最终的 ENF 估计结果。使用合成信号和由 130 个真实世界录音组成的 ENF-WHU 数据集对所提出的框架进行了评估，证明了其相对于现有单音和多音竞争对手的优势。这项工作进一步提高了 ENF 作为取证标准在现实世界中的适用性。