Robust ENF Estimation Based on Harmonic Enhancement and Maximum Weight Clique

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.