Statistical wavelet-based anomaly detection in big data with compressive sensing

Anomaly detection in big data is a key problem in the big data analytics domain. In this paper, the definitions of anomaly detection and big data were presented. Due to the sampling and storage burden and the inadequacy of privacy protection of anomaly detection based on uncompressed data, compressive sensing theory was introduced and used in the anomaly detection algorithm. The anomaly detection criterion based on wavelet packet transform and statistic process control theory was deduced. The proposed anomaly detection technique was used for through-wall human detection to demonstrate the effectiveness. The experiments for detecting humans behind a brick wall and gypsum based on ultra-wideband radar signal were carried out. The results showed that the proposed anomaly detection algorithm could effectively detect the existence of a human being through compressed signals and uncompressed data.