Anomaly Detection in Multichannel Data Using Sparse Representation in RADWT Frames

We introduce a new methodology for anomaly detection (AD) in multichannel fast oscillating signals based on nonparametric penalized regression. Assuming the share similar shapes and characteristics, estimation procedures are use of Rational-Dilation Wavelet Transform (RADWT), equipped with tunable Q-factor able to provide sparse representations functions different oscillations persistence. Under standard hypothesis Gaussian additive noise, we model by RADWT anomalies as each signal. Then perform AD imposing double penalty multiple regression obtained, promoting group sparsity both coefficients anomalies. The first constraint preserves common structure underlying signal components; second one aims identify presence/absence Numerical experiments show performance proposed method synthetic scenarios well real case.