Joint Robust Linear Regression and Anomaly Detection in Poisson noise using Expectation-Propagation

In this paper, we propose a new Expectation-Propagation (EP) algorithm to address the problem of joint robust linear regression and sparse anomaly detection from data corrupted by Poisson noise. Adopting an approximate Bayesian approach, an EP method is derived to approximate the posterior distribution of interest. The method accounts not only for additive anomalies, but also for destructive anomalies, i.e., anomalies that can lead to observations with amplitudes lower than the expected signals. Experiments conducted with both synthetic and real data illustrate the potential benefits of the proposed EP method in joint spectral unmixing and anomaly detection in the photon-starved regime of a Lidar system.