Compressive Spectral Anomaly Detection

We propose a novel compressive imager for detecting anomalous spectral profiles in a scene. We model the background spectrum as a low-dimensional subspace while assuming the anomalies to form a spatially-sparse set of spectral profiles different from the background. Our core contributions are in the form of a two-stage sensing mechanism. In the first stage, we estimate the subspace for the background spectrum by acquiring spectral measurements at a few randomly-selected pixels. In the second stage, we acquire spatially-multiplexed spectral measurements of the scene. We remove the contributions of the background spectrum from the spatially-multiplexed measurements by projecting onto the complementary subspace of the background spectrum; the resulting measurements are of a sparse matrix that encodes the presence and spectra of anomalies, which can be recovered using a Multiple Measurement Vector formulation. Theoretical analysis and simulations show significant speed up in acquisition time over other anomaly detection techniques. A lab prototype based on a DMD and a visible spectrometer validates our proposed imager.