Anomaly detection in clutter using spectrally enhanced Ladar

Discrete return (DR) Laser Detection and Ranging (Ladar) systems provide a series of echoes that reflect from objects in a scene. These can be first, last or multi-echo returns. In contrast, Full-Waveform (FW)-Ladar systems measure the intensity of light reflected from objects continuously over a period of time. In a camouflaged scenario, e.g., objects hidden behind dense foliage, a FW-Ladar penetrates such foliage and returns a sequence of echoes including buried faint echoes. The aim of this paper is to learn local-patterns of co-occurring echoes characterised by their measured spectra. A deviation from such patterns de fines an abnormal event in a forest/tree depth pro file. As far as the authors know, neither DR or FW-Ladar, along with several spectral measurements, has not been applied to anomaly detection. This work presents an algorithm that allows detection of spectral and temporal anomalies in FW-Multi Spectral Ladar (FW-MSL) data samples. An anomaly is defined as a full waveform temporal and spectral signature that does not conform to a prior expectation, represented using a learnt subspace (dictionary) and set of coefficients that capture co-occurring local-patterns using an overlapping temporal window. A modified optimization scheme is proposed for subspace learning based on stochastic approximations. The objective function is augmented with a discriminative term that represents the subspace's separability properties and supports anomaly characterisation. The algorithm detects several man-made objects and anomalous spectra hidden in a dense clutter of vegetation and also allows tree species classification.