Nonparametric Bayesian background estimation for hyperspectral anomaly detection

Abstract

We propose an anomaly detection algorithm based on nonparametric Bayesian (NB) background estimation for hyperspectral images. The background is modeled as a Gaussian mixture model (GMM) and the model parameters and order are estimated from the data in an unsupervised manner using nonparametric Bayesian methods called Chinese restaurant process mixtures (CRPM) and truncated Dirichlet process mixtures (TDPM). Since, in anomaly detection, the model parameters are estimated only using the background data in an unsupervised manner, we also propose to use a superpixel-based background data preparation method to obtain a slightly purified background data. In the proposed mixture models, the covariance matrix estimation problem is regularized by defining some conjugate priors to avoid obtaining an ill-conditioned covariance matrix. Finally, the GMM model whose parameters and model order are estimated by the proposed methods is used for anomaly detection. We compare the performances of the proposed methods with those of variational Bayesian, conventional GMM, and collaborative representation-based detector (CRD). Experiments on real hyperspectral data sets show that the proposed methods outperform the detection performance of the other methods.